partisanship and the effectiveness of oversight

Journal of Public Economics 94 (2010) 674–687

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Journal of Public Economics

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Partisanship and the effectiveness of oversight☆

Justin Fox a,⁎, Richard Van Weelden b

a Department of Political Science, Yale University, 77 Prospect Street, New Haven, CT 06520, United Statesb Department of Economics, Yale University, 28 Hillhouse Avenue, New Haven, CT 06520, United States

☆ An earlier version of this manuscript was circulatedReputational Cascades, and the Value of Oversight.” Aut⁎ Corresponding author. Tel.: +1 203 606 2608.

E-mail addresses: [email protected] (J. Fox), richar(R. Van Weelden).

1 See, for example, Bennett (2006) and Drew (2006).(1969) and Rosenblum (2008) for an overview of anpolitical discourse.

0047-2727/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.jpubeco.2010.05.003

a b s t r a c t
a r t i c l e i n f o
Article history:Received 20 May 2009Received in revised form 19 April 2010Accepted 3 May 2010Available online 12 May 2010

Keywords:PartisanshipChecks and balancesReputationHerdingVeto

We examine the welfare effects of partisanship in a model of checks and balances. An executive makes apolicy proposal and an overseer then decides whether or not to veto the executive's proposal. Both theexecutive and the overseer have private information as to the correct policy to pursue, and both aremotivated by the desire to appear competent. A partisan overseer is one who, in addition to seeking topromote her own reputation, cares how her decision will impact the executive's reputation. Our main resultis that partisanship can improve the efficacy of an oversight regime, as the distortions caused by a partisanoverseer's desire to affect the executive's reputation can offset the distortions caused by her desire toenhance her own. Our results provide a new rationale for divided government, as partisan considerations areoften necessary to prevent the overseer from rubber stamping all executive proposals.

under the title “Partisanship,hors are listed alphabetically.

[email protected]

More generally, see Hofstadterti-party thought in American

2 That partisanshiphas a long history. Fthe argument thatspirit, is not only nParties are a check ubounds, serve to ma

ll rights reserved.

© 2010 Elsevier B.V. All rights reserved.

No sooner has one party discovered or invented any ameliorationto the condition of man, or the order of society than theopposition party belies it, misconstrues it, misrepresents it,ridicules it, insults it, and persecutes it.– John Adams, 1813 letter to Thomas Jefferson

[Partisanship] consumes good and smart people and leads them toput politics ahead of progress…. [I]t prevents conversations aboutthe hard choices that need to be made to achieve real reform.– Michael Bloomberg, 2008 discussion on government reform onNewTalk.org

1. Introduction

The willingness of Congress to challenge executive initiatives —

whether misguided, illegal, or both — is critical to the public's well-being. Nevertheless, Congress is frequently criticized for failing toexercise its checks on executive power appropriately. In some casesCongress is accused of being overly acquiescent to executive demands(Feldman, 2006; Ornstein and Mann, 2006), and in other cases it isaccused of being needlessly obstructionist (Tanenhaus, 2000). Manyargue that partisanship is a principal cause of such inefficiencies.1

Implicit in such arguments is the belief that members of Congresswould do a better job if they were immune to partisan considerations.This faith in non-partisans, however, may not be justified. Politiciansuninterested in partisan point-scoring would still have personalambitions, and these ambitions can easily get in the way of acting inthe public interest. As such, it is far from clear that a Congresspopulated by non-partisans would exercise its checks on thePresident in a more socially responsible manner.

This paper considers the value of partisanship in a formal model ofchecks and balances in order to better understand how partisanshipinfluences oversight relationships. In particular, we examine a settingwith an “executive” and an “overseer,” and explore how partisanshipaffects the overseer's willingness to challenge executive policyproposals. Our central finding is that partisan rivalry, while frequentlyderided for leading to inefficient posturing by politicians, oftenenhances the effectiveness of oversight.2 This is because thedistortions caused by a partisan overseer's desire to affect theexecutive's reputation can offset the distortions caused by her desireto enhance her own.

As reflected in the opening quotes, critics of partisanship areparticularly concerned that partisans may oppose a policy simplybecause of who proposed it. In what follows we examine the welfare

could improve the efficacy of checks and balances is an idea thator example, an article in New York Gazette from the 1730s made“some opposition, though it proceed not entirely from a publicecessary in free governments but of great service to the public.pon one another, and by keeping the ambition of one another inintain public liberty” (Bailyn, 1968, 126).

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675J. Fox, R. Van Weelden / Journal of Public Economics 94 (2010) 674–687

effects of this incentive.Weabstract away from ideological conflict andconsider a setting in which the only difference among politicians is intheir ability to recognize which policy is in the public's interest, butwhere politicians are more concerned with the outcome of electionsthan with the outcome of the selected policy. As such, all overseers —whether they are partisans or non-partisans — are motivated by adesire to appear competent. A partisan overseer, in addition, ismotivated by a desire to influence the executive's reputation for beingcompetent.3, 4 Whether a partisan overseer profits when the execu-tive's reputation is damaged or enhanced depends upon the nature oftheir relationship—whether it is adversarial or collegial. For example,a partisan overseermay seek to damage the reputation of an executivefrom the other party while seeking to protect the reputation of anexecutive from her own party.5 As our model abstracts away fromideological conflict, our notion of partisanship corresponds to themostbase motive ascribed to partisans — the simple desire to hurt one'srivals and help one's friends;6 yet, we identify many circumstancesunder which a partisan does a better job than a non-partisan in usingher veto to promote the public's welfare.

That partisanship can have value in our model stems from the factthat an overseer's concern about her own reputation (for beingcompetent) can lead her to use her veto in a sub-optimal manner fromthe public's perspective. This sub-optimality can take one of twoforms: either the overseer is too reticent in exercising her check,approving even those initiatives it would be in the public's interest toveto, or she is too aggressive, rejecting initiatives it would be in thepublic's interest to accept. The former inefficiency can be particularlydramatic, manifesting itself in the overseer never exercising her veto.This possibility arises from the sequential nature of oversight: At thetime the overseer is called upon to act, everyone knows what theexecutive believes should be done. So if the overseer were to opposethe executive, then the public would know that either the executive orthe overseer is misinformed about the correct course of action; notknowing which policymaker is mistaken, the reputation of both canthen suffer. The oversight mechanism is thus potentially vulnerable to“reputational herding” (Ottaviani and Sorensen, 2001; Scharfstein andStein, 1990), whereby the incentive to safeguard one's own reputationcan lead experts to conceal disagreement.7 When such herdingresults, oversight is completely useless.

We show that one way to prevent a socially harmful herd fromforming is with an overseer who profits when the executive'sreputation falls. As such, a partisan overseer may outperform a non-partisan one. Since vetoes damage the executive, such partisans willbe more inclined than non-partisans to resist misguided executiveinitiatives— even if they damage their own reputations in the process.Surprisingly, if the overseer has private information about her owncompetence, it not necessary for the overseer to care more about theexecutive's reputation than her own in order to induce her to revealdisagreement by exercising her veto. This is because, in addition to

3 The executive also cares about his reputation for being competent and may alsoentertain partisan considerations.

4 Thus, one could formally belong to a party but not be a partisan, in the sensedefined here, if one did not care about the electoral prospects of fellow party members.Similarly, one could be a partisan without being a member of a party: the period afterthe American Revolution is regarded as a period of hyper-partisanship despite the factthat parties did not formally exist.

5 This could reflect an intrinsic preference of the overseer for the executive to be amember of her own party. Alternatively, it could reflect additional benefits orpatronage derived from having one's friends in positions of power. For example, asenator might wish to see her party's candidate elected president in the hopes of beingappointed to the cabinet.

6 This type of partisanship is the subject of a recent book by Lee (2009).7 Herd-like behavior is a familiar theme in accounts of Congressional behavior. For

example, in explaining the 98 to 1 vote in favor of the 2001 Patriot Act, DemocraticSenator Robert Byrd observed: “The original Patriot Act is a case study in the perils ofspeed, herd instinct and lack of vigilance when it comes to legislating in times of crisis”(Associated Press, 2006).

revealing disagreement between the executive and overseer, a vetoalso reveals positive information about the quality of the overseer'ssignal. That is, an overseer who observes a signal that the executive'sproposal is misguided will have greater incentive to act on that signalthe greater her perception of her own ability. This “selection effect”lessens the reputational penalty the overseer suffers from revealingdisagreement with the executive. As there is no comparable selectionfor the executive—whomust make his proposal before the overseer'sdecision — the reputational damage from a veto is greater for theexecutive, provided this selection effect is sufficiently important. Apartisan overseer will then have the necessary incentive to exerciseher check even if her primary concern is with her own reputation.

It is not always the case, however, that a non-partisan overseer willbe too reticent in exercising her veto. In fact, a non-partisan overseermay veto more often than is warranted in an effort to signal that sheperceives herself to be high ability.We show thatwhen a non-partisanis too aggressive in exercising her veto, the public benefits from anoverseer who has a stake in the executive appearing competent. So,whether it is optimal for the overseer to have an adversarial or collegialrelationship with the executive — i.e., whether divided or unifiedgovernment is desired — depends on how much private informationpolicymakers have about their respective abilities.

While we show that partisanship of an appropriate level canenhance the efficacy of the oversight regime, this does not mean thatpartisanship will always be beneficial. In some instances, the incentiveto herd on the executive is so strong that even an overseer withsignificant animus toward the executive never uses her veto; in otherinstances, there is a danger that an overseer with too much hostilitytoward the executive will be excessively obstructionist. Finally, if theoverseer is of the “wrong” partisanship (e.g., the overseer is a memberof the executive's party when it is divided government that isdesired), partisanship will only reinforce the distortions that arise in anon-partisan setting.

Before proceeding to the formal details of our model, we discussour work's connections to the literatures on parties and politicalagency. Since our model abstracts away from ideological competitionbetween parties, the benefits of partisanship considered here aredistinct from the benefits of political parties articulated elsewhere.8 Inaddition, our rationale for divided government— a rationale based onthe need for effective oversight of the executive — is distinct from themore familiar theory of “ideological balancing” (Fiorina, 1992; Alesinaand Rosenthal, 1995), whereby voters split their tickets in the hopethat the elected parties will split the difference between theirrespective platforms.

Our paper is part of a large literature on political agency problemsin which career concerns can cause policymakers to select policiesthat differ from those that their private information indicates wouldmaximize their constituents' welfare (Canes-Wrone et al., 2001;Maskin and Tirole, 2004; Prat, 2005). Wemodel these career concernsas a desire by politicians to appear competent. The key assumptionunderlying this approach is that long-term contracting is not possible,so voters re-elect the incumbent if and only if the incumbent isexpected to deliver a higher future payoff than the challenger.9

8 It is often argued that political parties provide information to voters aboutcandidate positions, helping voters to select appropriate candidates. Others argue thatstrong parties enhance government accountability. See, for example, AmericanPolitical Science Association Committee on Political Parties (1950) and Fiorina (1980).

9 This approach is distinct from the approach taken in the literature followingFerejohn (1986), a literature that characterizes the voting rules citizens should committo so as to provide proper incentives for politicians. This “contracting” approach hasbeen applied to settings of checks and balances in Persson et al. (1997) andStephenson and Nzelibe (2010). Both works concern themselves with whether checkson the executive can limit the agency slack that can arise when the policy objectives oflawmakers diverge from those of the public. Consequently, not only does the modelingapproach taken in these papers differ from that in ours, but so too does the substantivefocus.

11 Since there is no heterogeneity in policy preferences, we can without loss ofgenerality assume a representative voter.12 We use male pronouns for the Executive and female pronouns for the Overseer.13 Note, this asymmetry in payoffs is consistent with using a veto mechanism,whereby the status quo is only altered if both the Executive and Overseer agree.14 We assume the prior is one-half to ensure that the Executive's policy choice isrelated to his private information about which policy he thinks is best, since when theprior is sufficiently unbalanced, the Executive will herd on the ex-ante more likelyalternative to safeguard his reputation. That said, in an environment in which theExecutive has sufficient private information about his own competence, anequilibrium in which the Executive behaves informatively will exist even when the

676 J. Fox, R. Van Weelden / Journal of Public Economics 94 (2010) 674–687

Recently, an important line of scholarship has begun to examinewhether the media or a politician's rival, by reporting on the qualityof an incumbent's decision, can diminish the electoral pressuresthat lead incumbents to pursue sub-optimal policies. For example,Ashworth and Shotts (2008) examine whether the presence of aninformative media can lead executives to pander less to publicopinion. In their model, the media is assumed to report truthfullyits best estimate of the appropriateness of the executive's policyproposals. Our approach differs from Ashworth and Shotts's in thatour focus is not on the effects of oversight on executive behavior,but on whether overseers will do their job properly. In this sense,the paper most closely related to ours is Glazer (2007), whichconsiders a model with a political opposition that can comment onthe appropriateness of an executive's policy choice. He focuses onequilibria in which the opposition opposes any proposal theexecutive makes. As a result, Glazer's opposition provides nosocially valuable information about the appropriate course ofaction. Our focus, instead, is in showing how partisanship can beused to provide incentives for an overseer to provide suchinformation.

One paper that considers a notion of partisanship related to oursis Groseclose and McCarty (2001). Like us, they examine a model ofchecks and balances. And like us, they allow their legislature tohave a stake in the executive's reputation. However, instead offocusing on a setting of common values, as we do, they focus onideological conflict. They examine the possibility that the legisla-ture will propose policies that they know will be vetoed in order toreveal that the executive is an extremist. This is inefficient becausepolicies exist in their model that would not be vetoed and wouldmake their constituents better off. Such distortions in proposal-making arise entirely as a consequence of partisanship, so, incontrast to our results, in their framework partisanship interfereswith good policymaking.10

In considering how the efficiency of the oversight mechanismvaries with the partisan feelings of the overseer, our analysis alsorelates to a recent literature considering the principal's preferencesover different types of agents. This literature has shown that theprincipal may prefer an agent who is “biased,” as such an agent mayhave greater incentive to acquire information (Che and Kartik,2009; Gerardi and Yariv, 2008) or to act in the principal's interest inorder to be retained (Van Weelden, 2009). Among the papers inthis literature, one paper that is similar to ours in that it considershow an agent's bias can be used to counterbalance other distor-tions is Ivanov (2010); he introduces a strategic mediator toCrawford and Sobel's (1982) model of information transmissionand shows that the optimal mediator is biased in the directionopposite to the expert's bias.

The rest of this paper is organized as follows: Section 2 presentsthe model. Section 3 highlights some of the mechanics of our setupwhich drive the intuitions underlying our results. Section 4 formallycharacterizes the overseer's equilibrium behavior, both with andwithout partisanship. Section 5 explores the executive's incentivesand briefly considers how our conclusions concerning the value ofpartisanship hold up under alternative model specifications. Finally,we offer our conclusions. The proofs of our main results are includedin Appendix A, with the proofs of some supporting lemmas relegatedto Appendix B.

10 That is, partisanship has a negative effect on the payoff to the voter in this period.If a partisan legislature successfully reveals that the executive is an extremist to thevoters this may benefit the voter in future periods as the extreme executive would notbe re-elected. In our setting, in contrast, partisanship can result in a better policy beingselected in the current period as well.

2. Model

An Executive (E) and an Overseer (O) determine policy on behalfof a representative voter,11 henceforth referred to as the Principal,where it is assumed that all politicians share the Principal's state-contingent policy preferences. The game begins with the Executivedeciding whether to propose an alternative to the status quo. In theevent that a non-status-quo policy is proposed, the Overseer mustdecide whether to accept or reject the proposal. After policy isdetermined, the Principal assesses the respective ability levels of theExecutive and the Overseer. As both the Executive and the Overseerare career-minded (i.e., they ultimately want to be re-elected), bothwish to be perceived as being of high ability. Our objective is tounderstand how partisanship affects the Overseer's willingness to useher veto in a manner that promotes the Principal's welfare.12

2.1. Policy setting

We consider an environment with two policies: the status quo,which we denote by s, and a new policy, which we denote by n. Sincethe polity is familiar with the status quo, the payoff from maintainingit is known. We normalize this payoff to be−1. What is not known isthe payoff that would result from the new policy. This payoff dependson the underlying state of the world ω∈ {N, S}. When ω=N, thepayoff under the new policy is 0, andwhenω=S, the payoff under thenew policy is −κ, where κ∈(2, 4]. So, it is optimal to choose the newpolicy if and only if ω=N. That κN2 means that the net loss fromimplementing the new policy when ω=S is greater than the net gainfrom implementing it whenω=N, so to justify implementing the newpolicy, the probability placed on ω=Nmust be more than one-half.13

2.2. Uncertainty about the State of the World

Each state of the world occurs with equal probability — i.e.,Pr ω = Nð Þ = 1

2.14 At the time policy is selected, no actor knows the

state of the world with certainty. However, the Executive and theOverseer are better informed than the Principal about what the stateis likely to be: the Executive and the Overseer receive private signalsσE∈{n, s} and σO∈{n, s}, respectively, about the state of the world.Depending on policymaker j's ability aj—which can either be high (H)or low (L)— his or her signal of the state σj is either perfectly accurateor pure noise: Pr(σj=ω|aj=H)=1 and Pr σj = ω jaj = L

� �= 1

2. Thus,

a high-ability policymaker's signal of the state is perfectly informativeand a low-ability policymaker's signal of the state is completelyuninformative.15

prior is unbalanced. We discuss these issues more in the extensions.15 This assumption is not necessary to derive our main result. Provided that theaccuracy of the high-ability policymaker's signal of the state is greater than that of thelow-ability policymaker's, a non-partisan overseer will generally not act in a mannerwhich corresponds to the first best due to her desire to appear competent; thus, a roleremains for partisan incentives to counteract the distortions which arise from theOverseer's desire to protect her own reputation. The primary purpose, then, inassuming that the high-ability policymaker's signal is perfectly accurate while the low-ability policymaker's signal is pure noise is to simplify the expressions for thePrincipal's updated beliefs about the respective abilities of the Executive and theOverseer.


2.3. Uncertainty about the abilities of politicians

The Principal does not know the ability of either the Executive orthe Overseer. In addition, neither the Executive nor the Overseerknows his or her own ability with certainty. That said, we allow for theOverseer to know more about her own ability than the Principalknows. Specifically, the Overseer receives a private signal τO∈{l, h} ofher own ability that is accurate with probability q∈ 1

2;1

� �.16 We

interpret q as the degree of private information the Overseer hasabout her own ability. Allowing the Overseer to have privateinformation about her own ability means that more informationthan just her signal of the state can be revealed via her veto decision.As will be seen, q will play a critical role in determining whether thePrincipal desires the Overseer to have an adversarial or collegialrelationship with the Executive.

Nature determines the underlying ability of both the Executive andthe Overseer. With probability πE, the Executive is of high ability, andwith probability πO, the Overseer is of high ability. To simplify theanalysis, we set πO≡1

2and we focus on the case in which πE≡π≥1

2. So,

the ex-ante probability that the Executive's ability level is high is atleast as large as the probability that the Overseer's is high.17

2.4. Objectives of policymakers

The Executive and the Overseer want the Principal to makefavorable inferences about their respective ability levels. In fact, weassume that this is their primary objective. Nevertheless, bothpolicymakers place a small weight on policy considerations as well.Letting λE denote the probability the public assigns to the Executivebeing of high ability and letting γN0 denote the weight attached topolicy, the Executive's payoff is specified as λE+γu(α, ω), where u(α,ω) is the common policy payoff that is received when policy α∈{n, s}is implemented andω is the state of the world.18 Wewill refer to λE asthe Executive's reputation. That the Executive's payoff increaseslinearly in λE provides a simple and tractable reduced-formapproximation of the Executive's long-term career concerns.19

We specify the same preferences for the Overseer but allow for thepossibility that the Overseer is a partisan. We say that an overseer is apartisan if she cares not only about her own reputation for being ofhigh ability, which we denote by λO, but also cares about thereputation of the Executive. Formally, the Overseer's payoff isspecified as λO−βλE+γu(α, ω). Note that an overseer for whomβN0 profits when the Executive's reputation takes a hit, an overseerfor whom βb0 has an incentive to make the Executive look good, andan overseer for whom β=0 is unconcerned with the Executive'sreputation. Hence, an overseer for whom β≠0 is a partisan, whereasan overseer for whom β=0 is a non-partisan. Finally, we assume thatβ∈(−1, 1), so the Overseer places more weight on her ownreputation than on that of the Executive.

One final comment about our specification of the objectives of theExecutive and the Overseer: Since their policy preferences areperfectly aligned with those of the Principal, in the absence ofreputational concerns, both would be perfect agents of the Principal.However, we assume that reputational considerations swamp policy

16 That is, Pr(τO=h|aO=H)=Pr(τO= l|aO=L)=q.17 Setting πO = 1

2is not essential for our results and has the effect of simplifying the

algebra that follows. Also, our conclusions about partisanship promoting moreeffective oversight hold even when πb1

2.

18 We assume then that policymakers share the public's policy preferences. Byexamining the value of partisanship in an environment in which there are noideological differences among politicians, we stack the deck against partisanshiphaving any value.19 For example, consider a two-period model. Suppose that in between periods anelection is held in which the incumbent faces a challenger whose reputation isuniformly drawn from [0, 1]. If voters select the candidate thought to be of higherability, then λE corresponds to the Executive's probability of re-election.

considerations — i.e., γ is taken to be close to zero. Allowing policy toenter the Executive's and the Overseer's respective payoff functionsthen serves two roles. First, when two alternative actions yield nearlyidentical reputational payoffs, policy considerations break the tie.Second, that the Overseer takes account of policy will allow us to pindown the beliefs of the Principal upon observing an “out-of-equilibrium” action taken by the Overseer.

2.5. Timing of interactions

The timing of the interaction between the Executive, the Overseer,and the Principal is specified as follows:

1. The Executive observes his signal of the state σE, and the Overseerobserves both her signal of the state σO and her signal of her abilityτO.

2. The Executive proposes a policy p∈{n, s}, where p=n is the newpolicy and p=s is the status quo.

3. If the Executive proposes the new policy, then the Overseer decideswhether to accept (A) or reject (R) it. We denote the Overseer'sdecision by d, where d∈{A, R}. The realized policy, denoted α(p, d),is

α p; dð Þ = n if p = nandd = As otherwise

:

�20

4. Upon observing the interaction between the Executive and theOverseer, the Principal assigns reputations λE∈ [0, 1] and λO∈ [0,1] to the Executive and the Overseer, respectively.

5. After the Executive and Overseer receive their reputationalpayoffs, the state of the world is revealed and all players receivethe policy payoff u(α, ω).

While we assume reputational payoffs accrue prior to the state ofthe world being revealed, even when this assumption is relaxed, it isstill the case that the Principal can be better off with a partisanoverseer: As discussed in the extensions, partisanship can (poten-tially) mitigate the inefficiencies in overseer behavior which arisefrom her desire to appear competent so long as the state of the worldis not revealed with certainty prior to the reputational payoffsaccruing. As such, our model applies to settings in which politicianschoose policies whose appropriateness may not be fully learneduntil after the next election. Any policy that is written to achieve along-run objective, such as alleviating global warming or improvingpublic health, or for which key provisions do not take effectimmediately,21 will likely have this feature.

Before defining our solution concept, it should be noted that wehave introduced two asymmetries between the Executive and theOverseer: we allow for the Overseer, but not the Executive, to haveprivate information about her ability, and we allow the Overseer, butnot the Executive, to be a partisan. We do this to simplify the analysisof executive behavior, as our focus is on overseer behavior. In theextensions, we discuss why our conclusions about the value of havinga partisan overseer continue to hold even when the Executive hasprivate information or is a partisan.

2.6. Strategies and solution concept

We refer to a policymaker's private information as his or her type.Thus, the Executive's type is his signal of the state σE and theOverseer's type is her signal of her ability τO together with her signalof the state σO. We refer to an overseer for whom τO=h as the hightype and an overseer for whom τO= l as the low type.

20 In the event that p=s, set d≡∅, as the Overseer is not called upon to act.21 For instance, key provisions of the Bush tax cuts of 2001 were phased inincrementally, making it difficult to accurately assess their effects on the budget andthe economy until well into George W. Bush's second term.


The Principal is not an active player in our model; he simplyassigns reputations using Bayes's rule. So if the Principal knew theExecutive's type σE and the Overseer's type (τO, σO), then thereputation λj that the Principal would assign to policymaker j is:

Pr aj = H jσE; τO;σOð Þh i

=Pr σE; τO;σOð Þ jaj = Hh i

πj

Pr σE; τO;σOð Þ½ � :

However, the Principal will usually not know the policymakers'types with certainty. Thus, to assign reputations to the Executive andthe Overseer, for each policy choice p and veto decision d, the Principalmust have a belief ψ(p, d)(⋅) about their respective types. Formally,ψ(p, d)(⋅) is a probability measure over the model's type space. Givena belief ψ, the probability that player j's ability level is high when thepath of play is (p, d) is then

λj p; d;ψð Þ≡ ∑τO ;σOð Þ

∑σE

ψ p;dð Þ σE; τO;σOð Þ½ �Pr aj = H jσE; τO;σOð Þh i

: ðR1Þ

Hence, the Principal uses his beliefs ψ together with Eq. (R1) to assignreputations to the Executive and the Overseer.

A candidate for an equilibrium to our model consists of: a strategyfor the Executive (a mapping from his type into a policy choice); astrategy for the Overseer (a mapping from the Executive's policychoice and her type into a veto decision); a belief system for theOverseer (a mapping from the Executive's policy choice and theOverseer's type into a probability measure on the Executive's typespace); and a belief system for the Principal (ψ). These elementsconstitute a sequential equilibrium (Kreps and Wilson, 1982) if theExecutive's policy choice is optimal given the Overseer's strategy andthe Principal's beliefs ψ; the Overseer's veto decision is optimal givenher belief about the Executive's type and the Principal's beliefs ψ; andthe beliefs of the Overseer and the Principal are consistent with thespecified strategies.22, 23

As is common in games of incomplete information, ourmodel has amultiplicity of sequential equilibria. This is because sequentialequilibrium fails to completely pin down a player's beliefs at off-path information sets; consequently, “unnatural” pooling equilibriacan be supported by specifying “unnatural” beliefs at these informa-tion sets.24 In what follows, we analyze the behavior of the Overseerfollowing informative proposals by the Executive.25 So our concern iswith specifying beliefs following an off-path veto decision. We willrestrict attention to sequential equilibria with beliefs which satisfyCriterion D1 from Cho and Kreps (1987).26 In effect, this refinementrequires that if an out-of-equilibrium veto decision is ever observed,the Principal believes it was made by the overseer type who wouldmake this decision for the largest set of Principal beliefs.

22 Formally, let φ denote a strategy profile (possibly mixed), let φn denote a totallymixed strategy profile, and let ψn denote a collection of beliefs for the Principal, wherethese beliefs are derived from φn via Bayes's rule. The Principal's beliefs ψ areconsistent with strategy profile φ if there exists a sequence {φn} of totally mixedstrategy profiles that converges to φ such that {ψn} converges to ψ.23 As the Principal must update on two players, we use sequential equilibrium toensure that the Principal's belief about the Executive is derived from the Executive'sstrategy even after an off-path veto decision by the Overseer. For example, suppose theExecutive proposes p=n if and only if σE=n and the Overseer always rejects.Sequential equilibrium requires that after observing an off-path acceptance, thePrincipal believes the Executive observed σE=n.24 See either Cho and Kreps (1987) or Banks and Sobel (1987) for a comprehensivediscussion of this matter.25 In particular, we will restrict attention to equilibria in which the Executive alwaysfollows his signal of the state (i.e., he sets p=σE). Within this class of equilibria, thereare no off-path actions for the Executive.26 We adapt the original definition slightly, as our model is not a standard sender–receiver game. In earlier versions of this paper we referred to this as an adaptation ofuniversal divinity (Banks and Sobel, 1987), which corresponds to criterion D2 of Choand Kreps (1987), and is a more stringent restriction on off-path beliefs than we areimposing. We thank the anonymous referee for pointing this out.

Definition 1. Fix a sequential equilibriumwith beliefs ψ⁎ in which thenew policy is proposed with positive probability. Such an equilibriumsatisfies criterion D1 if, for any d′∈{A, R} that is never chosen on theequilibrium path, ψ⁎(n, d′)(σE, (τO, σO))=0 whenever there exists anoverseer-type (τO, σO) such that for d≠d′

fψ : λO n; d′;ψ� �

−βλE n; d′;ψ� �

+ γE u α n;d′� �

;ω� �

jp = n; τO;σOð Þh i

≥λO n;d;ψ�� −βλE n; d;ψ��

+ γE u α n; dð Þ;ωð Þ jp = n; τO;σOð Þ½ �g⫋fψ : λO n;d′;ψ

� �−βλE n;d′;ψ

� �+ γE u α n;d′

� �;ω

� �jp = n; τO;σO

� �h iN λO n; d;ψ��

−βλE n; d;ψ�� + γE u α n; dð Þ;ωð Þ jp = n; τO;σO

� �� g:

Since the reputational payoffs from a given veto decision areindependent of the Overseer's type, in effect, our refinement boilsdown to requiring the Principal to believe that any out-of-equilibriumveto decision is made by the overseer-type that nets the greatestpolicy gain from making it.27

2.7. Interpretation

One interpretation of our model is that of the President needingapproval from Congress in order for his policy initiatives to take effect.This is literally the case when it comes to formally declaring wars (seeArticle II, Section 7, of the U.S. Constitution). Further, although theConstitution specifies that all legislation emanate from Congress, inpractice, many important policy proposals in recent years have beenled by the White House (Posner and Vermeule, 2009).28 The modelalso captures aspects of the process of administrative lawmaking,whereby the Presidentmust decide how to apply statutory law to newcases and Congress must decide whether to let the President'sinterpretation stand. In applying our model to executive–legislativeinteractions in the U.S., we are treating Congress as a unitary actor.This basically amounts to assuming that Congress is controlled by themajority party or, alternatively, by the median member of Congress interms of our partisanship parameter β.

3. Overview and intuition

Before proceeding to the formal analysis of our model, we providesome intuitions as to how a partisan overseer can outperform a non-partisan overseer. We begin by considering the case in which theOverseer has no private information about her own competence.(That is, suppose that q = 1

2, so the Overseer's signal of her ability is

pure noise.) Further, suppose the Executive only proposes the newpolicy after observing a signal that the new policy is appropriate(σE=n). In order for the problem to be interesting, considerparameters under which the Principal desires that the Overseer vetoif her signal of the state is σO=s. However, if the Overseer caresalmost exclusively about her own reputation, vetoes will not beexercised in equilibrium.

From Eq. (R1), a policymaker's reputation from a given decision isa convex combination of her reputation in the event that the Overseerand Executive receive contradictory signals (σE=n, σO=s) and theevent that they receive identical signal (σE=n, σO=n). Importantly,the former event results in a lower reputation than the latter. WhenσE=n and σO=s, the Principal can infer that at least one of the twopolicymakers must have observed an incorrect signal and so must be

27 So for γ sufficiently small, if the Overseer is pooling on always accepting, thePrincipal should believe a rejection came from an overseer of type (τO, σO)=(h, s), andif pooling on always rejecting, the Principal should believe an acceptance came fromtype (τO, σO)=(h, n).28 For example, No Child Left Behind, Social Security reform, immigration reform, theBush tax cuts, the Wall Street bailout, and the various post-9/11 security measureswere all led by the Bush Administration. Similarly, welfare reform, health-care reform,intervention in the Mexican and Asian financial crises, and NAFTA were all led by theClinton White House.


of low ability. As a result, the greater the probability the Principalassigns to the Executive and Overseer receiving contradictory signals,the lower the reputation of both. But this means that vetoing damagesthe reputations of the Executive and the Overseer in any putativeequilibrium in which vetoing is indicative of the Overseer observing asignal that the Executive's policy proposal is misguided. So, whenreputational concerns dominate, the only equilibria are those inwhichthe Overseer always accepts or always rejects; as the Overseer placespositive weight on policy, the latter equilibrium is ruled out usingcriterion D1. Hence, the Overseer's desire to protect her ownreputation will result in her being unwilling to challenge theExecutive. In contrast, because the Executive's reputation is alsodamaged by a veto, if the Overseer has sufficient animus towards theExecutive— that is, β is sufficiently high— she will be willing to sufferthe reputational hit associated with casting her veto in order todamage the Executive. Hence, the distortions generated by partisan-ship can counteract the distortions created by the Overseer's desire toprotect her own reputation.

Notice, however, that when the Overseer has private informationabout her ability (that is, q N

12, so the Overseer's signal of her ability is

informative), the Overseer can be induced to veto more easily. As theOverseer places positive weight on policy, themost likely candidate toveto is a high-type overseer (τO=h) who observes signal σO=s;hence, vetoes can reveal positive information about the Overseer'sperception of her own ability, thereby muting the reputationalpenalty from disagreeing with the Executive. It is thus possible toinduce vetoes with much lower levels of partisanship when theOverseer has private information about her ability than when shedoes not. In fact, for sufficiently large values of q, the Overseer wouldbe willing to veto in the absence of partisanship, and may even beoverly-aggressive in doing so. We will show such a distortion can bemitigated by choosing an overseer who seeks to protect theExecutive's reputation (βb0).

4. Analysis of model

Our analysis focuses on the behavior of the Overseer given that theExecutive always follows his signal of the state — i.e., the Executivesets p=σE. This is natural behavior for the Executive.29 In the absenceof oversight, there is no opportunity for updating on the Executive'sability, so the Executive would propose the policy that maximizes thePrincipal's welfare. Under the parameters considered, this means thatthe Executive would follow his signal. The addition of a (potentially)active overseer will not, in expectation, change the Executive'sreputation, so the Executive will still propose the policy that is inthe Principal's best interest. As such, an equilibrium in which theExecutive follows his signal will always exist.30

Lemma 1. For any parameter profile of the model, there exists asequential equilibrium satisfying criterion D1 in which the Executivealways follows his signal of the state.

In light of the Executive setting p=σE, we establish two keyresults. First, we show that the behavior of a non-partisan overseerdiffers from that desired by the Principal — sometimes dramaticallyso. In fact, for reasonable parameters, oversight will have no valuewhatsoever, as the Overseer never exercises her veto. We thenestablish our main result: an overseer of the appropriate partisanship

29 In addition, so long as π N12, the Principal's policy payoff is maximized in the

equilibrium in which the Executive follows his signal of the state and the Overseer'sbehavior satisfies criterion D1. This then provides an additional justification forconsidering this equilibrium.30 For some parameters there will also exist equilibria in which the Executive pools(e.g., the Executive always proposes p=s and the Overseer vetoes any proposal).However, we are interested in examining the Overseer's behavior when the Executivebehaves informatively.

outperforms a non-partisan overseer in terms of promoting thePrincipal's welfare. Before characterizing the Overseer's equilibriumbehavior, however, we characterize how the Overseer “should”behave from the perspective of the Principal.

4.1. Normative benchmark

Suppose the new policy (p=n) has been proposed, so theOverseer must decide whether to veto. When the expected payofffrom the new policy is less than the status quo payoff of −1, thePrincipal would like the Overseer to exercise her veto. Since thePrincipal's payoff from α=n is 0 when ω=N and −κ when ω=S,the Overseer should veto if and only if, conditional on her information,the probability that ω=N is less than κ−1

κ. Recall that the Overseer

knows her private signal of her ability (τO) and her private signal ofthe state (σO). And since the Executive follows his signal of the state,the Overseer can infer the Executive's signal (σE) from his proposal.

Now note that the probability that ω=N given that σE=n is

Pr ω = N jσE = nð Þ =π + 1−πð Þ1

2

� �12

π + 1−πð Þ12

� �12

+ 1−πð Þ12

� �12

=1 + π

2;

where π is the prior probability that the Executive is of high ability.Since π≥1

2and κ≤4, it follows that Pr ω = N jσE = nð Þ≥κ−1

κ. So, the

Principal would like the Overseer to veto only if her privateinformation (τO, σO) leads her to doubt the appropriateness of thenew policy— i.e., σO=s and the Overseer believes herself to be of highability with sufficient probability.31 Recall that the Overseer'sperception of her ability depends on both her signal of her ability τOand on the signal's accuracy q.

The following lemma describes the Overseer's first-best strategyfrom the perspective of the Principal.

Lemma 2. (First-best strategy) Fix π, κ, and q, and suppose that theExecutive always follows his signal of the state. Then the Overseer'sfirst-best strategy is characterized by a threshold q#(π, κ)∈ [0, π).

(a) When τO=h, the Overseer should veto if and only if q≥q#(π, κ)and σO=s.

(b) When τO= l, the Overseer should veto if and only if q≤ [1−q#(π, κ)]≡q##(π, κ) and σO=s.

Given that the Overseer's signal of the state is evidence in favor ofthe status quo, Lemma 2 states that when the Overseer is the hightype, she should veto only if the accuracy of her signal of her ability issufficiently high.32 The low type should also veto when σO=s,provided the accuracy of her signal of her ability is not too high. Fig. 1provides a graphical characterization of the Overseer's first-beststrategy in terms of parameters π and q for the case in which κ=4.Fixing q, the accuracy of the Overseer's signal of her ability, we seethat when the prior π that the Executive is of high ability is sufficientlyhigh, the Overseer should never veto; for moderate values of π, onlythe high type should ever veto; and for low enough values of π, boththe high type and the low type should veto whenever σO=s.33

31 If the Overseer knew herself to be of low ability with certainty, her signal of thestate would be uninformative.32 Recall the distinction between type and ability. A high-type (low-type) overseer isone who observed a signal that she is of high (low) ability.33 Note that when q=π and τO=h, the probability that the Overseer is of high abilityis equal to the probability that the Executive is of high ability. Thus, in the event thatthe Executive and Overseer receive contradictory signals of the state, each state isequally likely. As κN2, the threshold accuracy q#(π, κ) for which vetoes are potentiallybeneficial is then lower than π.

36 Formally, “γ sufficiently small” means that there exists a γ (π,q,κ) such that theclaim holds for all γ∈(0,γ (π,q,κ)).37 Given that the Executive sets p=σE, the only other sequential equilibrium is onein which the Overseer always vetoes following the proposal of the new policy. So,along the path of play, the Overseer's reputation λO for being of high ability is equal toone-half. The latter equilibrium, however, is supported by off-path beliefs that are notconsistent with the criterion D1. The overseer-type with the greatest policy incentive

Fig. 1. First-best veto rule.


4.2. Behavior of a non-partisan Overseer

In this subsection, we consider the incentives of a non-partisanoverseer (β=0)whilemaintaining our assumption that the Executivealways follows his signal of the state. We show that there is adivergence between the equilibrium behavior of a careerist non-partisan and the behavior described in Lemma 2. This should not betoo much of a surprise, as there is no reason to expect that the actionsthat maximize the Overseer's reputation would correspond to thosethat maximize the Principal's welfare.

We begin by noting that for oversight to be beneficial, the Overseermust be willing to veto when her private information indicates thatthe new policy is misguided — necessary for this is that σO=s.However, if vetoes occurred only when σO=s, a veto would reveal theOverseer's signal of the state. A career-minded overseer may beunwilling to reveal that her signal favors the status quo. Why? Sincethe Executive only proposes the new policy when σE=n, conditionalon it being proposed, the probability that ω=N is greater than one-half. So, a signal of σO=s is more likely to be observed by an overseerwhose ability is low than one whose ability is high.34 Thus, all elsebeing equal, revealing that σO=s harms the Overseer's reputation.

Before concluding, however, that vetoing is reputationally costlyfor the Overseer, we note that by exercising her veto, the Overseermay reveal favorable information about her signal of her ability τO.This is because a high-type overseer (τO=h) has more reason to beskeptical of a proposal that contradicts her signal of the state than alow-type overseer (τO= l). And since the Overseer places positiveweight on policy, in equilibrium, a high type is more likely than a lowtype to exercise her veto. So there is a (potentially) reputationenhancing “selection effect” from vetoing, with this selection effectbeing strongest when only those overseers for whom τO=h veto.35

Via Bayes's rule, the probability that the Overseer is of high abilitywhen the new policy is proposed (so σE=n), τO=h, and σO=s is

Pr aO = H jσE = n; τO = h;σO = sð Þ = q−qπ1−qπ

:

The selection effect of revealing that τO=h compensates for the“disagreement effect” of revealing σO=s when σE=n if and only ifPr(aO=H|σE=n, τO=h, σO= s) is greater than 1

2, the prior probability

the Overseer is of high ability. This will be true if and only if theaccuracy qof theOverseer's signal of her ability is at least q� πð Þ≡ 1

2−π. So

if qbq⁎(π), a career-minded overseer would not be willing to reveal

34 Formally, Pr(σO= s|aO, p=n)=Pr(σO= s|ω=N, aO)Pr(ω=N|p=n)+Pr(σO=s|ω= S, aO)Pr(ω= S|p= n). So, Pr σO = s jaO = H; p = nð Þ = 1−π

2and Pr σO =ð

s jaO = L; p = nÞ = 12.

35 That high-ability experts could be more willing to choose the ex-ante less likelyoption is emphasized in Levy (2004).

that σO=s, even if it also revealed that τO=h, as doing so would harmher reputation. Vetoes would then never be exercised in equilibrium.

Proposition 1. (Non-partisan is a rubber stamp) Fix π, κ, q, and letβ=0.Suppose that qbq� πð Þ≡ 1

2−πand that the weight γ attached to policy is

sufficiently small.36 In the unique sequential equilibrium satisfyingcriterion D1 in which the Executive always follows his signal of thestate, the Overseer always approves the Executive's proposals.37

Thus, when the Overseer has little private information about her ownability (i.e., q is low) or the Executive's prior reputation is sufficientlyhigh (i.e., π is high), the Overseer will abdicate her responsibilities andact as a rubber stamp (see Fig. 2).38 Regardless of whether vetoing is inthe Principal's interest, the Overseer will never do so for fear of thereputational hit she would take. Notice that q⁎(π)NπNq#(π, κ); so, forany feasible (π, κ), there is a non-trivial range of q forwhich vetoes couldbe socially beneficial yet are never exercised.

It should be noted that the assumption that π≥12does not drive this

result.Whatmatters is not that the Executive's signal ismore accurate,on average, than the Overseer's but rather that the Executive's signal ismore accurate, on average, than noise. As such, the alternative whichthe Executive proposes will be correct with probability greater than 1

2.

The Overseer will then be unwilling to ever veto when qbq� πð Þ = 12−π

,

which can be satisfied for any πN0 provided q is sufficiently close to 12.

Moreover, while the range of q for which the Overseer will act as arubber stamp decreases as π decreases, the potential benefit to thePrincipal from the Overseer exercising her veto increases.

We now turn to characterizing the Overseer's equilibriumbehavior when qNq⁎(π). For such parameters, if vetoes occur onlywhen τO=h and σO=s, vetoing would enhance the Overseer'sreputation. Criterion D1 then rules out the equilibrium in which theOverseer always accepts. So, in equilibrium, the high type vetoes withprobability one when σO=s, and when reputational concerns areparamount, the low type vetoes with positive probability as well.

to accept is one for whom τO=h and σO=n. Criterion D1 requires that the Principalplace probability one on the Overseer's type being such. However, if this were thePrincipal's belief, an overseer for whom τO=h and σO=n would have both a policyand a reputational incentive to accept when p=n, thus breaking the putativesequential equilibrium.38 This is an example of a reputational herd (see Scharfstein and Stein, 1990;Ottaviani and Sorensen, 2001).

41 It is possible to specify parameters under which a partisan overseer can be induced toveto even without private information about her own ability q = 1

2

� �. Suppose the

Fig. 2. Behavior of careerist non-partisan overseer (i.e., γ≈0).


Proposition 2. (Non-partisan vetoes) Fix π, κ, q, and β=0. Further,suppose that qNq⁎(π). In the unique sequential equilibrium satisfyingcriterionD1 inwhich the Executive always follows his signal of the state, theOverseer always acceptswhenσO=n; the high type vetoeswithprobabilityone when σO=s; and so long as γ is sufficiently small, the low type vetoeswith a probability strictly between zero and one when σO=s.39

We conclude this subsection by discussing how a non-partisanoverseer's equilibrium behavior compares to the first-best strategyspecified in Lemma 2. Fig. 2, where we overlay the graph of q⁎ ontoFig. 1, facilitates this comparison. When reputational considerationsdominate (i.e., γ≈0), we have that a non-partisan is too reticent vis-a-vis the first-best strategy in regions II, III, and IV, whereas in region V, anon-partisan is too aggressive. Recall that in region V, the Principalprefers that only the high type veto, but we know from Proposition 2that the low type vetoes as well. The divergence between what thePrincipal wants andwhat the Overseer does ismost dramatic in regionIII, a region in which the Principal would like the Overseer to vetowhenever σO=s. However, as we know from Proposition 1, a non-partisan will be a rubber stamp in region III, as she will always sign offon thenewpolicy. So for suchparameters, a non-partisan is not just tooreticent but is entirely ineffective. TheOverseerwill also act as a rubberstamp in region II, a region in which the Principal desires that the hightype exercises her veto when observing σO=s.

4.3. Oversight with partisanship

We have yet to discuss the effect of a veto on the Executive'sreputation. Regardless of the Overseer's partisanship, since she placespositive weight on policy, those most skeptical of the Executive'sproposal (i.e., those who observed a signal that the status quo isappropriate) will be the ones to veto. Since the Overseer's signal of thestate σO is correlated with the true stateω, being vetoed decreases theprobability that the Executive's signal is correct. Therefore, vetoesalways damage the Executive's reputation.40

39 In addition to the sequential equilibrium specified, all other sequential equilibria(in which the Executive follows his signal) involve the Overseer pooling following theproposal of the new policy, either always accepting or always rejecting. We have alreadyexplainedwhy theequilibrium inwhich theOverseer always rejectsdoesnot satisfy criterionD1. The equilibrium in which the Overseer always accepts does not satisfy D1 because theoverseer-type with the greatest policy incentive to veto is one for whom τO=h and σO=s.CriterionD1 then requires the Principal to place probability one on theOverseer's type beingsuch. However, if this were the Principal's belief, the fact that qNq⁎(π) ensures that anoverseer for whom τO=h and σO=swould have both a policy and a reputational incentiveto reject when p=n, thus breaking the putative sequential equilibrium.40 This will always be true in any equilibrium in which the Overseer vetoes with a non-degenerate probability.Whenγ is small, criterion D1 is sufficient to ensure that this is alsothe case in any sequential equilibrium in which the Overseer pools on always accepting.

Remark 1. Being vetoed will decrease the Executive's reputation inequilibrium.

That vetoes result in the Executive's reputation taking a hit iscritical for this subsection's main result, which is that an overseer ofthe “appropriate” partisanship is often a more effective check on theExecutive than a non-partisan. Unlike a non-partisan, a partisan has astake in the Executive's reputation. And since vetoes affect theExecutive's reputation, by varying the level of partisanship β, one canaffect the Overseer's incentive to check the Executive.

To see the potential benefits of partisanship, recall thatwhen qbq⁎(π)and career concerns dominate, a non-partisan is a rubber stamp. So onlyan overseerwho profits from damaging the Executive's reputation (βN0)would ever veto. Since we have assumed that the Overseer cares moreabout her ownreputation thanabout theExecutive's, if vetoes are tooccurin equilibrium, the damage to the Executive's reputation that results froma veto must be larger than the damage to the Overseer's (provided γ issmall). This possibility arises because the Overseer has a greater incentiveto veto if she is the high type. Vetoing can then signal that the Overseer ismore likely to be the high type, which mitigates the damage to theOverseer's reputation from vetoing. At the same time, learning that thedisagreeing overseer is more likely to be the high type only exacerbatesthe damage to the Executive's reputation. Still, for a veto to damage theExecutive more than the Overseer, it is necessary that learning about theOverseer's signal of her ability is sufficiently important. That is, qmust besufficiently large.41

Proposition 3. (Partisanship can break overseer rubber stamping) Fix π,κ, and q. Suppose q∈(q#(π, κ), q⁎(π)). In addition, restrict attention tosequential equilibria satisfying criterion D1 in which the Executive sets

Executive proposes the new policy only when σE=n. Then, by Eq. (R1), a policymaker'sreputation conditional upon the new policy being proposed and the Overseer's decisiond∈{A, R} is a convex combination of Pr[aj=H|σE=n, σO=s] and Pr[aj=H|σE=n, σO=n],where for the Overseer, Pr aO = H jσE = n;σO = n½ � = 1 + π

2 + πand Pr aO = H jσE =½

n;σO = s� = 1−π2−π

, and for the Executive, Pr aE = H jσE = n;σO = n½ � = 3π2 + π

and

Pr aE = H jσE = n;σO = s½ � = π2−π

. Now, when γ≈0, the Overseer will condition her

veto decision upon her signal of the state only if her reputational payoff (λO-βλE) is(almost) the same from vetoing as it is from accepting. This requires that β≈ 1

2 1−πð Þ, and so

either πb12or β≥1. Consequently, when theOverseer has no private information about her

ability, we can induce informative vetoes onlywhenβ≈ 12 1−πð Þ. Notice, however, thatwhen

q N12, it is possible to induce vetoes for a muchwider range of partisanship; this is because

as the probability with which the low-type vetoes increases, vetoes become moredamaging to theOverseer and less damaging to the Executive, so the probability of vetoingwill vary continuously with changes in partisanship.


p=σE. For each value of π, there exists a number qP πð Þ≡ 12 + π−2π2bq

� πð Þsuch that we have:

(a) If qbq (π) and γ is sufficiently small, vetoes never occur, regardlessof the level of partisanship.

(b) If qNq (π) and γ is sufficiently small, there exists a non-degenerateinterval of partisanship levels [β

⁎, β⁎]∈(0, 1] such that for any β

in this interval, only the high type vetoes, doing so if and only ifσO=s. For β∈(β⁎, 1], the high type vetoes if and only if σO=s,and the low type who observes σO=s also vetoes with positiveprobability.

We know from Lemma 2 that when q∈(q#(π, κ), q⁎(π)), vetoes aresocially valuable. Yet, we also know from Proposition 1 that whenqbq⁎(π) and reputational concerns dominate, a non-partisan willnever veto. So Proposition 3 identifies conditions under which vetoeshave social value but only partisans ever exercise them. Thus, not onlycan a partisan provide more effective oversight than a non-partisan,but when qbq⁎(π) and γ≈0, partisanship is necessary for oversight tohave any value whatsoever.

Three additional observations concerning Proposition 3 areworth noting. The first is that with partisanship, when q∈(max{q#(π,κ),q##(π,κ), q (π)},q⁎(π)),42 it is possible to induce the Overseer to employthe first-best veto rule. We know from part (b) of Proposition 3 that forthese parameters there exists an interval of partisanship levels underwhich only the high-type overseer vetoes, doing so if and only if σO=s.This is exactly the behavior desired by the Principal. Our secondobservation is that while there is a danger of too much partisanship inregions I and II, no such danger exists in region III, a region where thePrincipal would like the Overseer to veto if and only if σO=s.43 Finally,while partisanship is potentially beneficial, there are situations inwhich apartisan overseer can beworse thanno overseer at all. Recall that q#(π, κ)is the threshold accuracy for which vetoes can ever be desirable. Noticealso that q (π) is the threshold accuracy for which it is possible to inducevetoes with a partisan overseer, provided γ is sufficiently small. Theranking of these numbers is ambiguous. So when q (π)bqbq#(π,κ), asufficiently partisan overseer would exercise her veto even thoughvetoes are never desired.

Before proceeding, we note an additional potential benefit ofpartisanship that we have not considered so far. We have evaluatedthe welfare of the Principal only in terms of the payoff from the policyimplemented in this period. It is possible, however, that the Principalalso benefits from learning about the respective competencies of theExecutive and Overseer — something that will only occur if theOverseer exercises her veto with positive probability. In that case ourwelfare analysis would underestimate the benefit of inducing vetoesand, hence, also the value of partisanship.

We now examine the value of partisanship when qNq⁎(π).Although non-partisan oversight has value at such parameters (i.e.,vetoes are exercised), when γ is small, a non-partisan will be eithertoo reticent or too aggressive vis-a-vis the first-best veto rule.Reticence arises when qbq##(π, κ) (region IV), while obstructionismarises when qNq##(π, κ) (region V). Partisanship can partially correctfor these inefficiencies.

Proposition 4. (Partisanship can ameliorate overseer reticence/ob-structionism) Fix π, κ, q, and γ. Suppose qNq⁎(π), and restrict attention tosequential equilibria satisfying criterion D1 in which the Executive setsp=σE. If the low type vetoes with a non-degenerate probability in a non-partisan environment, then the probability with which she vetoes in apartisan environment is locally increasing (at 0) in β.

42 This is a subset of region II.43 This point, of course, hinges on the fact that β is bounded above by 1. If theOverseer cared primarily about bringing down the Executive (i.e., β→∞), she wouldhave an incentive to veto the Executive even when from the perspective of thePrincipal she should not (i.e., when σO=n).

Thus, when a non-partisan is too reticent (region IV), an overseer forwhom βN0 would give the Principal higher utility. And when a non-partisan is too aggressive (region V), an overseer for whom βb0would give the Principal higher utility.

4.4. Discussion

We have shown that for a range of parameters, the Principal canbe better off with an overseer of the appropriate partisanship thanwith a non-partisan. So while opponents of partisanship havegrounds to be concerned about its excess, our analysis reveals apotential benefit: in systems of governance that depend onMadisonian checks and balances, under a range of conditions, asufficient level of partisanship among elected officials is required forchecks to be exercised. This means that the very “spirit of thefaction” that the inventors of checks and balances were so concernedabout constraining (see, for example, Federalist #10) may well benecessary for these checks to be effective.

We conclude this section with a discussion of our model's positiveimplications for the incidence of divided government. If we think of anoverseer for whom βN0 as a member of the party that seeks to replacethe Executive and of an overseer for whom βb0 as a member of theExecutive's own party, we can summarize Propositions 3 and 4 asfollows: provided that partisanship is of an appropriate level, inregions II through IV of Fig. 2, the Principal is best off with dividedgovernment, whereas in region V, the Principal is best off with unifiedgovernment. Consequently, the only situation in which unifiedgovernment can be beneficial is when the prior π that the Executiveis of high ability is high enough that vetoes by the low type areundesirable. In contrast, when π is low, so there is little confidence inthe Executive's ability, divided government is the optimal arrange-ment.44 The effect of a change in π on the desirability of dividedgovernment is not unambiguous, however. Increasing π not onlydecreases the value of vetoes by the low type but also increases theprobability that divided government is necessary to prevent theOverseer from becoming a rubber stamp.

Finally, in considering how voters adjust the makeup of Congressat midterm elections in response to their perceptions of the President,it is sensible to assume that the relevant parameters (π and q) areknown before β is determined. We may, however, also be interestedin the case where β must be determined before these parameters areknown — for example, before learning π. In such a situation, whetherdivided or unified government is preferable will depend on the beliefsabout the relevant parameters. So while partisanship of a particularform may be beneficial for certain realizations of the parameters,these potential gains must be balanced against the risk of a realizationin which this form of partisanship either exacerbates or inducesdistortions in the Overseer's behavior.

5. Extensions

The main argument of this paper has been that in a system ofchecks and balances, not only will an overseer of the appropriatepartisanship outperform a non-partisan one, but sometimes parti-sanship is necessary for checks to have any value whatsoever. Thatsaid, we havemade a number of assumptions along theway that couldpossibly affect our conclusions. This section briefly discusses theconsequences of modifying some of the more salient ones.

44 Existing forecasting models of midterm election often include a variable forpresidential popularity (e.g., Jones and Cuzán, 2006), with most finding that when thepresident is unpopular, his party does worse.


5.1. Executive behavior

We have not allowed the Executive to have private informationabout his ability or to be a partisan, as we have the Overseer. Whilethis has simplified our analysis, our conclusions about the value ofpartisan oversight hold when either asymmetry is relaxed. Thisfollows from the fact that the Executive will still behave informativelyin equilibrium, and so the Overseer's incentives will not be changed ina meaningful way.

We first consider the case in which the Executive is a partisan (whocaresmore abouthis own reputation than theOverseer's) and show thatthe equilibrium constructed in the previous section survives. To do so,we need only check that the Executive has no incentive to deviate fromhis prescribed strategy of followinghis signal of the state. First, note thatin the proposed equilibrium, the expected reputations of the Executiveand the Overseer are independent of the policy proposed: when eitherp=n or p=s is proposed, the expected reputations are simply theaverage abilities in the population— i.e., π and 1

2, respectively. Now, the

Executive could deviate by proposing the status quowhenσE=n. Doingso has no effect on the expected reputation of either policymaker(relative to proposing p=nwhen σE=n), yet leads to a lower expectedpolicy payoff for the Executive. Alternatively, the Executive coulddeviate by proposing the new policy when σE=s. Doing so raises theExecutive's risk of being vetoed relative to when he observes σE=n.Sincea vetohas a greater effect on theExecutive's reputation thanon theOverseer's reputation (provided γ is sufficiently small),45 the netreputational effect (relative to choosing the status quo) of this increasedveto-risk is negative from the Executive's perspective. As such, theExecutive has no incentive to deviate from his strategy.

We now consider the effect of allowing the Executive to haveprivate information about his ability. In particular, suppose theExecutive receives a private signal τE∈{l, h} that is correlated withhis true underlying ability. Since the low-type executive's signal of thestate is less accurate than the high type's, conditional on σE=n, thelow type's probability of being vetoed is greater (provided that vetoesare being exercised), and so the low type has a greater incentive tostick with the status quo. Therefore, in an equilibrium in which vetoesare informative, the high type will still follow his signal, but the lowtype will propose the status quo with positive probability afterobserving σE=n. While such a change in the Executive's strategyresults in the average ability of executives who propose the newpolicy being higher than the average ability in the population, it doesnot affect the analysis of the Overseer's decision. Moreover, whenqbq⁎(π) and γ≈0, equilibria continue to exist in which the Executivefollows his signal of the state and a non-partisan never vetoes.Consequently, evenwhen the Executive has private information abouthis ability, partisanship can have value in promoting more effectiveoversight.46

47 Fix π, κ, q, β=0, and γ≈0. Further, suppose that qbq##(π, κ). For such parameters,

Pr ω = N jσE = n; τO = l;σO = sð Þ∈ 12;κ−1κ

� �. Since Pr ω = N jσE = n; τO = l;σO =ð

sÞbκ−1κ

, the Principal desires that the Overseer veto whenever she observes σO=s.However, since Pr ω = N jσE = n; τO = l;σO = sð Þ N 1

2, there does not exist an

equilibrium in which the Executive sets p=σE and the Overseer vetoes if and onlyif σO=s: Letting λO(d, ω) denote the Overseer's reputation after rejection decision dwhen the state is revealed to be ω, under the prescribed strategies, we have that λO(A,

5.2. The no feedback assumption

We have assumed that the appropriateness of the policyimplemented is not revealed until after the Principal assignsreputations to the Executive and the Overseer. Even when thisassumption is relaxed — i.e., the Principal observes the state of theworld with probability ρN0 prior to assigning reputations — a non-

45 Fix |β|b1. In an equilibrium in which vetoes are informative and γ≈0, we havethat λO(n, A; ψ⁎)−λO(n, R; ψ⁎)≈β[λE(n, A; ψ⁎)−λE(n, R; ψ⁎)]. Since |β|b1, thedamage that results to the Executive's reputation from a veto must be greater than thechange that results in the Overseer's reputation.46 This is also true when the probability that ω=n is not equal to one-half. For anyprior on the state of the world there will exist an equilibrium in which the Executivebehaves informatively provided the Executive's signal of his own ability is sufficientlyaccurate. The analysis of the Overseer's behavior then goes through unchanged. Notethat the more unbalanced the prior, the greater the accuracy of the Executive's signalmust be for there to be an equilibrium in which the Executive behaves informatively.

partisan overseer will not necessarily behave as the Principaldesires.47 So even with feedback about the state, a partisan overseercan potentially outperform a non-partisan one. This requires,however, that feedback about the state is not certain (ρb1). If theOverseer's veto decision is to affect the Executive's reputation, it mustreveal information about the state of the world that would not berevealed anyway. Thus, if feedback were certain (ρ=1), the Overseercould not influence the Executive's reputation; consequently, theOverseer's partisanship would not influence her incentive to exerciseher veto. However, when feedback about the state of the world isuncertain (ρb1), the Overseer's veto decision will impact theExecutive's reputation in the event that the state is not revealed.Consequently, when ρb1, partisanship can potentially increase theeffectiveness of oversight.

5.3. The assumption that the Overseer and the Executive cannotdeliberate

It is worth considering what would happen if the Executive andthe Overseer could share their private information with each other.The simplest way to explore this possibility is to have the Executiveand the Overseer act jointly, deliberating privately and then selectinga policy. In acting jointly, we assume that their objective is tomaximize a weighted average of their reputations: θλE+(1−θ)λO,where θ∈ [0, 1]. While there are situations in which this decision-making mechanism would outperform an oversight regime withpartisanship, this is not true in general.

Suppose that (q, π) belongs to region II of Fig. 2, where q∈(q (π),π). For these parameters, the Principal desires that the selectedpolicy match the Executive's signal, except when σE=n, σO= s, andτO=h; in this case, the Principal desires that the status quo beselected. We know from Proposition 3 that this can be achieved withan oversight regime, provided partisanship is of the appropriatelevel. On the other hand, if the Executive and Overseer are actingjointly, this cannot be achieved. Note that the signal profile σE≠σO

and τO=h lowers each policymaker's probability of being of highability. So if the Principal's preferred decision rule were beingemployed, the average abilities of both policymakers would bestrictly higher when the new policy is selected.48 Reputationalconcerns would then prevent the policymakers from ever selectingthe status quo. So, there are situations in which partisan oversightoutperforms not only non-partisan oversight but also cooperativedecision-making by the policymakers.

6. Conclusions

This paper has examined the value of partisanship in promotingeffective oversight. We first demonstrated that oversight con-ducted by a non-partisan is not the panacea it is often made out to

N)=λO(R, S)NλO(R, N)=λO(A, S). Letting λO(d) denote theOverseer's reputationwhenthe state is not revealed, under the prescribed strategies, we have that λO(A)NλO(R)(see Lemma 4(f) of Appendix A). These facts, taken together with the fact thatPr ω = N jσE = n; τO = l;σO = sð Þ N 1

2, imply that the expected reputation of an

overseer who observed (l, s) is higher from accepting than rejecting. Hence, whencareer concerns are dominant, any equilibrium must have a low-type overseer whoobserved σO=s accepting with positive probability.48 Suppose qbq⁎(π). To prove that selecting the status quo harms the joint reputation oftheExecutiveand theOverseer, note: Pr(aj=H|α=s)=Pr(σE=s|α=s)Pr(aj=H|σE=s)+Pr(z|α=s)Pr(aj=H|z), where z=(σE=n, τO=h, σO=s). And since Pr(aj=H|σE=s)=πjand Pr(aj=H|z)bπj, Pr(aj=H|α=s)bπj, which in turn implies that Pr(aj=H|α=n)Nπj.

49 This is a consequence of three facts: policy enters the Overseer's payoff function;the high type's signal of the state is more accurate, on average, than the low type's;and the reputational payoffs from one's veto decision are independent of one's privateinformation about one's ability. So if a low type gains from vetoing when σO=s, then ahigh type gains even more from doing so when σO=s.50 For D1 to have bite, there must be beliefs for which the Overseer is willing to veto.This will always be possible when γ is not too large. When pooling on alwaysaccepting, the Overseer's reputation is one-half. When p=n is proposed, the overseer-

type with the highest reputation is (h, n), whose reputation is q 1 + πð Þ1 + qπ

. As the policy

loss from vetoing is never greater than one (for any profile of feasible parameters),γbq 1 + πð Þ

1 + qπ−1

2ensures that vetoing is not equilibrium dominated. For such γ, Criterion

D1 will then uniquely determine the Principal's beliefs following an off-path veto.


be: under reasonable conditions, a non-partisan overseer is unwillingto challenge an executive's policy initiatives. The reason for thisreticence is that revealing disagreement leads the public to be lessconfident not only in the ability of the executive but also in the abilityof the overseer. We then demonstrated that partisanship is amechanism by which such reticence can be overcome: an overseeris more willing to reveal disagreement if she also desires to see theexecutive's reputation fall. Moreover, even if a non-partisan wouldnot completely abdicate her responsibilities, there may still bedistortionswhich can bemitigated if the overseer is of the appropriatepartisanship. We thus obtain the surprising result that a partisanoverseer can often outperform a non-partisan one.

The insights about partisanship and its value developed in thispaper are quite general and apply beyond the setting of checks andbalances that we examine. For example, Ottaviani and Sorensen(2001) consider the question of who should speak first in acommittee setting, where the key concern is that later speakersmay suppress their disagreement with earlier speakers. Our resultssuggest that, in a committee environment, later speakers could beinduced to reveal disagreement if they benefited from damaging thereputations of previous speakers. So a certain level of animosity andcompetition between advisors may not necessarily be a bad thing.Another setting in which reputational considerations lead toinformation loss is Gentzkow and Shapiro's (2006) model of mediareporting. They illustrate how a media outlet's desire to appearaccurate may lead it to suppress information that challenges itsreaders' pre-conceived beliefs. Consequently, when the governmentis popular, some degree of animus between the media and thegovernment may be necessary if the media is to challenge thegovernment's assertions.

One interesting feature of our model is that there is noheterogeneity in the policy preferences of politicians, so there isno notion of ideology. As such, we have provided a novel theory ofdivided government, one based on the need for effective oversightrather than policy compromise. While abstracting from ideologicaldifferences has the virtue of allowing us to identify a role for themost base form of partisanship — the simple desire to manipulatethe re-election prospects of others — it comes with limitations, asmost policy questions have an element of ideological conflict.Examining the value of partisanship in such a setting is left forfuture work.

Acknowledgements

We thank Nigel Ashford, Michael Bailey, Dirk Bergemann, StephenCoate, Stephen Davies, Mark Fey, Sean Gailmard, Dino Gerardi, AlanGerber, Jacob Hacker, Shigeo Hirano, Gregory Huber, William Leblanc,Alessandro Lizzeri, Nolan McCarty, Kyle McNeel, Minor Myers, ArndPlagge, Kareen Rozen, Larry Samuelson, Lena Schaffer, MatthewStephenson, Thomas Stratmann, Erin Thomas, Kaj Thomsson, MichaelTing, Craig Volden, Shaina Wright, an anonymous referee and theeditor for helpful feedback.

Appendix A

Proof of Lemma 1. See Appendix B. □

Proof of Lemma 2. Suppose the Executive always follows his signalof the state. We argued in the main text that, conditional on herprivate information (τO, σO), the Overseer should veto if and only ifPr ω = N jσE = n;τO;σOð Þ≤κ−1

κ.

We first prove that when σO=n, vetoing is sub-optimal. Note that

Pr ω = N jσE = n;τO;σO = nð Þ N Pr ω = N jσE = nð Þ = 1 + π2

≥κ−1κ

;

where the last inequality follows because κ≤4 and π≥12. Hence,

vetoing is sub-optimal when σO=n.Now consider the case in which σO=s and τO=h. Then, by Bayes's

rule,

Pr ω = N jσE = n;τO = h;σO = sð Þ = 1 + π2

1−qð Þq 1−πð Þ + 1−qð Þ :

This probability is less than or equal to κ−1κ

if and only ifq≥ 2− 1−πð Þκ

2π + 1−πð Þκ≡q# π; κð Þ. Thus, when σO=s and τO=h, vetoing is

optimal if and only if q≥q#(π, κ). Notice also that q#(π, κ) is decreasingin κ and that q#(π, 2)=π. These facts, taken together with ourassumption that κN2, imply that q#(π, κ)∈ [0, π).

Finally, consider the case in which σO=s and τO= l. Then, byBayes's rule,

Pr ω = N jσE = n;τO = l;σO = sð Þ = 1 + π2

q1−qð Þ 1−πð Þ + q

:

This probability is less than or equal to κ−1κ

if and only if 1−q≥q#(π, κ), orequivalently, q≤1−q#(π, κ)≡q##(π, κ). Thus, when σO=s and τO= l,vetoing is optimal if and only if q≤q##(π, κ). □

Before proceeding, we note that there cannot exist an equilibriumin which the Overseer vetoes after observing that σO=n.

Lemma 3. Fix π, κ, q, γ, and β∈(−1, 1). In any sequential equilibriumsatisfying criterion D1 in which the Executive sets p=σE, vetoes occuronly when σO=s.

Proof. See Appendix B. □

It then follows that in any sequential equilibrium satisfying D1 inwhich the Executive follows his signal of the state, if vetoes occur, theyoccur only when σO=s. Hence, the Overseer's strategy can be fullycharacterized by a double (zh, zl), where zh denotes the probability withwhich the high type vetoes when σO=s and zl denotes the probabilitywith which the low type vetoes when σO=s. Since γN0, in anysequential equilibrium, if the low type vetoes with positive probability,then thehigh typemust vetowithprobability one.49 So in any sequentialequilibrium, the Overseer's strategy takes a “cut-point form,” whereeither zh∈[0,1) and zl=0, or zh=1 and zl=[0, 1].

We now turn to specifying the respective reputations that wouldbe assigned to the Executive (λE) and the Overseer (λO) following aveto decision of d∈{A, R} given that: (1) the Executive's strategy is tofollow his signal of the state; (2) the Overseer's strategy takes a cut-point form in which she vetoes only when σO=s; (3) the Principal'sbeliefs ψ are consistent with the strategies of the Executive and theOverseer; and (4) when zh=zl=0, if the Principal were to observe anoff-path veto, she would place probability one on the Overseer's typebeing (h, s). This belief is uniquely determined by criterion D1 whencareer concerns dominate.50


When zh∈ [0, 1) and zl=0, we have:

λO n;R;ψð Þ = q 1−πð Þ1−qπ

λE n;R;ψð Þ = 1−qð Þπ1−qπ

λO n;A;ψð Þ = 2−qzh + qπzh4−zh + qπzh

λE n;A;ψð Þ = 4π−πzh + qπzh4−zh + qπzh

And when zh=1 and zl∈ [0, 1], we have:

λO n;R;ψð Þ = 1−πð Þ q + 1−qð Þzl½ �1−qπ + zl 1−π + qπ½ �

λE n;R;ψð Þ = π 1−qð Þ + qzl½ �1−qπ + zl 1−π + qπ½ �

λO n;A;ψð Þ = 2− 1−πð Þ q + 1−qð Þzl½ �3 + qπ−zl 1−π + qπ½ �

λE n;A;ψð Þ = 4π−π 1−qð Þ + qzl½ �3 + qπ−zl 1−π + qπ½ �

To derive these reputations, we first characterize the Principal'sbeliefs ψ (about the respective types of the Executive and Overseer)as a function of the strategies of the Executive and the Overseer.We then derive reputations λj(·;·) from beliefs ψ via Eq. (R1). Asthese calculations are straightforward but algebraically intense, theyare left to Appendix B.

In proving our main results, it will be useful to work with afunction that maps overseer strategies (that have a cut-point form)into the Overseer's net reputational payoff from vetoing. We denotethis function by V, where

V zh; zl;βð Þ≡ λO n;R;ψð Þ−βλE n;R;ψð Þh i

− λO n;A;ψð Þ−βλE n;A;ψð Þh i

:

So,

V zh; zl;βð Þ

≡

q 1−πð Þ−β 1−qð Þπð Þ1−qπ

− 2−qzh + qπzh−β 4π−πzh + qπzhð Þ

4−zh + qπzh

if zh∈ 0;1½ Þ and zl = 0

1−πð Þ q + 1−qð Þzl½ �−β π 1−qð Þ + qzl½ �ð Þ1−qπ + zl 1−π + qπ½ �

− 2− 1−πð Þ q + 1−qð Þzl½ �−β 4π−π 1−qð Þ + qzl½ �ð Þ3 + qπ−zl 1−π + qπ½ �

if zh = 1 and zl∈ 0;1½ �:

8>>>>>>>><>>>>>>>>:

Hence, when V(·)N0 (b0), there is a reputational incentive to veto(accept).

Lemma 4. Some properties of V are:

(a) V is increasing in β;(b) V(zh, 0; β) is monotone in zh: when V(0, 0; β)=0, V(zh, 0; β) is

constant in zh; when V(0, 0; β)≠0, ∂V zh;0;βð Þ∂zh

= V 0;0;βð Þ½ �;

(c) V(0, 0; 0)N0 if qNq⁎(π),V(0, 0;0)b0 ifqbq⁎(π), andV(0, 0; 0)=0if q=q⁎(π);

(d) V(0, 0; 1)N0 if qN q(π), V(0, 0; 1)b0 if qb q(π), and V(0, 0; 1)=0if q=q(π);

(e) V(1, zl; β) is decreasing in zl;(f) V(1,1;β)b0.

Proof: See Appendix B. □

We introduce one final piece of notation that proves useful in thesubsequent proofs. Conditional on receiving a signal of one's abilityequal to τO, write u(τO) for the Overseer's net policy payoff from

exercising her veto when σO=s. Formally, u(τO)≡Eω[u(s, ω)|σE=n,(τO, σO=s)]−Eω[u(n, ω)|σE=n, (τO, σO=s)]. Thus, an overseer whoobserves τO∈{l, h} andσO=s iswilling to veto if and only ifV(zh, zl;β)+γu(τO)≥0.

Proof of Proposition 1. Fix π, q, and κ and set β=0. Further, supposethat qbq⁎(π) and restrict attention to sequential equilibria satisfyingcriterionD1 inwhich the Executive always follows his signal of the state.Weneed to show that there exists a threshold γ such that for allγb γ, theOverseer never vetoes. We begin by demonstrating that the netreputational payoff from vetoing V(zh, zl; β) is negative for all zh and zlwhich are consistentwith a cut-point strategy. To see that this is so, note:

0 N V 0;0;β = 0ð Þ≥V zh; zl;β = 0ð Þ:

Thefirst inequality follows fromour supposition that qbq⁎(π) and part(c) of Lemma 4. The second inequality follows from the first inequality

and parts (b) and (e) of Lemma 4. Defining―γ ≡ V 0;0;β = 0ð Þu hð Þ

��, it follows

that for all γbγ , V(zh, zl; β=0)+γu(τO)b0. Thus, when γbγ and theExecutive follows his signal of the state, the net payoff from vetoing isnegative. Consequently, when γbγ , given that the Executive setsp=σE, there is a unique sequential equilibrium satisfying D1, and inthis equilibrium, the Overseer always accepts. □

Proof of Proposition 2. Fix π, q, and κ and set β=0. Further, supposethat qNq⁎(π) and restrict attention to sequential equilibria satisfyingcriterion D1 in which the Executive sets p=σE.

Wefirst show that in any such equilibrium the high type vetoeswithprobability onewhenσO=s. If we have an equilibrium inwhich the lowtype vetoes with positive probability when σO=s, then it immediatelyfollows that the high type vetoes with probability one when σO=s. Soconsider an equilibrium in which the low type never vetoes. Sinceq⁎(π)NπNq#(π), our supposition that qNq⁎(π), taken together withLemma 2, implies that u(h)N0. Thus, to show that the high type vetoeswith probability one in an equilibrium in which zl=0, it is sufficient toshow that V(zh, 0; 0) is positive for all zh. To see that this is so, note:

0bV 0;0; 0ð Þ≤V zh;0; 0ð Þ:

This follows from parts (b) and (c) of Lemma 4.We now turn to establishing that when γ is sufficiently small, the

low type vetoes with a non-degenerate probability when σO=s. Wejust established that V(1, 0; 0)N0. And from part (f) of Lemma 4, weknow that V(1, 1; 0)b0. That V(1, 0; 0)N0 and V(1, 1; 0)b0 impliesthat there exists a γ N0 such that for all γ∈(0, γ ), V(1, 0; 0)+γu(l)N0 and V(1, 1; 0)+γu(l)b0. So, suppose that γbγ . Then we cannothave an equilibrium in which the low type either always accepts oralways rejects when observing σO=s. As an equilibriummust exist, itmust involve the low type randomizing. Hence, we have anequilibrium in which zh⁎=1 and zl⁎∈(0, 1), where zl⁎ is a solution to V(1, zl; 0)+γu(l)=0. SinceV(1, zl; 0) is decreasing in zl (part (e) of Lemma4), uniqueness of the low-type's mixing probability follows. □

Proof of Proposition 3. Proof of part (a). Fix π, q, and κ. Further,suppose that qbq (π) and restrict attention to sequential equilibriasatisfying criterion D1 in which the Executive sets p=σE. We need toshow that there exists a threshold γ such that for all γbγ the Overseeralways accepts for any β∈(−1, 1).We begin by establishing that V(zh,zl; β)b0 for all β and for all (zh, zl) which are consistent with a cut-point strategy. To see that is so, note:

0 N V 0;0; 1ð Þ≥V zh; zl; 1ð Þ≥V zh; zl;βð Þ:

The first inequality follows from part (d) of Lemma 4. The secondinequality follows from the first inequality and parts (b) and (e). The

final inequality follows from part (a). Defining Pγ≡ V 0;0; 1ð Þu hð Þ

��, it follows


that for all γbγ , we have that V(zh, zl; β)+γu(τO)b0. Thus, when γbγ and the Executive follows his signal of the state, the net payoff fromvetoing isnegative. Sowhenγbγ , in anysequential equilibriumsatisfyingD1 in which the Executive sets p=σE, the Overseer never vetoes.

Proof of part (b). Fix π, q, and κ. Further, suppose q∈(max{q#(π),

q (π)},q*(π)) and γb―γ ≡ V 0;0; 0ð Þu hð Þ

��. Finally, restrict attention to sequen-

tial equilibria satisfying D1 in which the Executive sets p=σE.We need to show that there exists an interval of partisanship levels

[β⁎, β⁎]∈(0, 1] such that only the high type vetoes, doing so with

probability one when σO=s. In effect, there are two claims here. First,if zh=1 and zl=0, then there exists an interval of partisanship levels[β

⁎, β⁎] such that neither the high type nor the low type has an

incentive to deviate. Second, when β∈ [β⁎, β⁎], there does not exist an

equilibrium (zh⁎, zl⁎) in which either zl⁎N0 or zh⁎b1.We begin with the first claim. If zh=1, zl=0, and neither type

wishes to deviate, then

V 1;0;βð Þ + γu hð Þ≥0 ð1Þ

and

V 1;0;βð Þ + γu lð Þ≤0: ð2Þ

That an interval of partisanship levels exists for which theseconditions hold can be seen from the following argument. By oursupposition that qbq⁎(π) and γbγ , we know from the proof ofProposition 1 that the left-hand side of inequality (1) is negativewhenβ=0. If we can show that the left-hand side of inequality (1) ispositive when β=1, then given the fact that V is increasing andcontinuous in β, there exists a unique level of partisanship that liesstrictly between 0 and 1 such that inequality (1) holds with equality.Denoting this level by β

⁎, it follows that for all β≥β

⁎, if zh=1 and

zl=0, the high type has an incentive to veto when σO=s.To see that the left-hand side of inequality (1) is positive when

β=1, begin by noting:

0bV 0;0; 1ð ÞbV 1;0; 1ð Þ:

This follows from our supposition that qNq (π) and (b) and (d) ofLemma 4. Finally, given our supposition that qNq#(π), from Lemma 2,we know that u(h)N0. That V(1, 0; 1)N0 and u(h)N0 implies that theleft-hand side of inequality (1) is positive when β=1.

Turning to the low type's payoff fromvetoing, since the left-hand sideof inequality (1) is negative when β=0, so is the left-hand side ofinequality (2), as u(h)Nu(l). Moreover, since the Overseer's netreputational payoff from vetoing is both increasing and linear in β, wehave: limβ→∞V(1, 0; β)+γu(l)N0. Accordingly, there exists a uniquelevel of partisanship such that inequality (2) holds with equality. Denotethis level by β(l). Consequently, when zh=1, zl=0, and βbβ(l), the lowtype has a strict incentive not to veto. Finally, since u(h)Nu(l), β(l)Nβ

⁎.

Putting the above arguments together, it follows that when zh=1and zl=0, there exists an interval of partisanship levels— namely, [β

⁎,

β(l)] — such that neither the high type nor the low type has anincentive to deviate from her respective strategy. Letting β⁎≡min{1,β(l)}, all that remains to show is that when β∈ [β

⁎, β⁎], there does not

exist an equilibrium (zh⁎, zl⁎) in which either zl⁎N0 or zh⁎b1.So, suppose that β∈ [β

⁎, β⁎]. And by way of contradiction, suppose

there exists an equilibrium (zh⁎, zl⁎) inwhich zl⁎N0. This implies that thelow type's net payoff from vetoing is non-negative. Since zl⁎N0, itfollows that zh⁎=1. Now note that

Vð1; z�l ;βÞ + γu lð ÞbV 1;0;βð Þ + γu lð Þ≤Vð1;0;β�Þ + γu lð Þ≤0:

The first inequality follows from part (e) of Lemma 4. The secondinequality follows from our supposition that β≤β⁎ and part (a) of

Lemma 4. The third inequality follows from the construction of β⁎.Thus, the net payoff to the low type from vetoing — i.e., V(1, zl⁎; β)+γu(l) — is negative, a contradiction.

Now suppose there exists an equilibrium in which zh⁎b1, eventhough β∈ [β

⁎, β⁎]. This implies that the high type's net payoff from

vetoing is non-positive. Since zh⁎b1, it follows that zl⁎=0. Now notethat since V(1, 0; β

⁎)+γu(h)=0 and u(h)N0, it must be that V(1, 0;

β⁎)b0. Therefore,

0 = V 1;0;β�ð Þ + γu hð ÞbVðz�h;0;β�Þ + γu hð Þ≤Vðz�h;0;βÞ + γu hð Þ:ð3Þ

The first equality is due to the construction ofβ⁎. SinceV(1, 0,β

⁎)b0, the

second inequality follows from part (b) of Lemma 4. The last inequalityfollows because β≥β

⁎and part (a) of Lemma 4. Thus, the net payoff to

the high type from vetoing — i.e., V(zh⁎, 0; β)+γu(h) — is positive, acontradiction.

Finally,we consider the case inwhichβ⁎b1 andβ∈(β⁎, 1].We needto show that in any equilibrium, zh⁎=1 and zl⁎N0. By the construction ofβ⁎, we have that V(1, 0; β)+γu(l)N0. This implies that in anyequilibrium in which zh⁎=1, the low type must veto with positiveprobability. Hence, all that remains to show is that there does not existan equilibrium inwhich zh⁎b1. Byway of contradiction, suppose such anequilibrium exists. Since zh⁎b1, the high-type's net payoff from vetoingmust benon-positive.Weknow from(3) thatV(zh⁎, 0;β⁎

)+γu(h)N0. Sofrom part (a) of Lemma 4, V(zh⁎, 0, β)+γu(h)N0, which yields acontradiction. □

Proof of Proposition 4. Fix π, q, κ, and γ. Further, suppose qNq⁎(π)and that γ is sufficiently small so the low type vetoes with a non-degenerate probability in a non-partisan environment. We know thatfor any β there exists an equilibrium in which the Executive followshis signal. We also know from the proof of Proposition 2 that theOverseer's equilibrium behavior when β=0 is given by the uniquesolution to V(1, zl; 0)+γu(l)=0 in zl. Denoting this solution by zl⁎ andapplying the implicit function theorem, we can find a function zl⁎(β)such that

∂z�l 0ð Þ∂β = −

∂V 1; z�l ; 0� �∂β

∂V 1; z�l ; 0� �∂z�l

:

Parts (a) and (e) of Lemma 4 imply that this derivative is positive. □

Appendix B. Supplementary proofs

Supplementary proofs associated with this article can be found, inthe online version, at doi:10.1016/j.jpubeco.2010.05.003.

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