eitm 2007 institutions week john aldrich duke university arthur lupia university of michigan
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EITM Fundamentals
What is EITM? Literature reviews? New training? NO Research design? YES
Why is it important? real problems. Better science yields social value.
What we hope to accomplish. Clarify the value and challenges of methodologically integrated
research. Help you conduct more effective research.
EITM Fundamentals
Our emphasis is asymmetric.
Theoretical Models We focus on formal models
Cooperative Game Theory Non-Cooperative Game Theory Agent-Based Modeling
Empirical Implications of… Large N-statistical studies Experiments More detailed analysis of substantive properties
This Week’s Outline
Monday: Principles of Institutional Modeling
Tuesday: Theory and Empirics Interact Evening Session: Introduction to Modeling (optional)
Wednesday: Coalition Governance Guest Speaker: Sona Golder
Thursday: Delegation and Political Parties Guest speaker: Michael Thies
Friday: Information & Experiments
Why EITM Matters
Science contributes to society by simplifying complex phenomena. Its value increases with the value of the
simplification.
Interesting topics are insufficient. You must be able to lead people from where they
are to a better conclusion.
Your research design problem Where are they?
Who is your target audience? What factual premises/truth claims will they
accept.
Where do they want to be? Which alternate conclusion will benefit them? What burden of proof and standard of evidence
do they impose?
Scientific Research Designs (KKV 7-8) 1. The goal is inference. 2. The procedures are public. 3. The conclusions are uncertain. 4. The content is the method.
It is a social phenomenon…
The Basic Research Design Problem N problems = . For any problem, N theories = . For any theory, N models = . For any problem, the number of empirical
specifications = .
What will you choose?
All political scientists make assumptions about: Players, Actions, Strategies, Information, Beliefs,
Outcomes, Payoffs, and Method of inference (e.g., “I know it when I see it,” path
dependence, Nash Equilibrium, logit plus LLN).
Some state their assumptions more precisely than others.
Conclusions depend on assumptions.
The Basic Research Design Problem N problems = . For any problem, N theories = . For any theory, N models = . For any problem, the number of empirical
specifications = .
Paper Presentation Format
M. Motivation NH. Null Hypotheses P. Premises
KEY. What choices did they make? Would you make the same ones?
C. Conclusions
Structure
1. Review several results. Specify the argument. Clarify theoretical implications.
2. Why EITM matters What do the results imply about concepts such as
collective will? Do others apply the results in a manner that is
consistent with the mathematics?
Key Premise and Questions
Collective choice is a necessary and useful part of social life. What characteristics do you want a collective choice to
have?
If there exist no decision rules that have all the characteristics you desire, which combinations of characteristics can you have?
Are contemporary claims about collective choice consistent with existing logic?
Social Choice Theory
Examines the relationship between individual will and collective decisions.
Focuses on preference aggregation and its implications for political/institutional engineering.
The foundations (cooperative game theory) are positive, the uses (how preferences should be aggregated) tend to be normative. Concepts: Equity. Utilitarian. Majority rule. Anonymity.
Monotonicity.
Social Choice Theory (peak activity late 1940’s-mid 1980’s) How do collective choices correspond to individual desires?
Elements of Cooperative Game Theory Alternatives: {x, y, z}S Individuals: iN. Preferences: x Pi y: strong (>). x Ri y weak ()
A preference profile is a preference matrix.
C(R,S) => Social/Collective Choice A CCR converts a set S and profile R into a subset of S called a
choice set.
Condorcet’s Paradox (18th C)
M. Is majority rule optimal?
NH. MMD aggregates preferences clearly.
P. At least 3 voters and 3 alternatives. Complete information. Originally, sincere voting.
C. MMD is not sufficient to produce a stable relationship between individual preferences and collective outcomes.
Example
Voter 1 2 3
Best A B C
B C A
Worst C A B
MR Agendas: (ABC)C, (ACB)B, (BCA)A.
The agenda determines the outcome. There is no 1:1 relationship between individual will and collective choice.
Arrow’s Theorem
M. How do individual desires affect collective choices?
NH (inexact). A CCR can always resolve interest conflicts.
P. At least 2 voters and 3 alternatives. People are their preferences. There is no adaptation.
C. No such CCR exists.
Arrow’s General Possibility TheoremCollective Rationality
Complete. x, y S, either x R y, y R x or both. Reflexive. x, y S, x R x. Transitive x, y, z S, x R y and y R z x R z.
C. A collectively rational CCR cannot satisfy the following four conditions simultaneously. If you want all but one of these desirable properties to hold for
every conceivable preference profile, then you must sacrifice the remaining property.
Arrow’s General Possibility Theorem Unrestricted Domain: The CCR allows us to consider any set of
preferences.
Pareto: If everyone prefers X to Y, then Y is not chosen when X is available.
Independence of Irrelevant Alternatives. x,yS, and all R, R’, x Ri y x R’i y C(S,R)=C(S,R’)
D There is no dictator. There is no i N, s.t. x, y S, x Pi y x P y.
Violations
Completeness: simple majority rule with many alternatives. Transitivity: see Condorcet paradox. Pareto: Random choice. IID: Borda Rule.
ri(x, R, S) = |{yS| x Pi y}| # of alts to which i prefers x.
r(x, R, S) = {iN| ri(x, R, S)} Borda votes for x. CBorda(R, S) = {xS| r(x, R, S) r(y, R, S) y S.} Win set.
Example. 1: xyzw. 2: xyzw. 3: zwxy.
What happens after y is removed?
Borda Violates IID
B 1 2 3 Total
x 3 3 1 7
y 2 2 0 4
z 1 1 3 5
w 0 0 2 2
C(R,S)=x
B 1 2 3 Total
x 2 2 0 4
z 1 1 2 4
w 0 0 1 1
C(R,S/y)={x,z}
Reactions to Arrow
A search for permissible properties of CCRs. Arrow actually examined social welfare functions,
but CCRs are functionally equivalent.
Inquiries into the robustness of the result.
McKelvey 1979
M. Arrow: R that yields an intransitive social ordering for any CCR. With what likelihood?
NH. Majority rule generally forces outcome towards “median” alternatives.
P. N voters, N >1 dim policy space, MMD. Solved by means of cooperative game theory
C. If conditions are right, MMD yields an indeterminate outcome.
The Extent of Intransitivity
Theorem: If m 2, n 3 and ~ total median, then x, y X, a sequence of alternatives, {0,…, N} with 0=x and N =y, such that i+1 > i, for 0iN-1.
“When transitivity breaks down, it completely breaks down, engulfing the whole space in a single cycle set.” Possible regardless of voter preferences.
Key assumptions
The chairman must know a lot about voter preferences to cause the result.
Voters make fine distinctions without becoming indifferent.
Voters vote sincerely & do not collude.
Claims about Arrow
Law “It is well established, via mathematical proofs, that every method of
social or collective choice – every arrangement whereby individual choices are pooled to arrive at a collective decision – violates at least one principle required for reasonable and fair democratic decision making.” Segal and Spaeth (1993: 62)
Political Science “Unfortunately, as Arrow has demonstrated, no method of decision
(short of a dictator) can guarantee the aggregation of citizen preferences transitively under all preference configurations, even if each citizens preferences are transitive.” (Jones 1994: 85)
Interpretations
Arrow – Nothing will work?
McKelvey – Chaos? Anything can happen?
Both interpretations are overstated.
Lupia and McCubbins (2005)
M. Social Choice Theory results are used in politics & law. But is their application consistent with the mathematics?
NH. Collective intent & majority will are vacuous.
P. The validity of current claims depend on what Arrow proved. SCT does not allow resource or cognitive limits.
C. Important aspects of social choice theory are “lost in translation.”
Arrow’s Claim
C: Given sufficient individuals and alternatives, there is no CCR for which conditions CUPID can hold simultaneously.
But one of these conditions is universal domain. This fact allowed the proof to be relatively short.
What Arrow Proved
Arrow proved that for every CCR there exists a preference profile for which conditions CPID cannot hold simultaneously.
He did not prove the same result for all preference profiles.
Therefore, for any CCR, Arrow’s Theorem allows CPID to be satisfied for up to P-1 preference profiles, with P possibly large.
Implications
Arrow did not prove that transitive collective preferences are impossible.
Arrow did not prove that achieving transitive collective preferences requires a dictator.
If you insist on universal domain, all but one of the others can be satisfied simultaneously.
Main Implication: If you want to understand collective choice when individuals have different preferences, institutions matter.
A Debate About the Meaning of ChoiceRiker: [P]olitics is the dismal
science because we have learned from it that there are no fundamental equilibria to predict. In the absence of such equilibria, we cannot know much about the future at all.
Disequilibrium “is the characteristic feature of politics.”
Shepsle; Shepsle and Weingast
“institutional structure … has an important independent impact on the existence of equilibrium”
Q: “Why so much stability?”
A: “Institutional arrangements do it.”
Riker’s Response
Institutions are no more than rules and rules are themselves the product of social decisions. Consequently, the rules are also not in equilibrium.”
The claim “Institutional arrangements do it” begs, rather than answers, the question “Why so much stability?”
Our Response
Seek N/S conditions for stability.
The roots of stability are found in: the requirements for collective action systematic and universal limits on human energy, cognition, and
communicative ability.
Stability is likely for many important collective choices.
What is Stability? A collective choice w is stable if and only if, holding S, R, and the
CCR constant, w has an empty win set. Example 1: Stability
1 2 3y y zz z yx x x
Example 2: Instability 1 2 3
y z xz x yx y z
The Problem
Two assumptions “stack the deck” in favor of finding instability in SCT’s.
There is no scarcity. Scarcity makes holding another vote or implementing a new
policy costly.
There is no complexity. Complexity makes people uncertain about the consequences of
change.
Add Scarcity and Complexity
Decision making is costly, like using a machine. What is the cost to individual i of using a collective choice rule? Maintaining the status quo, q, does not require use of the CCR.
Implementation is costly. What is the cost to individual i of implementing alternative x instead of the
status quo q.
Information asymmetries can make persuasion difficult and change prohibitive. Consider: The way things are versus how they might be.
Conclusion
Why do we observe so much stability? Collective action is not trivial. Complexity and scarcity are ubiquitous.
Implications
Instability results identify a bounded set of universal claims that are not logically valid. These results do not rule out all conditional claims about the
relationship between preference and choice.
SCT does not clarify institutional dynamics in the presence of potentially adaptive actors with resource and information limits. A different formal modeling approach – non-cooperative game
theory -- is needed.
Formal Models of Institutions
Allow precision Assumptions. Conclusions. Their relation.
Main topics How (exogenous) institutional variations affect choice or policy outcomes. Choice of institutions.
Provide a potentially powerful platform for empirical work. Theory need not precede empirics, but when it does it can help you be more
effective in using data to evaluate causal hypotheses.