voter turnout with postal voting

DOI: 10.1111/j.1752-5209.2009.0031.x

Voter Turnout with Postal VotingDaniel Solomon1

Somerville College, Oxford University

Abstract: This article presents a theoretical model of how electoral turnoutmight be affected by a move towards allowing citizens to cast their vote throughpostal votes only. The effect on turnout is compared with a system wherecitizens may vote by going to the polling place only. If part of the incentive tovote comes from signalling that one is the type of person who does vote, a goodcitizen, then the effect of a change to the electoral system might be ambiguous.Under certain circumstances turnout would fall with a move to postal voting.

Introduction

Recently, the governments of some demo-cratic constituencies have instituted a voting-procedure whereby all members of the franchise,if they choose to vote, can only vote by postalballot. This will be referred to as the OnlyPostal Voting (OP) rule.2 In several democraticconstituencies, the OP rule has entirely replaceda more traditional voting-procedure whereby allmembers of the franchise, if they chose to vote,could only vote by going to the polling-place inperson. This voting-mechanism will be referredto as the No Postal Voting (NP) rule. Examplesof such constituencies include: the state of Ore-gon (for all elections), New Zealand (for localelections) and the State of Washington (in 37 ofthe 39 counties for all elections).3

The paper’s primary motivation is to formu-late a theoretical model which examines whyvoter turnout might increase, decrease, or beunaffected by a switch from NP to OP. This mo-tivation arose from the fact that very little of theexisting literature examining the effect of postal-voting upon turnout, has conducted analysisfrom a formal economic modelling perspective.Instead, most of the literature has focused onstatistical analysis.4 Additionally, very little ofthe literature exclusively examines the effect, of

a switch from the NP to OP rule, upon turnout.5

Most of the literature looks at the effect uponturnout of mixed voting systems: wherein bothpolling-place and postal-voting are possible inthe same election. An analysis of these mixedvoting systems is not undertaken by the model.However, such voting systems are discussed.

This paper’s model is based upon Downs’s1957 ‘Calculus of Voting’ model, which mod-elled for the expected utility a member of thefranchise receives from voting for their preferredcandidate, or abstaining, in an election betweenher preferred candidate and her strictly non-preferred candidate. This paper takes ‘turnout’,for a given election, to be the proportion of thefranchise which votes, in that election. The ‘fran-chise’ is taken to be the body of registered votersas opposed to those citizens who are simply ofvoting age.

This paper assumes that a switch from theNP to OP rule will strictly lower the costs, tothe individual franchise member, of voting. Thispaper also assumes that there is a social normbenefit, to the individual franchise member, as-sociated with voting. This is a benefit to theindividual franchise member, from being pub-licly known to have voted at the polling-place.This paper assumes that the social norm benefit,

[email protected] OP rule is assumed to cover all voting-procedures wherein all members of the franchise may choose to vote,

but do not have the option of doing so by physically going to a polling-place. Typically, this covers: postal voting,internet voting, or some mixture of the two.

3The two exceptions are King and Pierce counties, wherein franchise members may vote by post or by going tothe polling-place in person.

4See Magleby (1987); Hamilton (1988); Luechinger et al. (2006).5The effect of a switch from the NP to OP rule upon turnout is examined by Karp (2000).

42 Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics SocietyPublished by Wiley-Blackwell

Voter Turnout with Postal Voting Daniel Solomon

which existed under the NP rule, is absent underthe OP rule.

If the individual franchise member votes un-der the NP rule, then they must go to the pollingplace in person. This action, under the NP rule,allows the individual franchise member to signaltheir type. This signal is a test which reliablyreveals (the individual franchise member’s) type.This paper assumes that by going to the polling-place in person the individual franchise memberis able to signal that she is the ‘type’ of personwho has adhered to a social norm of voting. Iassume that this, ceteris paribus, increases herexpected utility from voting.

The social norm signalling benefit is assumedto arise because a franchise member gains pos-itive utility from being publicly seen to be the‘type’ of person who votes. The source of thisincreased utility from signalling is unimportantfrom the perspective of this model, the impor-tant thing is that it exists. It might be thatsending this signal indicates publicly that thefranchise member is a ‘good citizen’ who is con-cerned with upholding the public welfare and thestate’s democratic institutions. Of course, thishypothesis about the provenance of the socialnorm signalling benefit of voting at the polling-place in person cannot be tested. The mostimportant thing for this model is that her ex-pected utility is increased by producing the sig-nal, ceteris paribus. How her expected utility isincreased by producing the signal is not impor-tant.

Ultimately, a switch from the NP to OP rulemay ceteris paribus: decrease turnout, increaseturnout, or leave turnout unchanged. The con-sequence of a switch, upon turnout, dependsupon the relative sizes of the decreased costsassociated with voting under the OP rule, com-pared to the decreased benefits associated withno longer being able to signal. Anecdotally, gov-ernments, when instituting a switch from theNP to OP rule, have claimed that such a switchwould inevitably increase voter turnout. Thispaper indicates that this is not necessarily thecase.

The paper then briefly looks at the historicaleffect of a switch from the NP to OP rule. Itlooks at US presidential elections, in the stateof Oregon, to see whether the move from NP

to OP was correlated with decreased turnout,increased turnout or no change in turnout.

Distribution of franchise members un-der the NP rule

Under the NP rule there are assumed to be nfranchise members. All n members of the fran-chise are assumed to be discretely and evenlydistributed at points on a straight line. Thisdistribution reflects the net expected utility, foreach franchise member, from the act of votingat the polling-place (under the NP rule). All nmembers of the franchise are assumed to be ho-mogenous apart from the different net expectedutilities they receive from voting at the polling-place.

- The franchise member at the top-end ofthe distribution, is called T, and receivesthe highest expected utility from votingat the polling-place, αNP .

- The franchise member at the bottom-endof the distribution, is called B, and receivesthe lowest expected utility from voting atthe polling-place, γNP .

- The median franchise member (with re-gard to her expected utility from voting atthe polling-place) is citizen X, she receivesan expected utility of βNP from voting atthe polling-place. (See Figure 1).

αNP is positive and γNP is negative. βNP maybe positive or negative. These signs for αNP ,βNP and γNP imply that at least one memberof the franchise votes and at least one abstains.This accounts for the empirical fact that in mostNP rule elections some members of the franchisevote while others abstain.

Figure 1: Although βNP > 0 has been depicted, this is not

necessarily the case and βNP < 0 is also possible

A franchise member only votes if her net ex-

Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics Society 43

Daniel Solomon Voter Turnout with Postal Voting

pected utility from voting is positive.6 There-fore:

1. All franchise members who receive ex-pected utility from voting at the polling-place: EU , where αNP ≥ EU ≥ 0, vote.

2. All franchise members who receive ex-pected utility from voting at the polling-place: EU , where 0 > EU > γNP don’tvote.

Distribution of franchise members underthe NP and OP rules

It is assumed that under both the NP and OPrules, the number of franchise members will re-main constant. Additionally, their utility func-tions will not change. Finally, the absolute dif-ference between franchise members’ expectedutilities from voting under both the NP and OPrules is assumed to remain constant:

a = αNP − βNP = αOP − βOP ,

a = βNP − γNP = βOP − γOP ,(2)

where: αOP is T’s expected utility from votingunder the OP rule; βOP is X’s expected utilityfrom voting under the OP rule; and γOP is B’sexpected utility from voting under the OP rule.

- Franchise member B will always have thelowest expected utility from voting (bothunder the NP and OP rules);

- franchise member T will always have thehighest expected utility from voting (un-der both rules); and

- franchise member Citizen X will alwayshave the median expected utility from vot-ing (under both rules).

Citizen X’s expected utility from voting un-der the NP and OP rules

Therefore, the effect on the proportion of thefranchise which votes, as a result of the govern-ment’s switch of the voting procedure from the

NP to OP rule, can be determined by observ-ing the effect the switch has upon X’s expectedutility from voting.

- If the switch increases citizen X’s expectedutility from voting, then the proportion ofthe franchise which votes after the switchwill be greater than the proportion whichvoted before it.

- If the switch decreases citizen X’s expectedutility from voting, then the proportion ofthe franchise which votes after the switchwill be smaller than the proportion whichvoted before it.

- If the switch does not alter citizen X’sexpected utility from voting, then the pro-portion of the franchise which votes afterthe switch will be the same as the propor-tion which voted before it.

Table 1: Possible outcomes of an election where X votes.

State Electoral outcome for X’spreferred candidate assum-ing X votes

Probability

s1 Wins by more than one vote p1

s2 Wins by exactly one vote p2

s3 Ties with his nearest rival p3

s4 Loses by exactly one vote p4

s5 Loses by more than onevote

p5

Citizen X’s expected utility from votingunder the NP rule

Assume that there is an election between twoheterogeneous contestants. Citizen X can takeone of two mutually-exclusive actions: V - votedeterministically for her strictly preferred can-didate (under the NP rule); or A - abstain.

Each of the states of the world listed in Ta-ble 1 may occur after the election. Prior to theelection Citizen X is aware of the probabilitiespi that state of the world i will occur where∑5

i=1 pi = 1.6Under the NP rule, we assume the franchise member whose expected utility from voting is zero votes. This

condition is not crucial to the analysis.

44 Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics Society


Under the NP rule, X’s expected utility fromvoting is

βNP = (p1 + p2 + p3 +p4

2)b+ r + s− C , (3)

where:

- b is the net benefit of X’s preferred candi-date gaining office, and X’s non-preferredcandidate not gaining office. This occursin s1 through s3, if X makes decision V.

- C is the cost - in terms of time, effort,etc.—to X of going to the polling place.

- r is the benefit X derives from the act ofvoting per se.7

- s is the benefit X derives from going tothe polling-place in person. This actionis what allows her to signal her ‘type’ asthe ‘type’ of person who has voted in thatparticular election.

Under the NP rule, X will choose to vote pro-vided that

EUNPX (V ) ≥ EUNPX (A) , (4)

where: EUNPX (A) = (p1 + p2 + p32 )b. So the

inequality above is equivalent to

(p3 + p4)b2

− C + r + s ≥ 0 , (5)

where p3 denotes the probability of state s3 (X’svote breaks an electoral tie) occurring; p4 de-notes the probability of state s4 (X’s vote makesan electoral tie) occurring. Intuitively, bothprobabilities may be set approximately equal to0.8 As such:

bp3

2≈ bp4

2≈ 0 . (6)

Therefore under the NP rule, X will choose tovote provided that: C < r + s.

citizen X’s expected utility from voting un-der the OP rule

Assume that there is an election between twoheterogeneous contestants. Citizen X can takeone of two mutually-exclusive actions: V–votefor her strictly preferred candidate (under theOP rule); or A–abstain.

Under the OP rule, X’s expected utility fromvoting is

EUOPX (V ) = βOP , (7)

where

βOP = (p1 + p2 + p3 +p4

2)b+ r − c , (8)

and c is the cost—in terms of time, effort etc.–toX of casting her postal-vote under the OP rule.Intuitively, the costs to X of casting her postal-vote c are strictly less than the costs she incursfrom going to the polling-place to vote underthe NP rule C: C > c > 0. Under the OP rule,X derives no social norm signalling benefit fromgoing to the polling-place in person so there isno benefit s.

Under the OP rule, X will choose to voteprovided that:

EUOPX (V ) ≥ EUOPX (A) , (9)

where: EUOPX (A) = (p1 + p2 + p32 )b. The in-

equality in 9 is therefore equivalent to

(p3 + p4)b2

− c+ r ≥ 0 , (10)

where as previously

bp3

2≈ bp4

2≈ 0 .

Under the OP rule, X will choose to vote pro-vided that: c < r.

7This is the element of the utility derived from voting that we take to be heterogeneous among the members ofthe franchise.

8In the most closely-contested US presidential election of the last century, President Kennedy defeated PresidentNixon by 49.72 per cent to 49.55 per cent of the votes cast. Nevertheless, the candidates were separated by 114,637votes. This demonstrates that, especially for large constituencies, even in the most closely-contested elections, theprobability that a single vote will make or break an electoral tie is approximately 0.



Result 1: When voter turnout increases

Suppose a switch from the NP to OP rulehas resulted in a strict increase in X’s ex-pected utility from voting: C − c > sand, EUOPX (V ) − EUOPX (A) is greater thanEUNPX (V ) − EUNPX (A). Then turnout willstrictly increase as a result of the switch giventhe franchise member distribution specifiedabove.

The positioning of voters when C − c > s

Result 2: When voter turnout decreases

Suppose C − c < s and that EUOPX (V ) −EUOPX (A) is strictly smaller than EUNPX (V )−EUNPX (A). In this case the switch from the NPto OP rule can resulted in a strict decrease inX’s expected utility from voting, and given theassumed franchise member distribution (sections2.1 and 2.2), a switch from the NP to OP rulestrictly decreases the proportion of the franchisewhich votes. (Fig 3)

The positioning of voters when C − c < s

Result 3: When voter turnout does notchange

Suppose C − c = s, and EUOPX (V )− EUOPX (A)is equal to EUNPX (V )−EUNPX (A). In this case,the government’s switch from the NP to OP ruledoes not altered X’s expected utility from votingand the turnout will not change as a result ofthe switch. (Fig 4)

The positioning of voters when C − c = s

Conclusions of the model

The theoretical model has shown the circum-stances in which, ceteris paribus, the effect uponvoter turnout of a switch from the NP rule tothe OP rule increases or decreases turnout, orleaves it unchanged. The model demonstratedthat the consequence of a switch, upon turnout,depends upon the relative sizes of the decreasein costs associated with voting under the OPrule, C − c, compared to the decreased benefitsassociated with no longer being able to signal,s. Anecdotally, governments, when institutinga switch from the NP to OP rule, have claimedthat such a switch would inevitably increasevoter turnout. The model indicates that thisclaim doesn’t necessarily hold true because it isnot necessarily the case that C − c > s.

It would be very difficult to test this modelagainst actual data on turnout in elections. Thedifficulty occurs for two reasons.

- Firstly, there are relatively few instances ofconstituencies switching from exclusivelyNP rule voting-procedures to exclusivelyOP rule voting-procedures.

- Secondly, in all the cases where such aswitch has occurred, it is (nearly) impos-sible to completely control for the effectthat other factors (political, social etc)may have had upon turnout. Therefore,it is (nearly) impossible to examine theeffect that a switch from the NP to OPrule—alone—has had on voter turnout.

The paper now considers potential shortcomingsof the model. The paper then concludes by ex-amining empirical data on turnout in the stateof Oregon before and after a switch from the NPto OP rule. A rigorous econometric examinationis beyond the scope of this paper.



Limitations of the model

Three potential criticisms of the model are:

- The paper only models for the compara-tively rare scenario whereby the govern-ment has switched the voting-procedurefrom purely the NP rule to purely the OPrule. A switch to some mixed voting ruleis more common.

- The social norm signalling benefit, s, thata citizen gets from voting at the polling-place in person has been treated as exoge-nous.

- The model assumes that OP rule electionsare certainly associated with higher costs(for voters) than NP rule elections.

Switching to mixed voting

The model assumed that government switchesthe voting-procedure in a given constituencyfrom purely the NP rule to purely the OP rule.The paper made this assumption in order tomodel for cases wherein this exact type of switchhas occurred. This exact type of switch is com-paratively rare amongst democratic constituen-cies, although examples of it do exist. The modeldid not analyze the far more common scenariowhereby government has switched from the NPrule to some mixed voting rule.

Under a mixed voting rule each member ofthe franchise, if she chooses to vote, can voteeither at the polling-place in person or by postalballot. The precise regulations for mixed votingrules vary widely between democratic constituen-cies.9 The most general case of a mixed votingrule is one wherein each member of the fran-chise, if she chooses to vote, may vote eitherat the polling-place or by postal ballot withoutnotifying government of any preference, medicalcondition etc.

For this type of mixed voting rule the modelwould predict weakly higher turnout than eitherthe NP rule or the OP rule. This is because, forall franchise members, having both voting op-tions available is weakly better than only havingone option available.

The nature of the signalling benefit

The model treated the value of the social normsignalling variable, s, as exogenous. More thor-ough consideration of s would be worthwhileas it might increase the utility of the model ifwe could say something ex ante about whichcommunities were likely to exhibit high or lowsignalling benefits from voting.

It is reasonable to assume that the value ofs is a decreasing function of the franchise size.If X lives in a small franchise, when she goes tothe polling-place to vote in person she will senda signal to a larger proportion of the franchisethat she is the ‘type’ of person who votes thanif she lives in a large franchise. It follows thata switch to an OP rule voting-system becomesmore likely to increase turnout as the franchisegrows larger. This is because as the franchisegrows larger, the value of s decreases while thecost of going to the polling-place to vote, C,does not.

It is also reasonable to argue that the valueof s depends upon the turnout which X expects.The utility of signalling that you are the ‘type’ ofperson who votes may well depend on how manyother people make the same signal. However,this could go in two directions.

- It could be that signalling benefits are de-rived by demonstrating that you are partof a voting majority, in which case higherexpected turnout will lead to increasedturnout. Here the benefit comes from sig-nalling homogeneity.

- Conversely, it could be that signalling ben-efits are derived from demonstrating thatone is part of a decent minority who per-forms their civic duty, in which case lowerturnout would increase the incentive tovote. Here the benefit comes from sig-nalling one’s difference.

The assumption that postal voting ischeaper for the voter

The voting-procedure rule selected may itselfaffect X’s costs and benefits associated with vot-ing and so affect turnout. Empirical evidence

9See Patterson and Caldeira (1985); Magleby (1987); White (2004, 2008).



suggests that there is a higher risk of fraud as-sociated with the OP rule than with the NPrule (Gronke, 2005). This higher risk of fraudmay encourage governments to institute high-security procedures for registering voters for OPrule elections. Less stringent security proceduresmay be employed for NP rule elections.

High-security OP rule registration proce-dures may be associated with higher costs - forprospective voters - than NP rule registrationprocedures. If this is the case, then OP ruleelections may cause voters to incur costs whichare greater than or equal to those of NP ruleelections. This argument challenges the model’sassumption that OP rule elections are necessar-ily associated with lower costs (for voters) thanNP rule elections.

These three potential criticisms have exam-ined possible flaws in the model. While thesediscussions do not reach definite conclusions,they may serve as suggestions for improving themodel and for the direction of future researchon these issues.

Evidence from Oregon

Prior to (and including) 1981, all elections inthe state of Oregon were conducted under theNP rule. After 3rd November 1998, all electionsin the state of Oregon were conducted under theOP rule.10 Has the switch from the NP to OPrule, for US presidential elections, in the state ofOregon, been correlated with decreased turnout,increased turnout or no change in turnout? Thisanalysis is purely suggestive and is not meantto constitute a rigorous econometric analysis.

The examination finds that turnout wasstrictly higher in US presidential elections, inthe state of Oregon, under the OP rule thanunder the NP rule. However, the increase inturnout was quite small. For the elections in1976 and 1980 average turnout was 76.4 per cent.For elections in 2000 and 2004 average turnoutwas 82.15 per cent. Therefore, per election, theswitch, in Oregon, from the NP to OP rule,has correlated with a 5.75 per cent increase inturnout (see Table 2).

Table 2 shows that the percentage of theOregon franchise which voted in US presidential

elections was higher under both the electionsfor which the OP rule was Oregon’s sole voting-procedure than under either of the elections forwhich the NP rule was Oregon’s sole voting-procedure. This indicates that the switch fromthe NP to OP rule has caused a strict increasein the proportion of the Oregon franchise whichvoted in US presidential elections.

At least four potential criticisms can beraised against this analysis:

1. The available data set is very small. (Atthe time of writing) only two US presi-dential elections have taken place since allelections in Oregon have been conductedunder the OP rule.

2. It is difficult to control for the effect thatother factors (political, social etc) mayhave had upon the turnout figures in Ta-ble 1. Therefore, it is difficult to examinethe effect that Oregon’s NP rule to OP ruleswitch - alone - has had on voter turnout.

3. It is possible to observe a correlationbetween a switch in Oregon’s voting-procedure and increased turnout for USpresidential elections in 2000 and 2004 rel-ative to 1976 and 1980. However, it isimpossible to observe a causal relationshipbetween these occurrences. The small dataset makes causation even harder to iden-tify.

4. The data are not wholly supportive ofthe conclusion that the voting-procedureswitch from the NP to OP rule has evencorrelated with a strict increase in theproportion of the Oregon franchise whichvoted in US presidential elections. This isbecause of the interim period between theabolition of NP and the introduction ofOP, some elections in this period had evenhigher turnout than the elections underOP.

At first glance, the data suggest that, in thecase of turnout in Oregon for US presidentialelections, the switch from the NP to OP rulehas caused a strict increase in the proportion ofthe Oregon franchise which voted. However, theincrease in turnout was quite small–only 5.75

10http://sos.state.or.us/elections/vbm/history.html



per cent of the franchise. The criticisms abovecast doubt on the significance of these claims.

Admittedly, the general conclusion thatpostal voting does increase voter turnout hasbeen supported by statistical analysis in otherconstituencies. Luechinger et al. (2006) reportthat there is ‘robust evidence that the introduc-tion of unconditional postal voting increasesvoter turnout’, and that the ‘average effecton turnout (of instituting ‘voting by mail’) isroughly (an increase of) 4.1 per cent for an av-erage turnout of 43 per cent between 1970 and2005 (in Switzerland).’11 Karp (2000) writesthat ‘all-mail elections tend to produce higherturnout’. However, they hold that the effectupon turnout is demographically dependent,specifically ‘voting only by mail is likely to in-crease turnout among those with higher socioe-conomic status’.

This implies that the institution of ‘votingonly by mail’ , while it is likely to increase overallturnout, may not increase turnout for particulargroups in the franchise. This would cause only asmall increase in overall turnout. The main sta-tistical studies of the effect of the OP rule uponturnout suggest that it has increased turnout,but not by a particularly large proportion of thefranchise. This finding is consistent with themodel’s prediction when C − c > s.

Table 2: Turnout for US Presidential elections in Oregon.12

Year Electoral system Turnout13

2004 OP 85.8%

2000 OP 78.5%

1996 Mixed 70.2%

1992 Mixed 82.4%

1988 Mixed 78.6%

1984 Mixed 76.2%

1980 NP 75.3%

1976 NP 77.5%

ReferencesA, Downs (1957), An Economic Theory of Democ-

racy, Harper and Row, New York.

Gronke, Paul (2005), Ballot integrity and voting bymail: The Oregon experience. A Report for theCommision on Federal Election Reform.

Hamilton, Randy H. (1988), ‘American all-mail bal-loting: A decade’s experience’, Public Administra-tion Review 48(5), 860–866.

Karp, J.A. (2000), ‘Going postal: How all-mailelections influence turnout’, Political Behavior22(number), 223–239.

Luechinger, Simon, Myra Rosinger and Alois Stutzer(2006), The impact of postal voting on partici-pation, evidence for switzerland, IEW - WorkingPapers iewwp297, Institute for Empirical Researchin Economics - IEW.

Magleby, David B. (1987), ‘Participation in MailBallot Elections’, Political Research Quarterly40(1), 79–91.

Patterson, Samuel C. and Gregory A. Caldeira(1985), ‘Mailing in the vote: Correlates and conse-quences of absentee voting’, American Journal ofPolitical Science 29(4), 766–788.

White, Isobel (2004), All postal voting.

White, Isobel (2008), Postal voting and electoralfraud.

Daniel Solomon has recently completed a degreein PPE at Somerville College, Oxford. He is plan-ning on studying for a masters in economics nextyear.

11This is available from http://iew.uzh.ch/wp/iewwp297.pdf12Data collected from: http://uselectionatlas.org/RESULTS/index.html


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