why bother voting? the paradox of voter turnout.magranov/documents/turnoutlecture1.pdf ·...

Why bother voting? The paradox of voterturnout.

October 25, 2015

Downs (1957)

I What makes people decide to vote or not to vote?

I Calculus of voting

I simple model of rational choice proposed by Downs (1957)I instrumental voting model: an action has value only if it

affects outcomes

I A voter, in deciding whether to vote or abstain, calculates theexpected utility of either action and votes if benefits exceedcosts.

Downs (1957)

I Calculus of voting

I simple model of rational choice proposed by Downs (1957)I instrumental voting model: an action has value only if it

affects outcomes

Downs (1957)

I Calculus of votingI simple model of rational choice proposed by Downs (1957)

I instrumental voting model: an action has value only if itaffects outcomes

Downs (1957)

I Calculus of votingI simple model of rational choice proposed by Downs (1957)I instrumental voting model: an action has value only if it

affects outcomes

Downs (1957)

I Calculus of votingI simple model of rational choice proposed by Downs (1957)I instrumental voting model: an action has value only if it

affects outcomes

Downs (1957), cont...

R = P · B − C > 0

I The benefits from voting (P · B) have two elements:

I B is the difference in expected utilities from the policies of thetwo candidates that compete in the election.

I The benefits of the voting are weighed by the probability (P)that one’s vote influences the outcome.

I P is the prob of being pivotal (prob that a single vote forcandidate j will change the outcome in favor of j)

I P depends on the number of voters and the expected closenessof the elections (the probability of a tie is much higher if thereis only 1000 voters than if there is 100000 of them)

R = P · B − C > 0

I C -term refers to the costs of voting:

I opportunity costs: the time it takes to register, go to the poll,and mark the ballot

I costs incurred before the elections: gathering informationabout the candidates and their policy proposals in order todecide between candidates

I Thus, in an election with a large number of voters the rationalcitizen should not vote, since the cost of voting is positive andthe probability to influence the outcome is extremely small(P · B is close to zero).

Paradox of (not) voting

I But, we observe that many people do vote.

I In fact, a clear majority votes in the most important elections,where the number of voters is extremely large and theprobability of casting a decisive vote is minuscule.

I Although one cannot reject the possibility that some votersvote instrumentally, it appears highly implausible that thelevel of real turnout rates can be explained on instrumentalgrounds.

I This inconsistency between the theory and real-world turnoutrates is known as the ”paradox of (not) voting”.

Paul Krugman ”Stop Making Sense”

New York Times, November 5, 2002”It’s Election Day, and it’s your duty as a citizen to be irrational. Let me

explain. Political scientists will tell you that voting suffers from a severe

”free rider” problem. Even if it’s very important to you that Mr. A beat

Mr. B, your individual vote is very unlikely to decide the outcome. So

the sensible thing is not to bother voting. Yet if everyone acts on that

logic, Mr. B — the candidate backed by corrupt special interests, which

pay for his get-out-the-vote operation — sweeps into office. In other

words, even if the candidates in an election offer radically different

programs, and you have a strong preference for one over the other, a

narrow calculation of self-interest says that it’s not worth taking the

trouble to go to the polling booth. Yet democracy depends on your

ability to rise above that calculation. If citizens want good government,

they must do what they want others with the same concerns to do —

namely, vote... Go out there and vote — and tell everyone you know to

do the same. America’s future depends on your irrationality.”

Plan for today

I Discuss various theories that aim to understand why peoplechoose to participate in elections:

I Instrumental theories: the main motivation of voters is toaffect the outcome

I Expressive theories: the act of voting itself gives utility, whichcan depend on various factors (how other people vote,...)

I Boundedly rational voter theories: weaken the fullrationality assumptions on voters.

I Group based theories: if voters voted as a group they wouldbe more likely to affect the outcome. This co-ordination ishard to achieve but there are some evolutionary explanationsas well as the use of parties as co-ordinating mechanisms.

I Information based theories: use information asymmetriesbetween voters to explain which voters are more likely toparticipate

Plan for today

Instrumental voting models

I We will start with instrumental voting models, that suggestthat voters are strategic and choose to participate in theelections in part because they want to inlfuence the outcomeof the elections

I Within this broad category, there are two types of models:

I decision-theoretic models - concentrate on the incentives forthe individual to participate in the elections (Downs (1957),Riker-Ordeshook (1968) and Ferejohn-Fiorina (1974))

I game-theoretic models - claim that decision to vote shouldbe embedded within a game between voters (Ledyard (1984),Palfrey-Rosenthal (1983) and (1985))

Riker and Ordeshook (1968)

I To rescue the rational choice model, Riker and Ordeshook(1968) modify Downs’s model by suggesting that citizens canderive psychic gratifications from the act of voting

I the satisfaction of ”complying with the ethic of voting”I out of citizens duty

I In other words, voters may derive some benefits from the actof voting independent of the effect that the vote can possiblyhave on the outcome of the election.

I Voters may feel satisfaction or utility from fulfilling their”citizen duty” and participating in the democratic process.

I the satisfaction of ”complying with the ethic of voting”

I out of citizens duty

Riker and Ordeshook (1968), cont...

I Reformulate the original equation into:

R = P · B +D − C

where D stands for the benefit from expressing oneself, i.e.consumption benefits that the voter gets from the act ofvoting.

I The addition of ”consumption” benefits to the calculus ofvoting can explain positive turnout levels.

I However, it does so at a severe price:

I first, because it still holds that P, and thus P · B, is close tozero ⇒ R = D − C , which means that the turnout isessentially driven by reasons unrelated to the central elementof the democratic process, namely electing a government

I second, because the consumption benefits seems like ad hocassumption

R = P · B +D − C

Ferejohn and Fiorina (1974)

I Another attempt to rescue the rational model.

I Authors argue that we ought to distinguish betweendecision-making under risk and decision-making underuncertainty.

I under the risk, probabilities of different outcomes are knownand should be taken into account

I under the uncertainty, such probabilities are unknown and thusshould not affect one’s choices

I Ferejohn and Fiorina examine one specific procedure -minimax regret criterion, under which one calculates theloss associated with various outcomes without estimating theprobabilities of these outcomes and chooses the option thatminimizes regret.

Ferejohn and Fiorina, cont...

I The minimax regretter asks herself how much regret shewould have if, on the one hand, she voted and her vote wasnot decisive, and, on the other hand, she did not vote and herpreferred candidate lost by one vote. If the latter regret isgreater than the former, she decides to vote.

I Let’s talk about a citizen, who gets utility = 1 if candidate 1wins election and utility = 0 if candidate 2 wins. In case of atie the coin flipped determines the outcome and the citizenreceives utility of 1

I This citizen has voting cost c expressed in the same utilityscale and decides whether to vote for candidate 1 (action V1),vote for candidate 2 (action V2) or abstain (action A)

I The payoff of this citizen depends on the state of naturewhich accumulates the information about the actions of allother voters.

I Denote by ni the number of voters that voted for candidate iexcluding the citizen under consideration.

I There are five mutually exclusive and exhausive states ofnature

I S1 ⇔ n1 > n2 + 1: candidate 1 wins by more than one voteregardless of citizen’s vote

I S2 ⇔ n1 = n2 + 1: candidate 1 wins by exactly one votewithout citizen’s vote

I S3 ⇔ n1 = n2: candidate 1 ties with candidate 2 withoutcitizen’s vote

I S4 ⇔ n1 = n2 − 1: candidate 1 loses by exactly one votewithout citizen’s vote

I S5 ⇔ n1 < n2 − 1: candidate 1 loses by more than one votewithout citizen’s vote

I Recall that c represents the cost of voting.

I Then

Payoff matrix of the citizen

S1 S2 S3 S4 S5V1 1− c 1− c 1− c 1

2 − c −cV2 1− c 1

2 − c −c −c −cA 1 1 1

I Recall that c represents the cost of voting.

I Then

Payoff matrix of the citizen

S1 S2 S3 S4 S5V1 1− c 1− c 1− c 1

2 − c −cV2 1− c 1

2 − c −c −c −cA 1 1 1

I The regret is the difference between what the citizen couldhave obtained under Sj if he knew it would happen withcertainty and was able to choose the action that yieldedmaximum return and what he obtains by choosing ai .

I Assume that c < 12 , then we can define the regret matrix

Regret matrix of the citizen

S1 S2 S3 S4 S5V1 c c 0 0 c

V2 c 12 + c 1 1

A 0 0 12 − c 1

2 − c 0

I The regret is the difference between what the citizen couldhave obtained under Sj if he knew it would happen withcertainty and was able to choose the action that yieldedmaximum return and what he obtains by choosing ai .

I Assume that c < 12 , then we can define the regret matrix

Regret matrix of the citizen

S1 S2 S3 S4 S5V1 c c 0 0 c

V2 c 12 + c 1 1

A 0 0 12 − c 1

2 − c 0

I The minimax regret criterion specifies that the citizenshould choose the act which minimizes his maximum regret

I the maximum regret for V1 is c , for V2 is 1 and for A is 12 − c

I Clearly, V2 is not a viable strategy. The citizen would vote forhis preferred candidate 1 rather than abstain if

max regret from V1 < max regret from A⇔ c <1

I Ferejohn and Fiorina conclude by noting that in atwo-candidate plurality winner contest, a citizen following theminimax regret decision rule votes for his preferred candidaterather than abstains if the utility gain from the election of hispreferred candidate exceeds four times the utility loss of thevoting act.

Criticism of Ferejohn and Fiorina

I Even though it may be exceedingly difficult to calculate theexact value of P, it is easy for the rational citizen to figureout that in a large electorate it is minuscule.

I a rational voter is able to give a rough guess of what P is likelyto be, and use expected utility model to compute E (P ·B),which means we are back to the same paradox.

I The minimax-regret hypothesis implies that a turnout rateindependent of the closeness of the election (inconsistent withempirical evidence).

I The minimax regret strategy implies that the presence of anextremist candidate should substantially increase turnout nomatter what is the degree of support she enjoys:

I if there are 10 candidates running ⇒ the minimax regrettershould envisage the worst scenario (the candidate she like theleast wins), without taking into account her probability ofwinning, and vote if this regret outweighs the cots of voting

Game-theoretic approach

I Game-theoretic approach suggests that people should take thedecisions made by others into explicit account.

I The reasoning is as follows:

I If everybody votes, the chance of having an effect on theoutcome of the election is very small.

I Because this holds for everybody, it would be rational for all toabstain – in which case one vote becomes decisive.

I If everybody came to this conclusion, all would vote – onceagain making it useless to vote.

I This line of reasoning can be repeated eternally.I Hence, the probability of being decisive is not fixed and

determined – as assumed under the expected utility (Downsand Riker-Ordeshook models) and minimax regret model(Ferejohn-Fiorina model) – but is instead determined throughthe strategic interaction between all potential voters.

I In other words, P becomes endogenous to the model.I A voter does not face a decision theoretic problem, but rather

a strategic game with other voters.

I This line of reasoning can be repeated eternally.

I Hence, the probability of being decisive is not fixed anddetermined – as assumed under the expected utility (Downsand Riker-Ordeshook models) and minimax regret model(Ferejohn-Fiorina model) – but is instead determined throughthe strategic interaction between all potential voters.

I In other words, P becomes endogenous to the model.

I A voter does not face a decision theoretic problem, but rathera strategic game with other voters.

Ledyard (1984)

I Author argues that the decision to vote should be embeddedwithin a game.

I He looks at a model of a voting game in which voters mustchoose to vote for one of two candidates or else abstain.

I Voters only care about influencing the election outcome (noconsumption benefit to voting) and all voters have strictlypositive costs to vote.

I He also adds candidates as strategic actors and shows thatwhen the two candidates take distinct positions, there mustbe positive turnout in equilibrium. The reason is clear:

I if nobody is voting, then the probability that a vote is pivotalis large and everyone has an incentive to vote

I Ledyard does not characterize the magnitude of turnout whencandidates have distinct positions.

I Ledyard shows that, in large elections, candidates willconverge to the median voter position and turnout will go tozero.

Ledyard (1984)

Palfrey and Rosenthal (1983)

I Follow up on the Ledyard’s paper

I characterize the magnitude of turnout when candidatepositions are fixed and different

I Each voter must choose whether to cast a costly vote for hispreferred candidate or to abstain

I the costs to vote are identical for all voters

I There are two kinds of equilibria: low turnout and highturnout

I to generate high turnout in equilibrium, it is necessary togenerate a high probability of being pivotal

I that happens when there are nearly identical numbers of voterssupporting each candidate (2 million voters support eachcandidate)

I a low turnout equilibrium is sustained by having supporters ofeach candidate randomize between turning out to support theircandidate with low probability and abstaining; this results inlow pivot probabilities

I When the uncertainty is introduced into the previous model,high turnout equilibria disappears.

I Assume that each voter i has a cost to vote ci ∈ [0, 1] and acandidate preference j ∈ {1, 2}.

I for any given cost to vote c , the actual number of voters withci ≤ c is a random variable

I Authors find symmetric Bayesian equilibria characterized bytwo cost points c1 and c2, such that all voters who prefercandidate j and whose cost is below cj vote for candidate j ,while all others abstain.

I As the size of the electorate gets large, the equilibrium costcutpoints converge to zero and turnout converges to zero.

I The introduction of uncertainty ensures that even if theexpected number of votes for each candidate is the same, asthe expected number of votes gets large, the probability theelection results in an exact tie goes to zero.

Botton line from Palfrey and Rosenthal (1985)

I Ultimately, the game-theoretic approach to costly voting triedto escape the paradox of not voting by showing that inequilibrium, election outcomes would be close and pivotprobabilities higher than in the decision theoretic literature.

I But the introduction of uncertainty about the actual numberof voters guarantees that even if elections are expected to beclose, the probability a vote is pivotal will be very low andturnout should be near zero.

I Palfrey and Rosenthal (1985): ”In the presence of a relativelysmall degree of strategic uncertainty... voters with positive netvoting costs will abstain.”

Schuessler ”A logic of expressive choice” (2000)

I Schuessler argues that political participation is not basedsolely on instrumental rewards.

I Instead, people receive expressive benefits from voting andother forms of political participation, such as the ability toassociate themselves with a particular party or candidate.

I Schuessler develops a formal model for explaining andpredicting expressive participation

I he further argues that campaign strategists recognize theexpressive benefits of voting today, and focus increasingly onthe symbols associated with voting for a particular candidateor party.

I According to Schuessler’s theory, a person voting in the 2000election may have been more concerned with being associatedwith the Republican, Democrati or Green parties, or theirrespective candidates, than with the election’s outcome.

I voting has a certain status attached to it, like drinking a typeof soda or driving a type of car.

Schuessler, cont...

I Schuessler helps to explains how campaigns in the U.S. havechanged over the past forty years with the introduction ofmarketing technologies.

I He makes a parallel between the marketing of soft drinks andmarketing political candidates

I Since the mid-twentieth century, the competition betweenPepsi and Coca-Cola was based more on lifestyle and imagethan on the price or quality of the products. For instance,Pepsi marketed its product to the ”Pepsi Generation,”suggesting that those who drank Pepsi were young and moremodern. However, Pepsi marketers didn’t directly claim thatPepsi drinkers were young; they wanted the actualdemographics of their consumers to remain ambiguous, toattract as many consumers as possible. With this style ofmarketing, soft drink choice had become a lifestyle choice.

Schuessler, cont...

I Campaign strategists have developed similar techniques toattract voters to certain candidates and voters. Campaignmottos, like Reagan’s ”It’s Morning Again in America,” orClinton’s ”Building a Bridge to the Twenty-First Century,” areprime examples of ambiguous ”feel-good” expressive messages.The messages were not urging people to vote for Reagan orClinton because of specific policy choices, but because theywould feel good about voting for them, and being associatedwith them. Indeed, most campaign mottos from recentelections focus more on symbols and feelings than on policychoices.

Group-based Models

I The Aristotelian idea that man is a social animal has led anumber of scholars to look at social networks to explainturnout at the polls.

I The argument is that voting might be rational for a group ofindividuals because the expected benefits may exceed thevoting costs at the group level (see Filer et al. (1993) andGrossman and Helpman (2001)).

I First, groups are likely to have larger benefits than individualsfrom political participation.

I The reason is that politicians may provide groups with extrabenefits – in terms of policies that come closer to the group’soptimum – to win the support of the group (Lapp, 1999).

I Second, as the political influence of a social group can beassumed to be proportional to its size (Schram and VanWinden, 1991), the group as a whole is more likely to have anon-negligible impact on the election outcome.

Group-based Models

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