# Polls and voter turnout

The 2020 US presidential electoral results that are streaming in yet again undermine the accuracy of pollsters. Inaccurate predictions made by polls, of course, raise an important line of causal inquiry into their inaccuracy. Polls may be inaccurate because of unrepresentative samples, because of a social desirability bias (that manifested rather prominently in polls conducted prior to the 2016 US presidential elections), because of incorrect estimations of voter turnout, because the publication of poll results change how voters vote due to reasons such as strategic voting, or because, as the paper I describe in this post suggests, polls change voters’ incentives to vote.

It should be noted that the last three reasons are substantively, and not just semantically, different. In regard to the third reason, polling agencies can overestimate voter turnout in a way that results in inaccurate predictions that has nothing to do with the poll itself changing turnout. For example, it may rain on Election Day in places that lean blue such that voters don’t turn out to vote. This would result in an inaccurate prediction of the Democratic lead based on a misapprehension of the voter turnout, but not be a consequence of the publication of polls. The fourth reason considers that poll results may change the behaviour or the strategies of rational voters and cause them to do things like vote for a candidate other than their most preferred option (in order to avoid the electoral victory of their least preferred candidate) if they realise that it is unlikely that their most preferred candidate wins, or choose to vote for the candidate they perceive will win the election so they will be on the “winning team” in the end (the bandwagon effect). Essentially, it pertains to how the publication of electoral polls may alter voters’ choices when they turn out to vote. The fifth reason refers very specifically to how poll results themselves may change people’s incentives to show up to vote in the first place. An example of this may be found in how voter complacency due to Clinton’s strong polling was deemed to be a big threat to a Democrat win in several states during her campaign, and culminated in an eventual electoral upset.

I’ve previously written about an experimental paper in which it was found that the publication of poll results affects participation in elections (here), and the paper in particular finds that the magnitude of the underdog effect (turning out to support of the candidate who is predicted to lose) is more pronounced as poll leads are larger, and the magnitude of the bandwagon effect (described above) is more pronounced for closer predictions of outcomes. It also finds that publishing poll results increases turnout. This post is a lengthier and more comprehensive discussion of how poll results may affect voter turnout, given that the previous post was a very short summary of a paper. It also summarises two very recent papers and their contradictory findings on how the perceived closeness of elections affects turnout.

But before I go into the papers and their findings, why is it important to investigate whether the publication of poll results affects voter turnout? First, establishing a causal relationship between poll results and voter turnout would be germane to an assessment of whether we should publish the results of polls. If voter participation rates are reduced by the publication of polls, and information on poll results has varying effects on the willingness to turn out to vote of different groups of voters, the publication of poll results could result in electoral outcomes that do not match the actual political preferences of the electorate.

Background

I have described the pivotal voter model in the rational voter paradigm very briefly in the previous post here, but the prior explanation offered was quite incomplete, so I go into greater depth here based on my understanding of it.

Decision-theoretic models put forth that the expected benefit from voting must be larger than the expected cost of voting for people to vote. In this case, the expected cost of casting a vote includes things like having to show up at the voting booth, pay cuts due to having to take time off from work, or in the case of mail-in voters for the most recent US presidential election, the cost of having to request and mail out their ballots. All of these costs are certain costs to the voter at the point at which they are deciding whether or not to vote, and therefore the expected cost is probability of cost = 1 multiplied by cost $c$, expressed as $c$. However, at the point of deciding to participate in an election, voters have incomplete information on who else will be voting, and what their preferences are. Therefore, the expected benefit of voting is expressed as $pB$ (the probability that one vote is decisive multiplied by the increase in utility to voters from casting the decisive vote). It follows that rational voters will vote if $pB > c$, and they won’t vote if $pB < c$.

There is a core problem with this decision-theoretic model. The prediction that follows from the model is that where there are many voters voting, the probability of each voter being decisive is extremely small, such that voter turnout will be low. However, if voter turnout is expected to be low, then the probability of being pivotal increases, therefore it is rational for voters to choose to vote. Therefore, for rational voters, the decision to participate in elections and the probability of being pivotal should be simultaneously determined.

The pivotal voter game-theoretic model put forth by Thomas Palfrey and Howard Rosenthal (1983) in “A Strategic Calculus of Voting” introduces a team game approach in which they model this simultaneity, but also uniquely contribute multiple symmetric and asymmetric equilibria. Team games model the tension between wanting to vote so your preferred outcome materialises, but also wanting to free-ride on the other players in your team and not vote because you perceive that your preferred outcome will materialise anyway. Palfrey and Rosenthal (1983) find, among other conclusions, that because majorities have much stronger incentive to free-ride on the votes of others in their group than minorities, minorities are more likely to vote. Turnout is strongly correlated with the relative sizes of the majorities and minorities.

This is obviously relevant to a discussion about how poll results affect turnout, because if you expect to be in the overwhelming majority from viewing poll results that indicate your preferred candidate has a strong lead, you have a stronger incentive to free-ride on the votes of others. The closer you perceive an election to be, the stronger you believe that your vote might be pivotal and the weaker your belief that you may obtain your preferred outcome while free-riding on the voters with the same political affiliation as you and not voting. The following two papers discuss how the anticipated closeness of elections from beliefs generated by the results of electoral polls affects voter turnout.

Leonardo Bursztyn, Davide Cantoni, Patricia Funk, Felix Schönenberger, and Noam Yuchtman (NBER Working Paper Series). “Identifying the Effect of Election Closeness on Voter Turnout: Evidence from Swiss Referenda.”

Introduction

Leonardo Bursztyn, Davide Cantoni, Patricia Funk, Felix Schönenberger, and Noam Yuchtman find evidence of a causal effect of expected closeness of elections on voter turnout in the context of Swiss referenda. It is important to note the institutional context here: every Swiss citizen of at least 18 years of age receives voting documents by regular mail at home, and then can choose to either cast their ballot at the polling booth on election day, or vote early through standard mail, through voting online, or through bringing a ballot personally to the closest electoral office. This institutional context means that there is some variation in when votes are cast, allowing the authors to examine the pre-trends and post-trends that are discussed below.

The quasi-experimental study conducted here controls for some confounding factors through which the closeness of elections might increase turnout to measure the direct impact of results of electoral polls on turnout. For instance, if a close and hotly contested election is associated with more political reporting, the higher amount of media coverage might increase turnout due to the salience of the election in the minds of the people. The closeness of the election is also obviously associated with close poll results. An observational study that does not control for this factor may conclude that close electoral results increase turnout, while the actual causal mechanism through which turnout is increased is increased political reporting due to the closeness of the election itself.

This paper excludes the causal mechanism of increased political reporting through two ways. First, from examining pre-trends in daily mail-in votes prior to the publication of close electoral polls, the authors find that there is little difference in turnout rates between referenda where polls indicated close elections and referenda where polls did not indicate close elections prior to the publication of close polls. This suggests that political reporting was not differentially active. Second, through counting the number of political advertisements before and after the publication of a close poll, the authors find that while close poll results do increase political reporting, this increase in political reporting occurs three days after poll release, and therefore cannot account for the increase in turnout in the first three days after poll release.

In order to examine the effect of poll release and the closeness of polls on Swiss voter turnout, the authors exploit variation in the day of poll release. Political polls in Switzerland are conducted by gfs.bern, a market and opinion research institute. Two rounds of polling are conducted: the first poll is released 5 weeks before any voting can take place. The second poll is released, on average, 11 days before election day, but out of the 52 polls examined, 2 were released 16 days before the voting date, 1 poll 13 days before, 2 polls 12 days before, 44 polls 11 days before, and 3 polls 10 days before.

Identification and Results

The authors use the following event-study specification:

$turnout_{vd} = \sum_{d} \beta_{d} Close_{v} + \alpha_{v} + \gamma_{d} + \epsilon_{vd}$

$\alpha_{v}$ and $\gamma_{d}$ account for vote and day-to-poll fixed effects. The sequence of $\beta_{d}$ in particular gives us information on how the closeness of a poll affects turnout in the days before and after the release of a close poll. From their empirical study, the authors find that there is no difference in turnout rates depending on the closeness of the poll that is to be released in the days preceding poll release, but on the first three days after poll release, voter turnouts are significantly higher by about 0.4 percentage points for a closer poll.

The authors further test two auxiliary predictions about i) the importance of polls in providing information on election closeness to voters (in the absence of which voters would have to rely on approximating election closeness from sampling locally among their friends and neighbours), which may not be representative, and ii) the impact of heterogeneity in poll results reporting on voter turnout. These predictions correspond to two hypotheses:

First, voters living in municipalities that are not representative of the political preferences of the larger electorate would rely more heavily on the information provided to them by polls to approximate the closeness of elections, since their own approximations are more likely to be unreliable. Therefore, in municipalities that are more politically unrepresentative of Switzerland, the publication of close poll results would have a larger effect on voter turnout.

Second, in municipalities that have greater newspaper coverage of close poll results, the publication of close poll results will have a larger effect on voter turnout.

Both hypotheses found robust support in the data.

The authors therefore conclude that the information about election closeness provided by political polls affects voter turnout. This is in alignment with a key prediction of the pivotal voter model: that rational voters are more likely to vote if they believe themselves to not be able to free ride on the votes of citizens with the same political affiliation as themselves to achieve their desired political outcomes.

Alan Gerber, Mitchell Hoffman, John Morgan, and Collin Raymond (AEJ: Applied Economics, 2020). “One in a Million: Field Experiments on Perceived Closeness of the Election and Voter Turnout.”

Introduction

The authors conducted two randomised controlled trials (RCTs) set in the United States to examine the impact of perceived closeness of elections on voter turnouts. The authors used data from gubernatorial elections without a major third-party candidate in the United States, and did not choose to use data from presidential elections as the electoral college makes it such that elections differ substantially from basic theory (I, as a voter in Nebraska, would first have to determine the probability that my vote is pivotal in my congressional district, and then consider whether my congressional district’s one electoral vote would be likely to be pivotal in the electoral college; if I were voting in Alaska instead, I would have to determine whether my vote is likely pivotal in my state, and then consider whether the three electoral votes allocated to my state would be pivotal in determining the president – the heterogeneity in state populations, electoral vote shares and electoral systems by state all make elections under the electoral college system very different from ones examined in basic voting theory).

In the first RCT conducted in 2010, the authors determine that they may lack statistical power, and that the setting of the RCT (an online survey platform) may lack external validity and not be generalizable to the population of voters, as online paid survey-takers may be different along certain key characteristics (education, income, etc.) from the general population. Therefore, the authors conducted a second RCT using postcards in 2014, coming to the same conclusions as they did in the first RCT about the impact of perceived election closeness on turnout. The 2010 RCT saw 6,700 participants, whereas the 2014 RCT saw 125,000 participants.

2010 RCT: Experimental Procedure

Surveys were sent to participants on KnowledgePanel, a website on which respondents take surveys for remuneration, 13 days before gubernatorial elections in their states. Subjects could complete the surveys up to midway
through Election Day. The survey included the following:

1. A question on whether the subject had voted (those who answered yes were removed)
2. Three political knowledge and interest questions
3. A question asking for subjects’ predictions of vote shares between Democratic and Republican candidates
4. A standard “explanation of probabilities” (Delavande and Manski, 2010)
5. A question asking subjects about the chance that they would vote; their chance of voting for the different candidates; and the chance the election would be decided by less than 100 or 1,000 votes (to approximate subjects’ perceptions of the probabilities of being pivotal)

Two election polls were selected for the treatment. The polls were chosen during the 40 days prior to the start of the RCT. The poll with the greatest margin between the Democratic and Republican candidates was chosen for the Not close treatment, and the poll that had the smallest margin between the Democratic and Republican candidates, but with the same candidate in the lead (i.e. if the Not close poll predicted that the Republican candidate would win by a landslide, then the Close poll would predict that the Republican candidate would win closely) was chosen for the Close treatment. If polls were tied in closeness (both for the Not close treatment and the Close treatment), the more recent one was selected. Subjects were randomised into three groups: the Not close group receiving the Not close poll, the Close group receiving the Close poll, and the control group not receiving poll information at all.

Immediately after treatment, subjects were again asked their prediction of the Democratic/Republican vote share and the chance that they would vote; their chance of voting for the different candidates; and the chance the election would be decided by less than 100 or 1,000 votes.

After the gubernatorial elections, the authors conducted a post-election survey containing a laboratory task to measure a possible bias in probabilistic thinking and questions on whether subjects voted and whom they voted for, along with a few other questions.

2010 RCT: Results

The authors found that participants’ beliefs about margins of victory tend to correspond with electoral results in reality. However, they tend to overpredict the possibility of a close election. This is consistent with past laboratory studies that have found that people overestimate small probabilities. It was also found that one-third of voters updated their beliefs about the predicted vote margin and the probabilities of 100 or 1,000 vote margins, with about two-thirds of voters not changing their beliefs, a number consistent with other information RCTs.

After controlling for an individual’s past voting history (i.e. excluding Always-voters and Never-voters, or voters whose voting behaviour is highly persistent), the authors find that there is no evidence of a change in voting behaviour based on perceived election closeness.

2014 RCT: Experimental Procedure

The authors restricted their sample to states which have voter records in order to observe turnout. In these states, they randomly assigned households to treatment groups and a control group. Thereafter, they sent poll information according to the assigned group to households, considering all registered voters in a household to be treated if a postcard had been sent to the household. In addition to treating households with Close and Not close poll information, the authors crossed this with an electorate size prediction treatment, creating four treatment groups: Close x Large electorate, Close x Small electorate, Not close x Large electorate and Not close x Small electorate.

2014 RCT: Results

The authors failed to find evidence that receiving a Close poll result, relative to receiving a Not close poll result, significantly affected voter turnout. While the authors found that information that the electorate is likely to be smaller decreased turnout by 0.18 percentage points (which does not cohere with the standard prediction that people are more likely to vote in a smaller electorate due to higher probability of being pivotal), this result was not significant.

Conclusion

We therefore have two contradictory results from these two papers: one finds that perceived closeness of elections based on poll results increases turnout, while the other finds that it has no effect on turnout. Purely speculatively, it may be the case that the context of Swiss referenda is quite different from the context of US gubernatorial elections, and when people are voting for a political representative (as opposed to on a policy issue), perceived closeness of elections does not affect turnout very much since voters make the decision on whether or not to vote based more on emotion and strength of political affiliation, and less on probability of being pivotal. In that way, they see the act of voting more as an affirmation of their commitment to the party, and less as a way to achieve their desired policy outcomes. Of course, the differences in identification method may also account for the different results.

If you’re interested in the details of the two different identification methods and the robustness tests conducted in both papers, links to the papers I’ve read and summarised in this post are available below:

• “Identifying the Effect of Election Closeness on Voter Turnout: Evidence from Swiss Referenda” here, latest version here
• “One in a Million: Field Experiments on Perceived Closeness of the Election and Voter Turnout” here