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ERUDITIO >> duke university’s undergraduate humanities journal

To Vote or Not to Vote:

The Calculus of Voting and How Election-Day Polls Affect Voter Turnout

Thomas Brady

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"In the process, I've tried " Jimmy Carter stated with his voice breaking while trying to recover his composure, "…I’ve tried to honor my commitment to you… Don't forget to vote, everybody." (Church 1). This Election Day speech, in 1980 at his campaign headquarters, signaled Jimmy Carter’s public acceptance of a single inevitable fact: He was going to lose. Sure enough, Jimmy Carter would be standing at a podium that night at 10:15 P.M. EST announcing his concession to Republican candidate Ronald Reagan. This means that Jimmy Carter was standing at the podium, conceding defeat, before the voting polls had even closed in California. It was only 7:15 P.M. on the west coast, with most polls closing at 9 P.M, yet the presidential election was essentially over. How could this be?

The answer is simple: Exit polling.

Election-day exit polls enabled a projection of a landslide victory for Reagan which was, in turn, broadcasted on every major news organization before most West Coast voters had even gotten out of work. Immediately, this brings a single question into mind: How many voters turned away from the polls, went back home to their families, and avoided the time and cost of voting after hearing the lopsided results of election day exit polls? While this paper will not attempt to empirically solve this question, it will try to explain how exit polls affect voter turnout from a theoretical approach. This approach will discuss exit polling in the context of a rational choice model—more specifically, the “calculus of voting.” The 1980 election results will then provide the empirical support necessary to translate this theoretical approach into a real world, tangible analysis of how exit polls can have affect on voter turnout. People may not “forget to vote” for Jimmy Carter, but could the additional information of exit polling change the rational choice model in such a way as to affect voter turnout?

The act of voting, the decision to choose to turn out and vote, can be defined in terms of a theoretical decision-making process. More specifically, voting can be discussed in terms of its “rationality”—a behavior, in this case voting, becomes rational as depending upon one’s “preferences.” These “preferences,” or one’s values, attitudes, and beliefs, are transformed into “utilities” when an individual considers the benefit of a various outcomes of a situation (Sudman 334). Rationality then inherently discusses a cost-benefit analysis in which a voter makes his/her decision based upon the “utility,” or benefit, of a desired outcome in light of a behavior’s costs. In a generalized sense, an action becomes rational if the utility of a desired outcome outweighs the various costs one must suffer in behaving a certain way.

Therefore, if a voter perceives high utility in having candidate A over candidate B then the low costs of voting would not outweigh the utility of a desired outcome and the voter would vote. The reverse, of course applies, in that if a voter is apathetic to either candidate, he will not vote as any cost of voting will outweigh a utility of 0 and deter him from voting. The voter is essentially computing the “expected utility” of the possible outcomes and their concurrent utilities. The expected value of voting requires the possible outcomes (a tie, win, or loss for the desired Candidate A over B,) their respective utility values, and the probability of these outcomes occurring. The expected value of voting must then outweigh the expected costs. In this sense, voting becomes an action or behavior intrinsically connected with expected utility of an outcome. Voting is therefore instrumental in gaining a desired outcome, aptly described by the “investment” theory of voter turnout (Sudman 335).

Expected costs are viewed as an “investment” in order to gain a desired outcome

However, the costs of voting— time, informing oneself, and choosing between candidates—are inescapable constants. Regardless of the outcome of the election, one will suffer the costs of turning out to vote. Or will they? What if one could enjoy these benefits without incurring the costs of turning out to vote? Such is the problem of voting as a matter of “collective action,” described here by John H. Aldrich, a professor at Duke University, as a situation in which “the outcome depends on actions taken by others as well as the decision maker” (252). In other words, a voter does not have to turn out and vote in order to reap the benefits of a desired outcome. Candidate A can be elected regardless of whether you, the voter, turned out and voted. If a voter can “free-ride” his way into a desired outcome without suffering the costs, the rationality of voting and its concurrent rational choice model must somehow predict and take into account the actions of others and the probability they will either turn out and vote or abstain.

The “calculus of voting” model, created by Anthony Downs in his An Economic Theory of Democracy, tries to come to terms with voting as a problem of collective action. In his book, Downs states it is preferable to adopt a narrow definition of rationality in which “the political function of elections in a democracy, we assume, is to select a government” and therefore “rational behaviour in connection with elections is behaviour oriented towards this end and no other” (Aldrich 256) He furthermore explains the rationality of voting in terms of a fundamental, cost-benefit analysis equation as follows:

R = PB – C

The value term ‘R,’ stands for the “Rationality” of voting, in which if R > 0 voting is deemed “rational,” and if R < 0 it would be considered “irrational” to vote. The “C” terms stands for the aforementioned costs of voting while the “B” term stands for the concurrent benefits of voting. It is important to note that if a voter is apathetic, the essential value for B term is “0” as there is no benefit between candidate A and candidate B. While there is no real controversy in considering the B-C relationship as a simple cost-benefit theoretical model, the “P” term of Downs’ equation becomes the most controversial. The “P” term can essentially be summarized by the concept of “decisiveness”: that is, a voter casts a “decisive” vote and breaks a tie between Candidate A and Candidate B (Aldrich 254). A decisive vote then is the action of highest utility within the framework of voting because this “invested” vote directly resulted in the voter’s desired outcome. More precisely, the P term describes the probability that a voter will cast the tie-breaking, decisive vote.

While this does not seem inherently controversial, the P term of this decision-theoretic model essentially negates the benefit of voting altogether. This is because the P term has been written off as essentially infinitesimal within a large electorate such as the United States. The notion of decisiveness essentially does not exist because of the inherently small probability of casting a tie-breaking vote (Blais 188). Furthermore, Considering the PB relationship of the equation, if the P term is considered “infinitesimal” (because the probability for a decisive vote is so small,) than the “B”enefit of voting will essentially equate to nothing. A voter could never conceivably have a high enough B value in order to balance off a P term that is, in mathematical terms, approaching zero. A PB value equivalent to 0, combined with the constant, inescapable costs of voting, with make the equation look something like this:

R = 0 – C, where C > 0 at all times.

R will then always be a negative value, rendering voting an irrational act entirely. Yet, why do people still turn out and vote? After all, voting turnout was the highest in 2004, at 60.7% with 122 million people voting, since the election of 1968 (Faler 2). People are behaving in a way that the calculus of voting essentially deems irrational. Perhaps, it has something to do with Rider and Ordershook’s invocation of a “D” term into the equation. Andre Blais, at the University of Montreal, tested and corroborated the importance of “duty” in an empirical survey performed in a smaller, Canadian election. He empirically secured the importance of duty in determining voter turnout, stating “In the high-duty subsample, none of the rational choice components[ie-benefit of one candidate over another, costs, etc] has a significant impact on the propensity to vote… people with a strong sense of duty overwhelmingly tended to vote” (Blais 195). This concept of “citizen duty,” while seemingly sensible in real world terms—as many people vote “in the name of democracy”—really has no place in an economic equation such as the calculus of voting. There is no way to put a value term on the amount of “duty” one person has over another. This renders “citizen duty” more of a sociological, psychological reasoning behind why people turn out and vote. However, duty does not solve this problem of the “paradox of voting,” where voters are continuing to vote when it seems inherently irrational to do so (Ledyard 2).

However, the interpretation of the calculus of voting by Rider and Ordershook seem to misinterpret the value term P in Downs’ equation. Aldrich gestures at this misinterpretation here, qualifying the key innovation of the calculus of voting as the fact that “each individual assigns a probability of each state of the world being true [each of the possible desired outcomes]” and “the probability that one vote will make the difference” (252). The P term cannot be discussed as a mathematical constant or number, or even as “infinitesimal” in a general sense, because the P term is dependent upon the individual’s perception of his ability to cast a tie-breaking vote—not the mathematical reality or probability as such. Moreover, this equation seems to necessitate a re-framing of the P term, moving it from “decisiveness” (a tie-breaking vote) to the perceived closeness of an election.

Downs, Rider, and the like seem to give the individual voter too much credit in determining the rationality of his/her own vote. Often times, a voter will misperceive the probability that he could cast a tie-breaking vote—rendering the actual numerical probability of such an event irrelevant. Irregardless, an individual, in reality, does not compute the utility of his or her turning out to vote with regards to the probability of decisiveness, but tries to ascertain how much his vote “counts.” The voter’s thinking is too narrowly framed with the empirically sound value of “P” as probability, but instead it’s a much more fuzzy, vague generalization. The voter’s rationalization is that the closer the election is perceived to be, the more his/her vote “counts” towards gaining the candidates victory and securing a voter’s desired outcome. While this does not hold in a rational framework, it is corroborated by the empirical evidence that an individual miscalculates the PB relationship in its Downsian, traditional sense. For instance, the aforementioned Andre Blais present a case study of an election in British Columbia in which surveys presented the following:

An item asked whether respondents had ever thought of the possibility that the outcome could be decided by a single vote, and that their own vote would be decisive. In Quebec, 33% of those surveyed said they had thought of this possibility, while in BC (where the question was put with the respect to the riding only), 38% indicated that they had thought

of it. Respondents were asked what the chances were that the outcome would be decided by a single vote, and four response categories were offered: ‘very high’, ‘somewhat high’, ‘somewhat low’ or ‘very low’. The modal response in both provinces was ‘very low’, this was chosen by 48% of respondents in Quebec and 59% in BC. However, another 22% of Quebeckers and 15% of British Columbians said the chances were ‘very high’ or ‘somewhat high’ (198).

Empirical literature therefore corroborates the notion that people have a huge misconception of the numerical probability of casting the “decisive” vote.

The same thinking applies with the analogy of playing the lottery. Millions of people “irrationally” play the lottery even though the expected utility of winning is infinitesimal. Why do they play? Perhaps, the “P” value of buying a lottery ticket, standing here for the probability of winning, is skewed in such a way that many people misperceive, miscalculate, and deceive themselves into thinking they have a chance of winning. While this seems convincing, this analogy more importantly points to the major difference between buying a lottery ticket and turning out to vote: Benefit. While both a lottery ticket and voting are relatively low cost, the utility/benefit of winning the lottery is a life-altering event—far outweighing the benefit between Candidate A or Candidate B in almost all cases. Voting therefore must be intrinsically understood as a low cost , low benefit economic behavior (Aldrich 258).

If turning out to vote is therefore a low cost, low benefit behavior, the concurrent assumption is that the decision of whether or not to vote will be made, as Aldrich puts it, “at the margin”(258). More precisely, voting behavior will be severely altered by any change in cost or benefit. For instance, if the government were to implement a penalty fee for abstention of voting, the turnout would grow exponentially because the costs for abstention have been raised from almost nothing. Therefore, there is not only a change in the perceived costs, but a change in the perceived benefit, even if only a small amount, should dramatically affect voter turnout.

So where does exit polling fit in? If exit polling can be shown to change the perceived benefit of voting—either positively or negatively—than voting should become a “more” or “less” rational activity respectively. With increased or decrease rationality, there is the theoretical expectation that voter turnout would then increase or decrease respectively. This functions on Aldrich’s theoretical assumption that “the probability of casting the deciding vote, should be higher, the closer the election is, ceteris paribus.” Furthermore, he states that holding all else constant, the higher the [perceived] P value [in the calculus of voting], the more likely it is that an individual will vote (Aldrich 259).

The election-day exit polling will therefore only affect voter turnout in so far as the election-day exit polls defy the voting population’s previous, pre-election day expectation (Jackson 620). Exit polls which confirm the pre-election day poll data—as to the distance or proximity between Candidate A or Candidate B—will not change the perceived benefit of voting and thus leave voter turnout unaffected. However, if an election has Candidate A winning by a large statistical margin over Candidate B, but the election-day exit polls show a dead heat, exit polls will have changed the perceived closeness of the election, raising the probability of casting the deciding vote as per Aldrich’s theoretical model, and thus raising voter turnout. (See endnote: The converse situation holds as well.)

The only qualification for introducing empirical data into the affect of election-day exit polling on voter turnout must be that the perceived closeness of the election was dramatically altered by the election-day exit polls. While this severely limits the number of elections worth sampling and studying, this was indeed the case in the 1980 election between the incumbent Jimmy Carter and the Republican challenger Ronald Reagan. The Gallup Pre-election polls showed Reagan at 47%, 44% Carter, 8% Anderson, and 1% other candidates (Kohut 1). With a statistical margin of error of 3.5%, this race has to be considered by anyone, a statistical dead heat. The actual margin of victory was a landslide for Reagan with 50.8% of the vote with his nearest competitor, Carter, more than nine percent behind at 41.0%. This election therefore qualifies as worthy of the consideration that exit polls negatively affected the number of people who turned out for Carter due to a decreased value in how much their vote would “count,” as based on their conception of the theoretical “P” value.

John E. Jackson’s “Election Night Reporting and Voter Turnout” presents an analysis of a subset of data collected from respondents, surveyed both before and after the 1980 election. The problem at hand for Jackson was to prove that voters and non-voters 1) heard the election-day exit polls via media coverage and that 2) these results either persuaded them to vote or not to vote (in relation to their surveyed, pre-election “tendency” percentage to turn out and vote.) (Jackson 625). The time these exit polls were released was not problematic as detailed in Jackson’s article that, “An NBC News release from 5 November 1980 claims that at 6:30 P.M. EST on election night, John Chancellor announced that Reagan appeared ‘headed for a substantial victory.’”(Jackson 1983 626). Therefore, a voter could have heard the exit poll data at 6:30 P.M. (3:30 PST) with the polls open until 9 P.M. This is the very reason why, as Jackson notes, the affect of exit polls on voter turnout should be considered a “West Coast Phenomenon” because the exit poll data was available for nearly two and a half hours before the polls closed even on the east coast.

However, the votes were re-framed under the consideration of several essential relationships of this case study: turnout and intent, time left to vote, region of the country, and exposure. Under exposure, there were several subsets in which each individual voter was assessed upon the type of media he/she was exposed to, whether the voter was exposed to exit poll data, Carter’s concession speech, or both. This is an essential characteristic which could dramatically skew Jackson’s results and for which the case study is highly criticized. Carter’s concession speech was public information at 7:30 PST, which could effectively render the election of 1980 an “impure” vision of how exit polls affect voter turnout (Jackson 628). A concession speech, of course, effectively ends the election and has a dramatic effect on the consciousness of the voter in a way that an exit poll can never parallel. Jackson therefore created an “exposure variable coefficient” in the hopes to compensate for this variation for the normal election day.

Jackson’s results were statistically persuasive and significant in following the actions of voters in this election. He found that “an average eligible West Coast respondent in the full fall survey, who had not voted by 6 P.M, his or her expected probability of voting between then and the poll closing was reduced by 22% (from 88% to 66%)” (Jackson 629). In terms of probability of turnout, Jackson states his findings were as follows, “The reduction in expected turnout probability attributable to hearing the outcome projected, Carter’s speech, or both reaches a maximum of just over 0.2 for Western residents who have between a 0.5 to 0.7 probability…to vote” (629). This was the case even for those who had nearly a 99% intention of voting as well—in which the exit polls were said to reduce their probability to turn out by nearly 8%. It is also interesting to note that while average turnout probability was calculated to be reduced by 12% on the West Coast, the east coast was only reduced by 6%. This is most likely due to the shorter amount of time between the polls closing and exposure to exit poll data. Furthermore, this may be enough of a discrepancy to question why Jackson goes out of his way to state that exit polls are not a “West Coast Phenomenon.”

Jackson’s study as a whole seems to support the notion that election-day exit polling has a significant affect upon voter turnout. While this does not directly correlate exit poll data with its affect on the aforementioned theoretical PB relationship and the P value as a whole, this paper functions upon the assumption that the singular, greatest affect of exit polls is in their ability to change the perception of the closeness of elections. In doing so, the exit polls change the voter’s perception of their “decisiveness” in the election—either more or less decisive as the exit polls show the election to be closer or further than previously expected. The voter therefore changes his behavior based on a more generalized, encompassing understanding of the calculus of voting in which he or she understands their action to be more or less “rational” with their newly-formed perception of the election. Did people forget to vote for Carter? Probably not.

Works Cited

1. Aldrich, John H. “Rational Choice and Voter Turnout.” American Journal of Political Science, Vol. 37, No. 1. (Feb., 1993), pp. 246-278.

2. Blais, Andre. “The Calculus of Voting.” European Journal of Political Research, Vol. 37: 181-201. January 2000.

3. Church, George J. “Reagan Coast-to-Coast.” Time Magazine. November 1980. <http://www.time.com/time/magazine/article/0,9171,950482-3,00.html > Accessed 13 November 2007.

4. Faler, Brian A. “Election Turnout in 2004 Was Highest Since 1968.” The Washington Post. < http://www.washingtonpost.com/wp-dyn/articles/A10492-2005Jan14.html> Accessed 15 November 2007.

5. Jackson, John E. “Election Night Reporting and Voter Turnout.” American Journal of Political Science, Vol. 27, No. 4. (Nov., 1983), pp. 615-635.

6. Kohut, Andrew. “1981: A REVIEW OF THE GALLUP PRE-ELECTION METHODOLOGY IN 1980.” The Gallup Organization. <http://www.amstat.org/sections/srms/Proceedings/papers/1981_010.pdf> Accessed 15 November 2007.

7. Ledyard, John O. “The Paradox of Voting and Candidate Competition: A General Equilibrium Analysis.” California Institute of Technology, Division of the Humanities and Social Sciences. <http://www.hss.caltech.edu/SSPapers/sswp224.pdf> Accessed 15 November 2007.

8. Riker W. and P. Ordershook.1968. “A Theory of the Calculus of Voting.” American Political Science Review 62: 25-42

9. Sudman, Seymour. “Do Exit Polls Influence Voting Behavior?” The Public Opinion Quarterly, Vol. 50, No. 3. (Autumn, 1986), pp. 331-339.