The Paradox of Voting Revisited

Julian Jamison outlines why we vote, questions whether everyone should, and proposes ways to incentivize informed voting.

One of the classic problems in political economy (i.e. studying political science with the eye of an economist) is the paradox of voting: given the extremely insignificant chance that any individual vote will make the difference between one side’s winning or losing, why do people vote? After all, even with absentee ballots, it does take some time and effort to vote, especially for those who educate themselves on the issues. There is quite a bit of work devoted to this question, with some reasonable answers. In this piece, rather than trying to summarize the entire literature, I will simply present a framework for studying the question, along with a partial solution in my view.

To put all my cards on the table, I should state upfront that I do not vote, which is a source of great consternation to many friends and relatives. I did in fact vote for the US presidential election in 1992, which was the first election for which I was eligible. It seemed like a fun thing to do at the time, and I certainly do not regret it, nor am I by any means trying to convince anyone not to vote. But enough about me.

Let us start with a simple model: the utility that an individual gets from voting is roughly proportional to PP*ME + WG – C, where PP is the probability of being pivotal, ME is the marginal effect of the preferred outcome, WG is the warm glow of having done one’s civic duty, and C is the total cost of voting.

To be slightly more precise, PP is the expected probability that a particular voter X will change the outcome from A to B (where B is what X prefers), which is equal to the probability that all voters other than X split their votes equally between A and B, plus half the chance that the other voters choose A by one vote, in which case X induces a tie by voting. Meanwhile, ME is X’s utility for B minus X’s utility for A. In other words, ME is what X gains by changing the outcome. Multiplying these factors produces the expected increase in utility from voting. Since ME is bounded above, and PP is almost always extremely small, this product is usually smaller than C, creating the paradox. WG, however, incorporates the internal psychic benefit of voting, which for the present purposes I will take as fixed and exogenous but varying across the population. There is no reason that WG cannot be large relative to C, which is a direct solution to the paradox. While not entirely satisfying, perhaps, because it does not explain where WG comes from, it is nonetheless intuitively reasonable.

More interesting is what the model implies about various situations. For instance, some people argue that all citizens should rationally vote, even if they have a small or nonexistent WG, but the model makes it clear that this does not hold up. One argument often given is to ask rhetorically: “What if everyone followed this reasoning and hence nobody voted?” But in that case, PP becomes 1, so it is clearly optimal to vote (and I for one most certainly would!). This is not circular reasoning: given a distribution of values for WG, only those above some threshold WG will vote.

We can also see that there is a difference between elections about single issues, such as California state propositions, and elections between candidates. The latter get most of the attention, but they are actually probably less relevant for most voters. The reason is that few people have preferences aligning perfectly with any given candidate; rather, they agree about some issues and disagree about others. Indeed, throughout history, a chorus of complaints regarding politicians makes it clear that there is usually general unhappiness about the options available. Within the model, this implies that ME is small in most cases. On the other hand, for a particular issue about which a voter cares significantly, ME could be quite large. Likewise, so-called “single-issue” voters, who pay attention to only one dimension even when choosing between candidates, are much more likely to vote because they too perceive a larger ME.

Another argument sometimes given is that one’s vote can be effectively multiplied if it also encourages others to vote. Obviously this cannot be true for everyone as the sum total of potential voters is fixed, but it does not even fully hold for influential folks, as they do not need to actually vote themselves in order to encourage others to do so. One last argument is that not voting disrespects the men and women in uniform who fought and died for our right to vote, but the whole point is that it is a right to vote. They fought for our freedom, including the freedom to participate in democracy as we like. Totalitarian countries require everyone to vote for a reason, and yet in so doing it undermines their legitimacy.

The model also tells us something about whom we are likely to see at the polls on election day: those who (perhaps incorrectly) believe that they could be pivotal; those who care ardently about the outcome; and those who simply enjoy voting. If the people who care most are those who have the most to gain or lose, then that middle overrepresentation is probably an efficient outcome. But I am not convinced that this is always the case, and I am certainly not convinced that the other two categories are efficient. Instead, I would like to see those who are most informed go to the polls most often. One way to do so would be to give a quiz at the time of voting and then weight each individual vote by their score on the quiz. Of course this would be difficult to implement and would strike many as unfair, so it will never happen.

Another way to encourage more informed voting would be to choose in advance, perhaps six months before each election, a random subset of registered voters, and have only their votes count. Those individuals would face a high PP by construction, so they would almost all vote and would have a particularly strong incentive to become informed. If the names of the randomly chosen subset were not made public, this would limit the amount of targeted campaigning that would surely otherwise occur. Of course anyone could claim to be on the list, but that would be nothing more than cheap talk. On the other hand, one advantage of the names being public is that candidates would have an incentive to talk directly to some of their constituents, being forced to try to convince them one-on-one of the superiority of their chosen policy positions. Among other things, this would decrease the importance of advertising money in elections, an issue highlighted by the recent Citizens United Supreme Court decision.

Finally, it is worth considering the advantages of other forms of government. The pros may not outweigh the cons, but there is a real loss due to democracy. A benevolent dictatorship has certain efficiency advantages, as I have noticed when comparing private firms and militaries with a clear hierarchy to academic departments, where faculty meetings often involve endless amounts of discussion and rounds of voting about every minor detail. That is a nontrivial deadweight loss, not just to the individuals involved, but also to everyone who could have benefited from that time being spent more productively.

Of course, there is great value to having a government chosen by the masses, and so we will let democracy win this battle for now. Even so, everyone does not need to vote to make democracy function. Indeed, it is an efficient outcome for many people not to vote. Finally, the system we have in place does not adequately ensure that the people who show up to the polls are the most qualified citizens we should have choosing our leaders.

Julian Jamison is a senior economist at the Federal Reserve Bank of Boston, a visiting faculty member at Yale University, and a fellow at the Harvard Kennedy School.

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