This essay is part of our collection on the ethics of voting. See the full collection here. 

A great many people found themselves nodding quietly in agreement last month as we were enjoined by this or that speaker to vote our consciences. But upon reflection, this good advice is not only a moral challenge—it’s also an intellectual one. How should one vote when confronted with a set of unpleasant alternatives? As it happens, the academic literature actually provides some useful guidance on this score, and of course, the details matter.

First, there is the question of the time horizon. If one cares only about the outcome of the current election, then voting can be thought of entirely in terms of its impact on the identity of the election winner. If, on the other hand, election winners and political parties are influenced by their margin of victory, then one’s vote can be used to send a signal, not just to affect the identity of the election winner.

Voting to Win

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If one takes the Vince Lombardi approach to an election and seeks only to influence the final outcome, then a relentless logic dictates how to vote. In a system using the simple plurality rule, in which the candidate receiving the most votes wins, one should consider all the ways in which an extra vote could change the outcome, either by creating an exact tie or by breaking one.

Suppose that there are three candidates running. Let’s call them Larry, Curly, and Moe. Suppose, moreover, that one suspects that most of the rest of the electorate are voting for either Curly or Larry. You always thought Moe was the best of the three, but you quietly agree that Larry is better than Curly. Of course, there is a chance that any given individual doesn’t bother to vote, or changes her or his allegiance, so we should view the actual vote outcome as random, even though a randomly chosen voter is vastly more likely to support one of the two favorites. Let’s suppose that in the case of a tie vote the election outcome is resolved by a randomization device. This could be a coin toss, casting lots, drawing straws, a hand of five card stud, or a trip through the court system, each of which is used to resolve ties in some US jurisdictions. In case of a tie, each candidate is equally likely to be selected by the randomization process.

There are sixteen scenarios in which you could affect the identity of the winner. It could be that given all of the other votes, Larry leads Curly by one vote, with Moe’s total lagging behind Curly’s. In this case, a vote for Curly generates a tie between Curly and Larry, while voting for either of the other candidates leads to Larry winning. Likewise, if Curly leads Larry by one vote, while Moe garners fewer votes than Larry, then a vote for Larry leads to a tie, whereas any other vote leads to Curly winning the election. Or we could have a tie between Curly and Larry, in which case a vote in favor of either moves us from a hand of five card stud to outright victory for the candidate you favored, while a vote for Moe leaves the two leading candidates at the poker table. There are thirteen other scenarios in which your vote elects the winner, in each of which Moe has some chance of winning.

Yet the first three cases are far more likely than all of the other thirteen scenarios combined. Each of the three shares the feature that a vote for Moe makes it more likely that Curly will win instead of Larry, while doing nothing to elect Moe. This logic leads voters to abandon lagging candidates in favor of the winner or the “first loser” who comes in second. It gives rise to what is known as “Duverger’s Law”: in electoral systems using simple plurality rule, only two candidates obtain appreciable shares of the vote. Exceptions to this rule are so unusual (Wilson vs. Taft and Roosevelt in the 1912 presidential election, Buckley vs. Goodell and Ottinger in the 1970 election of the US senator from New York) that political scientists collect them like rare baseball cards.  The remorseless logic of Duverger’s law is the standard explanation for the close association between two-party systems and electoral systems that employ simple plurality rule.

In a US presidential election, the process is complicated by the Electoral College. Outside of Maine and Nebraska, the states cast all of their electoral votes for the candidate winning a plurality in their state. That means that although one vote is potentially pivotal for one’s state, it is only indirectly so for the election winner. However, the ineluctable logic of Duverger’s law remains in force—however remote the possibility of your vote deciding the election, the probability of casting a decisive vote in favor of any candidate other than the two most popular is infinitesimal relative to the chances of deciding the election for one of the two candidates with the most widespread support.

Electoral Margins, Protest Votes, and Heroic Defeats

It may be the case that, Coach Lombardi notwithstanding, politicians care about more than winning—or, at least, they care about more than winning in the current election cycle.  In this case, winning by a little leaves politicians more careful than does winning by a lot.

This is not implausible. Presidents who win by a wide margin often speak of having a “mandate” to implement their agenda. Consider the difference between the precarious 2000 victory of George W. Bush and the ample margin by which Ronald Reagan won reelection in 1984. While Reagan was able to pass the Tax Reform Act of 1986 despite the House of Representatives being controlled by the opposition political party, Bush was hard pressed to contain the defection of Senator Jeffords to the opposition party, and he had a difficult time legislating, at least until after the terrorist attacks of September 11, 2001. Lukewarm electoral support for the election winner suggests that she and her party are in danger of losing subsequent elections, and so they behave more cautiously. At the next election this can also lead the party of the winner disposed to support a candidate other than the incumbent.

There are a several variations on this theme. It may be that voters cast ballots for one party’s presidential candidate and then elect members of the opposition party to Congress as counterweights. This is consistent with midterm election reversals, as voters use off-year elections to complete the job of counterbalancing a president about whose agenda they are ambivalent.

What if the two parties each field unacceptable candidates? One could vote for a third-party candidate, or register an “undervote,” marking the ballot for local and congressional candidates but leaving the presidential segment of the ballot unmarked. The challenge in supporting either a third party or casting an “undervote” is that the signal that one’s vote is available to the first party offering an acceptable candidate may be misinterpreted as an active endorsement of the Libertarian or Green candidate, or that an undervote is attributed to the voter not being able to manage the ballot papers. Remember the Buchanan vote in West Palm Beach?

Voting Your Conscience in 2016

This is where positive political science leaves us. In the end, it remains true that we must consult our consciences. Suppose that your scruples—like mine—do not permit a vote for either Mrs. Clinton or Mr. Trump. Our country faces increasing challenges in the coming years: the “fiscal ice age,” an increasingly unstable international panorama, and the slowing pace of technological innovation—and then there are the potential vacancies on the Supreme Court and the rest of the federal bench that will need to be filled. If the political parties believe they can win by imposing a candidate who is just barely less reprehensible than the competition, it seems likely that they will find a way to extract what economists call “rents” in the process. In that case, we will face a choice between two toxic major party candidates not just this once, but again and again. Yet the increasingly severe set of policy challenges that will confront us in future years demands that we have better, more eudaemonic, and more competent candidates.

We have thirteen weeks to coordinate the clearest way to send the signal that we will not vote for either party’s candidate until at least one party puts forward a contender who is morally as well as experientially qualified. I suspect that any surge in support for third-party candidates and undervotes this year will be correctly attributed to disgust with the major party options.