Zach Barrett has a great new paper out critiquing the binomial model of voting. The binomial model, which you can find in Democracy and Decision, among many other books, models voters as if they were weighted coins. Asking whether you will break a tie is like asking whether a weighted coin of a certain sort will come up heads exactly half the time. While the binomial model was the dominant model for a while, it seems people generally use Edlin, Gelman, and Kaplan's estimates of decisiveness instead now, though they also have their critics.
In The Ethics of Voting, I did some calculations using Geoff Brennan and Loren Lomasky's formation of the binomial model. Barrett's paper presents an extremely strong case that the binomial model's estimates of decisiveness have to be too low. I think he's right about that and his paper makes a strong case that the probability of decisiveness is much higher.
All that said, it's worth reflecting on how the issue of decisiveness affects the issues that constitute the ethics of voting. Here's a relevant passage from the 2011 book:
I am not going to argue that because your vote is insignificant, you should not vote. There are reasons to vote—and not to vote—even if individual votes don’t matter much. Some economists say it’s irrational to vote. That’s not my position.[i]
Instead, I introduce this issue here for the purpose of explaining how it affects my argument. From my perspective, the insignificance of individual votes is neutral in how easy it makes it for me to argue for the conclusions of this book. Since I want to argue citizens have no duty to vote, the insignificance of individual votes is, at first glance, helpful. It’s easier to argue that someone lacks a duty to perform an action when the individual action does no significant good. On the other hand, since I’m going to argue that people sometimes have a duty to abstain, the insignificance of individual votes is a problem for me. It’s much harder to argue that people should not vote badly when individual bad votes do no significant harm.
[i] Since this book is about the ethics of voting rather than the (prudential) rationality of voting, I don’t try to establish that voting is rational or irrational. If someone asked me whether voting is prudentially rational, here’s my quick response: ...it’s generally prudent to be the kind of person who doesn’t care that much about whether it’s prudent to vote. Individual acts might be irrational, but it might be rational to be the kind of person that doesn’t care much about the rationality of individual acts.
The bolded parts outline the essential dilemma. If it turns out that in certain cases, as Edlin, Gelman, and Kaplan think, or as Barrett argues, voters have a pretty decent chance of being decisive, then (so long as there is a real difference in expected value between the candidates) their votes can have high expected utility. This makes it much easier to argue that it's rational to vote, and also easier to argue that some people can have a duty to vote. However, if some votes have high expected utility, then some votes can also have correspondingly high expected disutility. If certain votes matter, it's also much easier to argue that some people should refrain from voting, because their individual votes are the equivalent of imposing a massive loss. If, as Edlin, Gelman, and Kaplan say, a swing voter in NM's vote can be have an expected social utility of $50,000, then that same voter can also have an equal expected social disutility.
In The Ethics of Voting, I wanted to argue for both of these claims:
- There is no duty to vote per se. Rather, most of the somewhat decent arguments for a duty to vote at best show that voting is one of many optional ways, and not even a particularly good way, to discharge some underlying duty. For instance, most people would better discharge a duty to promote the common good by becoming motorcycle mechanics than by voting consistently in every election.
- There is a conditional duty which attaches to voting: If you choose to vote, you are morally obligated to vote well, which requires you take care, become informed enough, think rationally enough, and vote in good faith for what you justifiably think best promotes overall justice rather than for your narrow self-interest.
If individual voters matter a lot, it's harder to argue for 1 but easier to argue for 2. In the book, I presume individual votes mattered little, which makes it easier to argue for 1 but harder to argue for 2.
(Sorry about the formatting issues in this post. I can't get it to eliminate the weird spacing.)