Why Approval Voting is Better with a Runoff

Approval Voting doesn’t need a runoff like Plurality does, but it still helps some.

There are several benefits of adding a runoff to an Approval Voting contest:

1. Greater strategic straightforwardness. In an Approval Voting race, having a basic awareness of who is viable, and acting on that knowledge in a reasonable manner, helps a lot. For example, there could be a “reverse spoiler”, i.e. a candidate who is wildly unpopular and who many voters consider to be drastically worse than anyone else. Strategic voters would basically ignore this candidate — since she’s so unpopular she can’t plausibly win — but less strategic voters might opt to vote for every candidate but her, thereby throwing their votes away. This can occur either with or without a runoff, but, in the two-way runoff election, every voter has equal influence regardless of how they vote in the first round.
2. Outcomes that better reflect the will of the electorate. Given perfectly strategic voters with perfect information, Approval Voting, even without a runoff, will always elect the Condorcet winner. This does not need to happen when voters don’t know everyone else’s preferences or when they fail to vote strategically, such as in the case of a reverse spoiler. The runoff adds slack: if the Condorcet winner makes it into the top two, that candidate will win. Computer simulations confirm that having a runoff leads to better candidates getting elected.
3. Avoiding the chicken dilemma. Suppose there are 100 voters in a 3-candidate Approval Voting race without a runoff, and the voters have the following preferences:
   31: D1 > D2 > R
   30: D2 > D1 > R
   39: R > D1 = D2
   Futhermore, assume the D voters care far more about having some D candidate win than about having their preferred D candidate win. If all of the D voters vote for both D1 and D2 they will tie, but if a single one of them bullet votes (i.e. only votes for their one favorite candidate), that candidate will win. In fact, whichever of the D candidates has more of their supporters bullet vote will in — unless so many of them bullet vote that R wins, a very bad outcome since R would lose in a landslide to either of the other candidates head-to-head.
   Adding a runoff means that R cannot win. Real-world complications mean the chicken dilemma is nowhere near as problematic as it might appear from this toy example, but avoiding it is still a plus.
4. More time to evaluate the top two candidates. If there are a dozen candidates and some voters don’t want to take the time to research all of them, they could sit out the first election and only vote in the runoff. More generally, voters can research two candidates more deeply than they can research a crowded field. This is a benefit of runoffs in general, and has nothing to do with approval voting in particular.

(Another argument, which I do not consider to be valid, is that we need a runoff to ensure a majority. But no voting method can ensure a majority, and there’s nothing particularly special about majorities anyway.)

None of these arguments (except for #4) applies as strongly to Approval as it does to Plurality. No-runoff Plurality has moderately worse strategic straightforwardness than no-runoff Approval because any strategically naive voter whose favorite candidate isn’t viable will throw their vote away under Plurality. (Under Approval Voting, such a voter may vote for a viable candidate as well.) This means that adding a round in which all ballots have equal influence makes a bigger difference under Plurality. Even a widely hated candidate can win under Plurality if there’s enough vote-splitting, so adding a runoff has a greater chance of changing the winner under Plurality. This includes the case of the chicken dilemma, which is practically designed to be a scenario in which Approval Voting struggles but is still one in which Plurality still performs vastly worse. Adding a runoff is a very big deal for Plurality (lifting it from terrible to merely bad), but a relatively modest improvement for Approval Voting.

There are also downsides to having a runoff. I consider most of the arguments to be very weak, if not completely invalid, but the first one is indisputable.

1. It’s more expensive. Conducting an election, regardless of whether or not it’s a runoff, takes time, effort, and money. This is true for the jurisdiction conducting the election and for individual voters who take the time to fill out their ballots and, if they don’t have vote-by-mail, to go to a polling place. Because of this consideration, I don’t claim that every single jurisdiction would be better off with Approval + Runoff than with no-runoff Approval; the added costs are more important in some places than others.
2. Approval + Runoff fails Favorite Betrayal. In no-runoff Approval Voting, it’s always strategically optimal to vote for your favorite candidate. No exceptions. On the other hand, suppose there’s Approval + Runoff election in which your favorite candidate is an extremist who you expect to lose the runoff if he makes it there, but your second choice is a moderate who you expect to win the runoff if she makes it there. If you vote for both of them it’s possible that your favorite will make it to the runoff instead of your second choice and then lose the runoff to a candidate you like far less — but you can avoid this by only voting for your second choice. While it’s hypothetically possible for such situations to occur, in practice it’s just about always best to vote for both your first and second choices. Two reasons:
   First, if your first choice makes it to the runoff instead of your second choice this is evidence that your first choice is actually the more broadly popular of the two, so underlying expectations that allowing for favorite betrayal being a good strategy are rather weird.
   Second, your first and second choices might both make it to the runoff, thereby ensuring a good outcome — even if there’s a candidate you don’t like who would beat either of your preferred candidates head-to-head.
   Approval + Runoff technically fails Favorite Betrayal, but this is an extremely minor failure and we shouldn’t have pass-fail criteria be dealbreakers.
3. Approval + Runoff enables a hypothetical pushover strategy. If you and a bunch of like-minded people all vote for a candidate you think has no chance of winning a runoff (in addition to voting for the candidates you like), you can have a candidate-you-like vs. pushover candidate matchup in the runoff that you’re virtually assured of winning. However, this strategy is usually terrible because the pushover might make it to the runoff instead of a candidate you actually like. (Another way this could backfire is if the “pushover” actually wins.)

There are three categories of arguments for or against having runoffs: those focused on electing the best winners, those focused on strategic voting, and those focused on giving voters, candidates, and jurisdictions the best election experience possible. The first two categories favor having a runoff, but I largely consider the third one to be beyond the scope of this blog. I don’t have a strong opinion on how long campaigns should last or how frequently people should vote, and people who want short campaigns and infrequent voting can very reasonably prefer no-runoff Approval Voting. The runoff does yield better winners and does reduce the importance of strategy, but these differences are not overwhelming.