Lee Drutman’s Faulty Critique of Approval Voting

Lee Drutman recently wrote a post called “Approval voting vs ranked-choice voting: A hypothetical election”, aimed at demonstrating the superiority of his favored instant runoff voting (IRV) voting method over approval voting. (IRV has been marketed in recent years as “ranked choice voting”, but there are actually a multitude of ranked voting methods.)

By the time we reach the title, Drutman is already off to a bad start. Probably the most common novice fallacy in voting theory is to fixate on a specific cherry-picked anecdotal electoral scenario (“a hypothetical election”) rather than average results over a statistically significant sample of elections, as was done with Warren Smith’s Bayesian regret calculations and Jameson Quinn’s voter satisfaction efficiency calculations. You can see sample results from their respective simulations here.

Voter satisfaction efficiency (50/50 strategy to honesty selected, i.e. the brown dots)

Bayesian regret (Further left means more honesty, right more strategy.)

Quinn’s VSE graph, with the colored dots, showed IRV performing a bit better than approval voting with honest voters, but approval voting quickly overtaking IRV with even a modest fraction of strategic voters. Smith’s simulations, which used similar but substantially different modeling, had more definitive results: approval voting was better with 100% strategic voting than IRV was with 100% honest voting.

Drutman’s Scenario

Having noted the fallacy of analyzing specific scenarios rather than statistical aggregates, let’s go ahead and analyze the specific scenario Drutman posed, for the sake of argument.

Elizabeth Warren, Donald Trump, and Michael Bloomberg. Let’s say that a month before the election, 40% of voters prefer Warren, 40% of voters prefer Trump, and 20% of voters prefer Bloomberg. If a majority of Bloomberg voters prefer Warren to Trump, Warren wins. If a majority of Bloomberg voters prefer Trump to Warren, Trump wins.

Note that this implies Bloomberg being eliminated first. But consider that almost all Warren voters would have Trump as their last choice, and vice versa, making the ranked preferences behind Drutman’s model look roughly like this.

40% Warren Bloomberg Trump
40% Trump Bloomberg Warren
20% Bloomberg

Bloomberg notably trounces both of his opponents head-to-head, preferred by a 60-40 landslide against both Warren and Trump. It could not be clearer that Bloomberg is thus the most popular overall candidate in this scenario that Drutman himself made up. And yet, with only 20% first-place support, Bloomberg would be the first candidate eliminated in the IRV tabulation process that Drutman advocates.

So in attempting to contrive a scenario to make approval voting look bad, the first and most obvious thing Drutman has done is demonstrate the “center squeeze” effect of his preferred instant runoff voting method, where a broadly appealing consensus candidate gets squeezed out by more partisan candidates from both sides.

Both Warren and Trump should appeal to as many Bloomberg voters as possible, to win true majority support.

Here Drutman uses one of the IRV community’s favorite catch phrases, “true majority support”. But as we just saw, Drutman’s own example appears to celebrate IRV’s refusal to elect the candidate who is preferred by a landslide majority to both rivals.

And this is a strange argument to make contra approval voting, which provides the same incentive. That is, Warren and Trump want to appeal to Bloomberg supporters in the hopes of winning “second choice approval”.

Approval Outcome

Drutman postulates this outcome.

Assuming everyone votes sincerely and not strategically (checking all the candidates they are okay with) Bloomberg would win. In addition to the 20% who like him best, you also have another 50% who are fine with him (75% of Warren’s 40%, plus 50% of Trump’s 40%, so 30% plus 20%), bringing Bloomberg’s total to 70%. By contrast, Warren would get 55% (her 40% plus 15% (75% of Bloomberg’s 20%), and Trump would get 45% (his 40% plus 5% (25% of Bloomberg’s 20%). So the final approval voting tally would be Bloomberg 70%, Warren 55%, and Trump 45%.

This is actually a pretty reasonable model, although the assumption that “everyone votes sincerely” is unrealistic. Based on my nearly two decades of research, including involvement with exit polling experiments, I would expect roughly half of voters to be largely or even mostly strategic, which is to say that they would incorporate expectations of viability into their approval thresholds.

But Drutman quickly goes off track around the game theory.

Say you prefer Warren to Trump, but also Bloomberg to Trump. Should you vote for Warren and Bloomberg? Or just for Warren? Each vote for Bloomberg improves Bloomberg’s chances, and if everybody who was okay with Bloomberg voted for him, he’d win. So, if you really want Warren to win, you should just vote for Warren.

This last sentence (bolding mine for emphasis) is drastically wrong. Just consider that under the status quo, Green Party voters really want the Green Party to win; and yet, most of them vote for the the Democrat rather than the Green. Because as any election researcher worth his salt should know, voters act strategically. Drutman has made a cardinal mistake by ignoring one of the most fundamental ideas in game theory: the iterated prisoner’s dilemma.

See, Warren voters know that if they just vote for Warren, that could indeed switch the winner from Bloomberg to Warren. But only if none of the other candidates’ supporters think this way too! For instance, if the Bloomberg voters suspect this is going to happen, then the same logic would lead them to do the same thing! They would only vote for Bloomberg, in an effort to counteract this strategic defection.

But both factions inevitably realize that this strategy will cause Trump to win, and therefore it is simply unsafe to employ this strategy. And the same even goes for Trump’s supporters. If they think Warren supporters are going to bullet vote en masse, causing a blowout for Warren, then they have a huge incentive to also approve Bloomberg, to at least prevent the election of an ardent progressive activist like Warren.

This process of iteration is crucial to a serious game theoretical analysis. And thus it should be of little surprise that one of the most prolific advocates of approval voting is an NYU professor of political science and game theory, Steven Brams. Yet for all his academic laurels, Drutman’s rhetoric gives no indication that he is familiar with the work of Brams or other game theory experts in the field.

Polling

Drutman continues:

But, with polls tied 40–40, what if Trump wins?

Wait, what? 40–40 would have been the polling with plurality voting, where you can only select one candidate. With approval voting used in elections, we would expect for it to be used in polling too. In which case the polls would be..Bloomberg 70%, Warren 55%, and Trump 45%, or something thereabouts, which was the outcome Drutman posited. He seems to jump back and forth from the status quo to the approval voting world whenever it suits his present argument.

Approval voting strategies are highly contingent on polling.

This is absolutely correct. But this is true of any deterministic voting method. Indeed, here’s Andy Jennings, who did his math PhD thesis on voting methods and co-founded the Center for Election Science, giving us a simple explanation of how it’s unsafe to vote for your favorite candidate with Drutman’s favored IRV method, unless the polls and other indicators of electability say she’s a frontrunner.

Not only that, but the strategy with IRV is much more harmful, because once you’ve strategically floated your electable “lesser evil” up to the top of the rankings, you’ve by definition buried your sincere favorite. Which you would never want to do with approval voting, since it satisfies the favorite betrayal criterion.

As Drutman continues, it just keeps getting worse:

And without polling, voters would be even more hopeful about their candidates’ chances of winning, and less likely to approve of anyone else, since approving of a lesser choice essentially is giving up on your first choice winning. This is not a problem in ranked-choice voting. The strategies are the same regardless of small variations in polling, and voters can vote sincerely with or without available polling.

Everything in this paragraph is false. First, he suggests that a lack of polling would make people more “hopeful” of their favorite’s chances of winning. But if you have no data about electability, then all candidates are by definition equally likely to win, and thus your best strategy is to vote for everyone you like more than the average of all the candidates.

And yet again he repeats the classic fallacy of assuming voters only care about their favorite.

approving of a lesser choice essentially is giving up on your first choice winning

Simply false. Suppose I believe Ideal=5, Good=4, Bad=0, and Ideal has a whopping 79% chance of winning, with Bad having a 20% chance of winning, and Good having virtually no hope. Then my expected utility is 3.99. So I should approve everyone I prefer to that, which means Ideal and Good.

A 79% chance does not amount to “giving up”. Drutman apparently hasn’t studied the basic expected value calculations that form the basis of strategic voting.

Conclusion

Lee Drutman has garnered a considerable following in the voting reform community, anchored by his political science PhD. But when we get into the guts of his arguments, there seems to be a total lack of familiarity with the core subject matter, and it is hard to see on what basis Drutman can be considered an expert in the field at all.