One of the things that I’ve never succeeded in doing is figuring out how to do a popular or accessible presentation of some of the major findings in “voting theory.” The academic literature gets pretty complicated pretty quickly, but it has a single, unequivocal conclusion: of the basic family of voting procedures, none is intrinsically superior. If you start by working out a list of desirable, intuitively plausible criteria that you want a voting system to satisfy, you will find that no system satisfies them all. As a result, the best way to evaluate a system, in my view, is pragmatically – in terms of its likely consequences, which is to say, by the type of government and political dynamics that it is likely to generate.

There are, however, a huge number of organizations and activists pushing for various types of electoral reform – almost always claiming virtues for these systems that they do not possess. This makes me a bit crazy. It’s hard to get into debate though without getting really technical.

Right now there’s a huge amount of buzz in Ontario about introducing a ranked ballot system at the municipal level. Part of the push for this came from Toronto during the Rob Ford days, when so many people absolutely wanted Ford out, but were worried about vote-splitting between the non-Ford candidates. The preferred ranked balloting system seems to be instant run-off (IRV), where people indicate a first, second, third, etc. preference on their ballot. When the ballots are tallied, a “virtual” run-off is conducted, so the person who received the fewest first-place votes gets eliminated, then all the people who ranked that person first get their second-place votes re-assigned, as though they were first-place votes for the selected candidate. If necessary, this process is repeated until someone eventually gets more than 50% of the votes.

I’m not a big fan of this voting system, because it adds complexity without generating any improvement over plurality rule, which is what we have now. First of all, the idea that people should get more than 50% is just a strange fixation, that has no intrinsic rationale. As soon as you have more than two options, you simply cannot require that a winner get more than 50%. So you have to introduce rules that forcibly constrain the outcome, which will necessarily introduce an element of arbitrariness into what you wind up with. (So while plurality rule “arbitrarily” picks the person who got the most votes and says “winner,” IRV “arbitrarily” picks the person who got the least votes and says “loser,” then reassigns that person’s voters. Both are equally arbitrary, and can generate equally perverse or unintuitive results.)

Anyone who contemplates the Condorcet voting paradox deeply and for long enough should come to realize that insisting on 50% or more on any complex question just doesn’t make any sense. (That is something I have taken a crack at explaining, in something that unfortunately never made it into print.)

Anyhow, in class today I was teaching some of this stuff and got into a discussion of IRV and came up with an example that actually works pretty well at illustrating some of the flaws with that system. For starters though, consider the sort of thing that proponents of IRV like to claim. RaBIT (Ranked Ballot Initiative of Toronto) is an organization that promotes it here in Ontario, and on their website you can read the following:

Instant runoff voting ensures that no one can win with less than 50% of the vote. It eliminates the risk of ‘vote splitting’, where two or more candidates ‘split’ the votes of a certain group. It also means that no one has to vote strategically – you can vote with your heart each time.

This is pretty typical of the claims that get made in support of ranked ballot systems. The first sentence is the usual fixation on the magic number of 50%, which I would like to emphasize, is unmotivated. In a 3+ party system you can only get to that by forcing. The second and third sentences are simply false. So here’s my example – it’s a variation on a standard set-up, used to show how IRV can fail to elect the Condorcet winner (I’ll explain that in a bit). Imagine a simple electorate of 25 people, and three candidates: Ford, Chow and Tory. Their preferences are as follows:

10 people prefer Ford, then Tory, then Chow 8 people prefer Chow, then Tory, then Ford 7 people prefer Tory, then Chow then Ford

You can think about these as fractions of the electorate as well. If you do, then these numbers are not so far off how public opinion was breaking down in an early segment of the Toronto mayoralty race. So Ford is obviously the polarizing candidate: he is popular with some, but dead last in everyone else’s rankings. If you had a plurality rule election, Chow and Tory would split the opposition vote, leaving Ford to win with 10 votes out of 25. This is what opponents of plurality rule don’t like. Apart from the 50% fetish, they don’t like the fact that this scenario gives Chow voters a powerful incentive to vote for Tory, in order to block Ford (and vice versa) rather than “voting their heart.”

Okay, so what happens with IRV? Here Tory gets the least votes, so he gets eliminated, and since all 7 of his supporters ranked Chow second, she gets all those votes once he is eliminated. So she wins the election under IRV rules – by 15 to 10. Seems like a happy outcome, no? This is what motivates a lot of IRV fans.

We need to look a bit more carefully though. The first thing to notices is that Tory is actually the Condorcet winner here – what that means is that in a head-to-head contest against either Ford or Chow, he would emerge the winner. Against Ford, he wins by 15 to 10. Against Chow, he wins even more convincingly, by 17 to 8. So how is it that he doesn’t win the IRV election? It’s because he’s a lot of peoples’ second choice, but not enough people’s first choice. See that’s the arbitrariness in IRV – it picks just one person and bumps that person out, then counts the second-place votes of just that one person.

Many people think that’s an important flaw in IRV – although it is worth emphasizing that it’s also a flaw in plurality, after all, Ford would have won under standard plurality rule. Still, it means that after the election, in which Chow wins (with 50% or more votes!) more than two-thirds of the electorate will be saying to themselves, “wow, I would much rather have had Tory than Chow.” This just illustrates, again, that in order to get over the 50% threshold when there are 3 or more options, you need to do some forcing, which can in turn produce perverse results.

Anyhow, for now then let’s call it a tie between plurality and IRV. So what about the claim that “no one has to vote strategically – you can vote with your heart each time.” Well no one ever has to vote strategically. It all depends how much you want your preferences to prevail. If you look at the IRV outcome, with Chow winning, Ford voters are clearly the most dissatisfied with that outcome (they rank her last). And because Tory wins over Chow in a head-to-head contest, Ford voters have an obvious incentive here to vote strategically (under IRV). Instead of voting for their most preferred candidate (Ford), they should vote for Tory, to ensure that he doesn’t get eliminated, so that he can go on to win over Chow.

So it is absolutely and categorically false to say that IRV eliminates the incentive for strategic voting. All it does is invert it. (This is something that everyone should know from history as well – in 2002 too many French voters failed to vote strategically in the Presidential election — which uses a run-off system — leading the Socialist Party candidate Lionel Jospin to be eliminated in the first round, forcing them all to vote for Jacques Chirac to keep the far right out of power.)

Also, notice that Ford voters have a plausible complaint under IRV that they are being treated arbitrarily. After all, Tory lost the election, and his voters got to have their second-ranked choice count. (Their votes were therefore not “wasted,” to use another highly dubious expression that gets tossed about in these debates). Ford, however, also lost the election, but for some reason, the second-ranked choices of his voters don’t count. They are “wasted.” As a result, his voters get their worst outcome, rather than their second worst outcome, while Tory voters get their second-worst outcome, rather than their worst worst outcome. So Tory voters get more say in the outcome than Ford voters. Why? Because Tory was the bigger loser.

Food for thought. Contrary to the heading of this post, this is not really an argument against ranked balloting. The purpose is just to show that it’s no better than what we have now. It would of course be unfortunate if the system were to be adopted based on the false claims that are being made on its behalf. I also think that the issue of complexity and transparency is important. One significant virtue of plurality rule is that everyone at least understands why the person who won is the winner. But that’s an argument for another day.