Against ranked ballot electoral systems

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.


Against ranked ballot electoral systems — 16 Comments

  1. Joseph Heath:

    Thank you for the thoughtful article. I will read it again (and perhaps again), as it clarifies some of the objections I have to ranked ballots. Without having studied the matter sufficiently, I have had the feeling that, with ranked ballots, it is the voting system, rather than voters, that elects a representative.

    Clair Culliford

  2. What may be appropriate for a City election in Toronto may not be so in Nova Scotia Provincial and Federal elections. The principals of Parliamentary Democracy have been perverted by the practices of all political parties in their exercise of candidate nomination control and excessive advertising of party and leader. To restore the right and responsibility for constituents to select their representative without outside influence there must be change. Change must allow for representation free from control by others. In your opinion, IRV may be no better in Toronto, but in my opinion, it would be infinitely better in a Canada controlled by party politics.

  3. Hello Professor Heath,

    Thank you for another enlightening post. Please excuse my ignorance, but I am wondering why we might not adopt a cumulative voting scheme where each citizen is allocated a “voting budget” (say, scaled to 1) and the highest number of votes wins. Using the numbers from your example, suppose 10 Ford supporters spend (0.8F, 0.2T), 8 Chow supporters spend (0.8C, 0.2T) and 7 Tory supporters spend (0.8T, 0.2C), yielding the outcome (8F, 9.2T, 7.8C. By switching to a cardinal rather than ordinal system, would voter preferences be rendered more transparent because the “the degree” of strategic voting is individually customized? Would this system also meet the “easily understood” criterion?

    Also, how can one assess the fairness of a voting system without considering which institutional powers are up for grabs? In the case of Toronto, might we say that the RaBIT group is unduly fetishizing the significance of voting systems where equal (or perhaps more) consideration should be given to more mundane governance reforms? [e.g. the 2005 Governing Toronto Advisory Panel Report by Buller, Connell, and Choudhry]

    • Hi Avery. Just quickly, because I’m running off to a meeting: the objections that I’m raising against IRV definitely push in the direction of Borda counting, or a modification thereof (which is what you’re proposing), where everyone’s first, second, third, etc. preferences get counted, assigned a weight, and tallied up. Borda though has its own difficulties (esp. non-transparency, but it also can fail elect the person who would win a straight 50%+ in a conventional election). It also greatly expands the importance of strategic voting (often you’d be foolish to assign the points in a way that reflects your true preferences). So IRV is for many people I think a compromise between the extremes of full Borda and plurality. Anyhow, as I say to my students, this is all just pushing the bump around under the rug. Every electoral system has deficiencies — because fundamentally they are trying to get a majority decision in cases where there may simply be none. I really feel like people need to go back to the Condorcet paradox and stare at those preferences for long enough, until it becomes clear that, in looking for the “will of the majority,” we are searching for something that simply does not exist.

      • As a thought experiment I wonder if it would be possible to model how people actually make voting decisions and feel about various parties taking power which could then be used to develop some hypothetical “optimal” electoral system. My sense is that such a model would require unrealistic assumptions to be made, but it is still fun to conceptualize.

        It seems to me that this model would apply weights to some ranking system with the weights being defined by aggregate data of the population (assuming a normal distribution). This data could be collected though experiments where we figure out what the impact on the individuals “utility” of various parties winning (utility of first choice, vs. 2, 3, 4, least favorite). It seems to me that people often have one party they very much support, and another they would be relatively happy with, and one party in particular they would absolutely hate to be in power.

        Tom might be a fan of the conservative party so if they win his happiness associated with the result of the election is 100%, if the liberals win he might be okay with this outcome (so 50% utility), but if the NDP won he might be negatively impacted (let’s say -50%).

        We could hypothetically make the vote amounts weight to 1 so that he effectively has one vote. This would mean that a party with 10 million “votes” has an effectively equivalent support of 10 million instead of that amount saying the party is their first choice.

        I added the example of negative utility because it seems to me this is how people think about voting (e.g. wanting anyone but the conservatives to win). What are your thoughts on negative voting? It seems to me that this is a critical element missing in electoral systems (in the goal of reflecting the views of citizens) and I suspect its largely because it can probably be exploited by strategic voting.

  4. The flaw in the IRO System you describe, is not using it as the voter expects it to be used! If you are RANKING candidates, then USE the rankings! As a scientist, just looking at your example, it is apparent to me that Tory is the guy that most of the people would care to have. And I can prove it. Consider this mathematical illustration of your example:
    There are three candidates (n=3). Voters rank the candidates first (A), second (B) and third (C). So you need to attach “value” to those rankings to reflect the preferences of the voters: A= n, B=(n-1), C=(n-2). Then your voting result shake out like this:
    Ford = [10 x n]+[8 x (n-2)]+ [7 x (n-2)] = 30+8+7 = 45
    Chow = [10 x (n-2)]+[8 x n]+[7 x (n-1)] = 10+24+14 = 48
    Tory = [10 x (n-1)]+[8 x (n-1)]+[7 x n] = 20+16+21 = 57 Winner
    The candidate with the larger number wins. You eliminate the need for the arbitrary 50% rule. It would be easy to have computers make these calculations and the people would get their most favourable candidate.

  5. I believe you’re conflating a ranked ballot with the IRV system. A ranked ballot, combined with an assumption of transitive preferences on the individual level, is sufficient to evaluate an election using any of the equivalent Condorcet methods.

    Additionally, IRV certainly has its flaws, but it’s not clear to me that its flaws are greater than that of first past the post. In a three-candidate election such as this one, I believe that IRV can return the non-Condorcet winner only under a subset of the circumstances where FPTP would also fail. The four-or-more-candidate election can have different sets of failures, but elections with 4+ viable candidates are also less common in Canadian politics.

    • Thanks. Your post on reddit was a bit more clear, so I’ll copy it here:

      This post is a bit misleading. It confuses a ranked ballot, which is a means of expressing preferences, with IRV elections, which is a means of turning those ranks into a single winner.
      A ranked ballot is also sufficient for a full Condorcet count, to evaluate those pairwise preferences if we presume that individual voters have transitive preferences (that is, ranking A then B then C means that the voter prefers A to B, B to C, and A to C.)

      It would be nice if everyone stuck to this vocabulary, so a ranked ballot is a type of ballot, which can then be subjected to various different aggregation methods. But as Alessandro pointed out, I was just using the terminology that has become current in Ontario (e.g. in the legislation that I linked to).

      The wonk in me is attracted to the Condorcet methods. The fact that these get no political traction is, I assume, due to their non-transparency (to the average voter). If there are other reasons I would be interested to hear them.

      Your claim about the IRV failures being a subset of the FPTP failures is something I’ve often wondered about. I’m not enough of an expert to know, and am too lazy to look it up, so if you can dig up a literature reference I would be grateful.

  6. I’d like to put in a request for a post on FPTP vs PR systems, which you’ve mentioned in the past is due to your preference for majority governments.

  7. The 2002 French election does not illustrate IRV’s flaws. In fact, IRV would almost certainly have prevented far right candidate Jean-Marie Le Pen from reaching the final round in 2002.
    In France, voters choose one candidate. If no candidate wins 50% or more of votes in the first round, the top two candidates face off in a final round two weeks later.
    If France had an IRV system in which voters could rank candidates in order of preference, Lionel Jospin would almost certainly have been the finalist against Jacques Chirac instead of Le Pen in 2002. Under IRV, French voters would vote once, not twice. Jospin likely would have lost to Chirac, but we`ll never know.
    In Michel Houellebecq`s apocalyptic novel Soumission, he imagines a Muslim fundamentalist being elected president of France after defeating in the second round Le Pen’s daughter Marine, who now leads the National Front. Houellebecq’s scenario is theoretically possible. With many candidates, National Front and Muslim party candidates could end up as the top two in the first round. But, the solution is to change the French system to IRV.

    [MODERATOR: This comment was amended in accordance to the wishes of the commenter.]

    • Well Jospin received fewer first-place votes than Le Pen, so with just the three candidates IRV would have eliminated him as well. I take it what you are thinking is that he, unlike Le Pen, would have been the second choice of a lot of the 4th, 5th, 6th, etc. lowest candidates, and so the fact that IRV eliminates people sequentially (unlike the French system) means that, by the time it was down to only three candidates, Jospin would have received enough transferred votes from those who were eliminated that it would have moved him ahead of Le Pen. Fair point.

  8. Thinking about the Rob Ford example, I would suggest that Instant Runoff has a significant benefit compared to FPTP: it makes it much easier to exercise the “Gong Show” aspect of the election process, getting rid of an unsatisfactory incumbent. If a large majority of voters are dissatisfied with the incumbent, no coordination is required — they just need to rank him or her last.

    In a parliamentary system like ours, where a majority government has a great deal of freedom of action, I would suggest that making it easier to alternate governments is a benefit rather than a cost.

    Whether that’s enough to offset the cost in transparency and complexity is another question, of course. I think it’s not too complicated to understand, compared to the Single Transferable Vote proposal that failed in BC a few years back; and Australia has used it successfully for a long time. But FPTP is certainly simpler.

  9. Prof. Heath,

    This is the best argument against IRV I’ve read. Let me respond with my perspective as an IRV advocate.

    To successfully advocate for something you need to agitate. To agitate you need to make an appeal to an individual’s values, and one of the easiest ways to agitate people into opening up to the idea of IRV is to make the admittedly simplistic point that electing a leader with anything less than 50% support is sub-optimal in terms of democratic outcomes. People feel that on a gut level.

    But most of us advocating for IRV in Toronto are doing so for far more pragmatic reasons that extend beyond the goal of making perfectly fair group decisions to a larger goal of achievable, incremental democratic reform. The political reality is that IRV is the most achievable form of elections-based democratic reform in Toronto. People get it, it’s easy to sell, councillors are okay with it, and it’s incrementally better than FPTP in the sense that it changes the nature of the campaigns themselves, by which I mean that the elimination of the FPTP type of vote-splitting accomplishes two very positive things: (1) it softens the incentive to play full-on negative wedge politics and (2) it helps reduce both the incumbency advantage and the exclusionary forces that lead to the nomination of establishment candidates. In other words, you change the incentives so that campaigns are more positive and consensus based, and you open up the field to a broader range of diverse candidates.

    In theory, this should result in a city council with greater policy making capacity. In practice, the introduction of IRV in American municipalities has lead to greater voter participation and engagement and a greater diversity of candidates and election winners. Surveys have also shown that the public has found IRV campaigns to be more positive and engaging, with a greater focus on issues vs. slogans.

  10. I agree with Samuel Hammond’s comment: I would be very interested in your thoughts on proportional representation vs. first-past-the-post.

  11. I’m a big fan of electoral reform, moreso as it relates to federal and provincial legislatures rather than as it relates to electing mayors – I will support any of the current mainstream alternatives to FPTP, including IRV.

    I used to be roughly equally supportive of all alternatives to FPTP, but recently IRV has become my clearly least favourite alternative, but not for the reasons outlined here.

    Instead I’ve been influenced by some work that was done over on, where IRV was applied to recent federal election vote tallies, and the results were more “different” than I was prepared to accept – IRV seems to overcompensate for the main flaw that I see with FPTP.

    While the Condorcet principle does influence my thinking, I certainly can’t make that criteria an extremely important criteria in my evaluation of voting systems. Ie in the Ford/Tory/Chow scenario used in the post, 15 of 25 people put Ford in third place, and apparently with great certainty. In my view that should mean something.