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STEPHEN A BLOCH's avatar

Thanks for this essay. To put your criticism in different words, Instant Runoff Voting pays much more attention to the top of your ranking than to the bottom, and in this sense is only a slight improvement over single-vote plurality. Both systems favor candidates with passionate supporters, ignoring their equally-passionate opponents. Both systems aim to maximize the number of voters extremely happy with the election results, with no concern for minimizing the number of voters extremely unhappy with the election results.

That last point matters, because people extremely unhappy with election results are the ones who turn to violence, or (less extremely) give up on voting. A divisive candidate whom a substantial fraction of the people despise or fear will have a more difficult time governing (and is more likely to do it oppressively) than a consensus, compromise candidate whom most people find tolerable. Indeed, a candidate who was elected through compromise is probably more likely to govern that way, rather than seeking out performative conflict and saying "my way or the highway".

One could go to the opposite extreme, to "single-vote anti-plurality voting", where voters cast a single vote against the candidate they most dislike, and whoever gets the fewest anti-votes wins. I don't think anybody seriously proposes that approach, because in an election with more than a few candidates, it can easily elect a candidate nobody knows anything about, one with no qualifications except the lack of a record.

My standard example to distinguish these is the 4-candidate scenario in which A, B, and C split the first-place votes while D gets all the second-place votes. In single-vote plurality, one of A, B, or C wins by the luck of the draw. In IRV, D is immediately eliminated for getting no first-place votes, and one of A, B, or C wins narrowly depending on which one is the other two's supporters' third-place choice. In Condorcet, D wins because 2/3 of voters prefer D to each of A, B, and C. Anti-plurality will probably elect D, but D could be tied with any of the others.

Another commonly-studied voting system, as you probably know, is the Borda count, in which your first choice in a 4-candidate race gets 3 points, your second choice 2, your third choice 1, and the candidate with the most points wins. In the above scenario, each of A, B, and C gets at most 1-2/3 points per voter while D gets 2 points per voter, so again D wins, as in Condorcet.

Both Borda and Condorcet systems are symmetrical, in that they pay exactly as much attention to upvotes as to downvotes. But where Condorcet only cares how many voters prefer Anne over Bob at all, Borda also cares _how strongly_ they prefer Anne over Bob, as measured by _how far_ Anne is above Bob in a ranking. Where single-vote plurality (and anti-plurality) only ask very little information from the voters, and IRV asks for more but intentionally throws away as much of it as possible, Borda and Condorcet both ask for full rankings but Borda uses slightly more of that information than Condorcet does.

In rare cases, Borda goes farther than Condorcet in favoring consensus candidates over divisive ones. Consider the 3-candidate scenario in which 51% of voters rank A > B > C, while 49% rank B > C > A. A is the Condorcet winner, but 49% of voters really hate A and really like B, while nobody hates B, so the Borda election goes to B.

I'd be interested to hear your thoughts on Condorcet vs. Borda. I suspect we're in agreement that either one would be a huge improvement over single-vote plurality, and a substantial improvement over IRV.

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