I think it is unfortunate that Instant Runoff Voting (commonly called Ranked-Choice Voting, though it is not the only system for counting ranked ballots) is get

I think it is unfortunate that Instant Runoff Voting (commonly called Ranked-Choice Voting, though it is not the only system for counting ranked ballots) is getting all the buzz these days. Someone posted this link to a very nice explanation, complete with spiffy simulations, then deleted their comment: https://ncase.me/ballot/ https://ncase.me/ballot/ Approval Voting is much simpler to implement and use than IRV, and much less prone to produce anomalous results. More discussion can be found here: https://electionscience.org/ https://electionscience.org/ I think the Marquis de Condorcet got the entire field off on the wrong foot with a conceptual framework in which voting is about expressing preferences between candidates. Voting theorists have tended ever since to think in terms of preferential voting. The result is an unconscious bias to the effect that a voter's evaluations of the candidates tend to be roughly evenly spaced: that the gap between their first choice and their second is roughly equal to that between their second and third, etc. You can hear that bias, for example, in this statement from FairVote.org: [A]pproval voting [has the] practical flaw of not allowing voters to support a second choice without potentially causing the defeat of their first choice. It's true in AV that if you vote for two candidates, your ballot contributes equally to the potential victory of either; you don't get to say which you prefer. But calling this a "flaw" assumes that you couldn't be somewhat indifferent between those two candidates, at least relative to the degree of your dislike for the other(s). That assumption is pervasive, albeit implicit, in the arguments I have seen made against AV, and it is indeed nothing but an assumption. A much better conceptual framework is to imagine an N-cube, where N is the number of candidates, and each voter's position as a point in that cube. Then the problem of designing a voting system becomes that of identifying which corner the mean of the positions of the voters is closest to. In principle a voting system could allow each voter to supply a real number in [0, 1] for each candidate, and we could simply add them up and see which is largest. In practice it makes more sense to quantize the space to some extent. Score Voting gives the voter a set of possible values, e.g., integers in [0, 10]. Approval Voting boils that down to the bare minimum of {0, 1}. (My opinion is that once the electorate is large enough, there is little benefit to allowing more than two choices; the greater quantization noise of AV gets averaged out.) Armed with that, we can now look back at the preferential systems. Is there a way to interpret a preferential ballot in the N-cube framework? Yes, there is. We cut the unit N-cube up along diagonal hyperplanes; for instance, in 3 dimensions (i.e. for a 3-candidate race), the X=Y plane, the Y=Z plane, and the X=Z plane. This gives us 6 prismatically shaped regions. We compute the barycenter of each — the center of mass, under the assumption of uniform density — and look at their coordinates. These turn out to be permutations of [1/4, 1/2, 3/4] — a linear sequence. In short, what falls out of this exercise is equivalent, modulo linear transformation, to the Borda Count. So the Borda Count optimizes for the case in which the voters' positions cluster near the barycenters of those regions: where their evaluation of the middle candidate, in a 3-candidate race, is about halfway between those of the other two. If you listen closely to the arguments presented by preferential-voting advocates, you can hear them assuming that this is likely to be the case. But there's no reason it should be, and in practice I haven't observed that it tends to be.