"Two and a half" candidates

The problem with a lot of voting systems such as Borda, IRV, and (albeit to a somewhat lesser extent) Condorcet is that they were really invented by the following flawed process:

  1. Realize that plurality voting, while it works well if there are two candidates, often performs badly if there are more.
  2. Consider the case of two main candidates A & B, plus an additional "half" a candidate C, that is, a third candidate who has not enough support to have any hope of winning, but enough so that he, by distortionary effects like the "spoiler" and "vote splitting" and cloning pathologies, sometimes can swing the A versus B election in a harmful and annoying way.
  3. Try to invent a new voting system that performs well in these "two and a half" candidate elections.
  4. Proclaim success.

The problem here is the final step "proclaim success." That was not justified. Really, you need to go further by considering the full set of scenarios with three, not two-and-a-half, candidates. E.g. situations where you no longer are allowed to pre-suppose that the third candidate never has a chance to win.

In that case, you quickly see that IRV and Borda no longer are much good and still suffer from spoiler and lesser-evil pathologies (plus more, e.g. IRV suffering from non-monotonicity and winner=loser reversal failures, and Borda suffering weird effects when you eliminate "irrelevant loser" candidates). Condorcet also suffers from these. There are also honest voting can hurt you paradoxes.

Even better, we should even go further still and start to consider three-and-a-half candidate situations. We then encounter the horrific DH3 pathology afflicting Borda and Condorcet.

Range voting performs well throughout the whole space of three-and-a-half candidate situations and is immune to DH3, favorite-betrayal, spoiler, cloning, vote-splitting, monotonicity-failure, and honest-voting-hurts effects.

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