Instant-runoff is a terrible voting system and should never be used, see http://zesty.ca/voting/sim/ . Approval voting is simpler and better. Condorcet is best except that it is somewhat complicated.
I had dug into the math behind this at some point and recall that Borda was argued (e.g. by Saari's "Basic Geometry of Voting") to be the "best" in the sense of invariance under impossible-to-satisfy group preference cycles (A > B > C >A), with Condorcet a close second.
If you have any references arguing for Condorcet over Borda, I would be very interested to read them.
Edit: For people unfamiliar with the jargon, Borda is ranked-list voting, with the winner being the candidate with the highest average rank. Condorcet is pairwise-comparison voting with the winner being the candidate that wins the highest fraction of pairwise comparisons.
In this jargon, "first past the post" systems select the person with the highest fraction of being ranked first; this is argued in the literature to be intimately tied to the two-party dominance in the US.
_dps|14 years ago
If you have any references arguing for Condorcet over Borda, I would be very interested to read them.
Edit: For people unfamiliar with the jargon, Borda is ranked-list voting, with the winner being the candidate with the highest average rank. Condorcet is pairwise-comparison voting with the winner being the candidate that wins the highest fraction of pairwise comparisons.
In this jargon, "first past the post" systems select the person with the highest fraction of being ranked first; this is argued in the literature to be intimately tied to the two-party dominance in the US.