score voting is king, condorcet not so much
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Many people treat Condorcet's VSE edge as settled. It isn't. It rests on two assumptions that quietly do all the work: that voters perceive viability perfectly, and that they mostly vote honestly. Relax either and it collapses.
I took Quinn's VSE engine and made one change. His runs let strategic voters read the true standings exactly, so their strategy is always aimed at genuinely weak candidates and barely dents Condorcet. I replaced that with a viability signal that's 50% true, 50% random, since real electorates misjudge who can win all the time (a Democrat written off in a red state, etc.). Now strategy sometimes buries a candidate who'd actually have won, the favorite-betrayal failure cardinal methods are immune to. (STAR voting technically isn't, but voters strategize intuitively would have no idea how STAR actually works, in real life—so just assume it's score voting.)
Then I rigged the rest in Condorcet's favor: cardinal methods (0–5 score, approval, STAR) run at 90% strategic; Condorcet methods get a very favorable 10% and a favorable 40% strategic. Maximum strategy against the cardinal methods, little against the ordinal ones.
Spatial bimodal electorate (two ideological camps, candidates along the axis):
method regime VSE Score (0–5) 90% strat 0.946 Ranked Pairs 10% strat 0.932 Schulze 10% strat 0.929 Approval 90% strat 0.924 Ranked Pairs 40% strat 0.918 STAR 90% strat 0.918 Schulze 40% strat 0.913 Polya / urn electorate (Quinn's default):
method regime VSE Score (0–5) 90% strat 0.876 Ranked Pairs 10% strat 0.870 STAR 90% strat 0.865 Approval 90% strat 0.858 Schulze 10% strat 0.855 Ranked Pairs 40% strat 0.854 Schulze 40% strat 0.846 Even with the deck stacked this hard, fully strategic Score beats every Condorcet configuration on both models, including the most favorable. And once a realistic 40% of Condorcet voters strategize, strategic Approval passes Ranked Pairs on both and beats Schulze across the board.
The spatial model, if anything, favors Condorcet: it puts voters and candidates on a real ideological axis where head-to-head comparisons mean the most. Score wins there anyway.
The strategy model is just frontrunner polarization, what plurality voters already do reflexively: "I don't think X can win, so I'll bury them and rank the viable compromise first." Biden > Warren > Trump, Cornyn > Talarico > Paxton. The honesty-and-perfect-viability assumptions are the only thing holding Condorcet's edge up, and neither survives contact with how people actually vote.
(±95% CIs ≈ 0.005 spatial, 0.009 Polya. Built on Quinn's engine with a half-random viability signal; happy to share the patched code.)
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@clay Some interesting stuff there. It's been said that score suffers worse with one-sided strategy than other methods. That is - if the supporters of one candidate strategise more than the supporters of another, then the result will be more skewed (favour the strategisers) under score than some other methods. Would you agree with that, and do you see it as a problem?