Condorcet-cardinal hybrid methods: Difference between revisions
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whereupon '''A wins''' using every one of these Condorcet methods: Tideman [[ranked pairs]], Basic Condorcet, [[Simpson-Kramer|Simpson-Kramer min-max]], and [[Schulze]] beatpaths. (Success!)<ref>{{Cite web|url=https://rangevoting.org/CondStratProb.html|title=With strategic voters, Condorcet voting can fail to elect Condorcet Winner|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref></blockquote>This problem is averted with [[Smith//Score]] or [[Smith//Approval]] if the C>A voters (voters who prefer C to A) move their [[approval threshold]] between C and A, because they can make C have 11 approvals to A's 10. Essentially, they can re-simulate the pairwise matchup between C and A (where C has 11 votes to A's 10) using [[Strategic voting#Definitions|min-max]] strategy to fix the result. This isn't as easy with [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] or [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]]; for the most part (ignoring things like the [[Tied at the top rule]], etc.), the only way for C>A voters to fix the result is to [[Favorite Betrayal|Favorite Betray]]. In some sense, this all takes advantage of how rated methods have Nash [[Equilibrium|Equilibriums]] on the Condorcet winner. Another thing to note about these methods' resistance to Favorite Betrayal is that even if voters do decide to Favorite Betray, they can still give a high rating to their favorite candidate; this means that even if, in a given election, a candidate fails to win due to Favorite Betrayal, it is still easy for voters to determine approximately how much support that candidate has (in addition, of course, to observing how many votes the candidate gets in head-to-head matchups against weak candidates, which gives a rough measure of how many voters support that candidate at all). Therefore, they can figure out whether they don't have to Favorite Betray in the next election.
One way to demonstrate the result in a rated Condorcet method election is to organize the candidates by [[Smith set ranking]] (if using a Smith-efficient hybrid) and then within each Smith set, organize the candidates by number of points/approvals, showing this number in the cell comparing each candidate to themselves. Also, a candidate's quality can be indicated simply by referring to which Smith set they were in and how many points they got; for example, with [[Smith//Approval]], a candidate in the 5th Smith set (the Smith set when candidates in the Smith set are removed, with the new candidates in the Smith set forming the 2nd Smith set, etc.) with 54 approvals would be considered worse than anyone in the 1st through 4th Smith sets, as well as anyone in the 5th Smith set with more than 54 approvals. However, note that these methods are best used to indicate which candidate came closest to being the winner when all candidates remain in the election; the common "repeatedly remove the winner and recalculate the election result" method of finding the [[order of finish]] can yield a different result. 3-candidate example:
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