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.
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:
25 A| >B>C
34 B| >C>A
6 B>C| >A
35 C>A| >B
The Smith//Approval ranking by the method mentioned in the article is A>C>B, because all 3 candidates are in a cycle and the approvals are A 60 C 41 B 40. But if A drops out of the election, then the Smith//Approval ranking by either method becomes B>C, because B [[Pairwise beat|pairwise beats]] C, and thus becomes the only member of the 1st Smith set, with C being in the 2nd Smith set. So the "remove the winner and recalculate the result" method of finding the order of finish would say that the Smith//Approval ranking should be A>B>C.
Most [[strategic voting]] in these methods revolves around [[burying]] a rival candidate and making your preferred candidate enter the [[Smith set]], where they might win by having more points/approvals.
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