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== Condorcet ==
It is arguable whether a voter can have maximal preferences between more than one transitive pair of candidates. Utilitarianism says if you maximally prefer A to B, then you must not prefer B to C, while Condorcet says you can for as many pairs as you like. An interesting method that goes one step away from utilitarianism towards Condorcet is "3-slot/tiered Smith//Approval": the voter may rank each candidate either 1st, 2nd, or last, and may approve either only their 1st choices, or also their 2nd choices. With only 1 tier, this would reduce to regular Approval voting.
Here are some facts about how various voting methods interact with Condorcet winners:
* [[FPTP]] and any [[majority criterion]]-satisfying voting method will elect a CW with a majority of 1st choices
* [[IRV]] and any [[dominant mutual third]]-passing system will elect a CW with over 1/3rd of 1st choices (or who can attain that after eliminations)
* Any [[:Category:Runoff-based voting methods|Category:Runoff-based voting methods]] will elect a CW who is in the runoff (supposing voters could express their preference for the CW)
* [[Approval voting]] and [[Score voting]] (and most [[cardinal method]]<nowiki/>s) have some kind of strategic equilibrium for the CW, especially if they are a [[Majority Condorcet winner]].
A basic reason to prefer [[:Category:Condorcet-cardinal hybrid methods]] over most other Condorcet methods (or at least, over the [[:Category:Defeat-dropping Condorcet methods]]) is that they allow the voters who prefer a CW to defend that candidate without needing to do Favorite Betrayal as much (though there may be errors with this analysis). As a general example, suppose there are two main candidates, with one being the CW, and there are some 3rd parties without about half as many pairwise votes in favor of them as the main candidates. The voters who prefer the losing main candidate can bury the CW under the minor candidates, and in the ensuing cycle, the non-CW main faction will win. There isn't anything that voters who prefer the CW as 1st choice can do to fix this, but the voters who rank a 3rd party 1st and the CW above the non-CW main candidate can do FB to prevent their favorite candidate from pairwise beating the CW. This ends the cycle and allows the CW's pairwise victory over the other main candidate to take precedence again. In rated Condorcet methods, however, FB isn't quite as necessary if the CW [[majority-beat]]<nowiki/>s the non-CW main candidate; this is because those who prefer the CW can do [[Min-max voting]] to give the CW maximal points by the majority and the non-CW no support by a majority; this will guaranteeably give CW enough points to win. More specific example of this at <ref>https://www.rangevoting.org/CondStratProb.html</ref> and some explanation of how majorities can force their preference in rated methods in the [[Approval voting]] article.
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