STAR voting: Difference between revisions
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In summary, STAR voting satisfies the [[monotonicity criterion]], the [[resolvability criterion]], and [[reversal symmetry]]. It does not satisfy either the [[Condorcet criterion]] (i.e., is not a [[Condorcet method]]) or the [[Condorcet loser criterion]], although with all-strategic voters and perfect information the Condorcet winner is a [[Nash equilibrium]].<ref>Laslier, J.-F. (2006) [http://halshs.archives-ouvertes.fr/docs/00/12/17/51/PDF/stratapproval4.pdf "Strategic approval voting in a large electorate,"] ''IDEP Working Papers'' No. 405 (Marseille, France: Institut D'Economie Publique)</ref> It does not satisfy the [[later-no-harm criterion]], meaning that giving a positive rating to a less preferred candidate can cause a more preferred candidate to lose.
STAR passes the [[Majority criterion|majority criterion]], and thus is equivalent to [[Choose-one FPTP voting|choose-one FPTP voting]] whenever voters indicate all of their preferences, only in the one- or two-candidate cases (because a majority of voters will have scored their 1st choice higher than all other candidates, and with only at most two candidates in the race, the runoff must include all candidates, so majority's 1st choice will win the runoff), and passes the [[Majority criterion for rated ballots|majority criterion for rated ballots]] in the ''n''-candidate case if the majority gives no support to at least (''n'' - 2) of the candidates (because the majority's 1st choice will have over 50% [[Approval rating|approval]], while the most approval the (''n'' - 2) candidates with the fewest points can get is strictly less than 50%, due to receiving support from at most 50% - 1 of the voters. Thus, the majority's 1st choice will be one of the top two highest-scored candidates and enter the runoff, and then win).
In general, STAR voting passes a weak form of the [[mutual majority criterion]]. This is because whenever at least half of the voters give every candidate in a set of candidates the maximal score and at least all but one candidate not in the set the minimal score, and all candidates not in the set a lower score than any candidates in the set (i.e. a less than maximal score), then they guarantee that at least one of the candidates in the set at least ties to enter the runoff, or ties or wins overall (because every candidate in the set has at least 50% approval, and all but one of the candidates not in the set has at most 50% approval, with only one candidate not in the set possibly having over 50% approval. Therefore, at worst, all candidates in the set are tied with some candidates not in the set to take the second spot in the runoff; if at least one candidate in the set enters the runoff, one of the candidates in the set is guaranteed to at least tie in the runoff, since at least half of the voters scored them higher than the other candidate, unless both candidates in the runoff are candidates from the set, in which case, one of the candidates from the set is guaranteed to win). If a majority does this, they guarantee one of the candidates in the set enters the runoff and wins, rather than only tie to enter the runoff or tie or win overall (because the candidates in the set will have over 50% approval, with the most approval any of all but one of the candidates not in the set possibly getting being less than 50% approval, therefore at least one of the candidates in the set will be among the two highest-scored candidates, and then one of the candidates in the set will win the runoff because either a majority scored them higher than the other candidate, or both candidates in the runoff are candidates from the set).
== Discussion ==
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