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 the [[Condorcet criterion]] (i.e., is not a [[Condorcet method]]), 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, like any voting method with a final [[runoff]], passes the [[Condorcet loser criterion]], so long as voters indicate their preference for candidates other than the Condorcet loser. 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.

=== Majority-related criteria ===

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).

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== Precinct summability ==

STAR voting can most simply be counted by first adding up the scores, and then doing a second round of tallying where the two highest-scoring candidates are compared on every ballot. It can be made precinct-summable (countable in one round) by using [[pairwise counting]] to determine who voters prefer in every possible automatic runoff. ~~Example:~~

STAR voting can most simply be counted by first adding up the scores, and then doing a second round of tallying where the two highest-scoring candidates are compared on every ballot. It can be made precinct-summable (countable in one round) by using [[pairwise counting]] to determine who voters prefer in every possible automatic runoff.

=== Comprehensive example ===

Suppose there are 3 precincts, with 5 voters in each of them, and there are four "candidates": White Chocolate, Dark Chocolate, Milk Chocolate, and Chocolate with Almonds. In Precinct 1, we have the following votes:

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(Note that precinct-summability becomes more complex when dealing with write-in candidates. See [[Pairwise counting#Notes]] for ideas on how to deal with this; essentially, the most comprehensive way is to count the number of voters who score a candidate, filling in that number of votes preferring that candidate above each other candidate in a head-to-head matchup, and subtract a vote from each head-to-head matchup where the voter scored another candidate above or equal to the scored candidate. Since write-ins so rarely win, in practice, it is possible to simply record how many voters scored the write-in and what score they gave that candidate, and only do a second round of tallying in the rare case that the write-in makes it to the automatic runoff. If it is predicted that the write-in may garner significant support, then the election officials can be told to record this candidate's head-to-head matchups as well.)

=== Alternative examples ===

More complex example of the STAR result being calculated from precinct-summable data (example modified from https://star.vote/txzfc3c9/):

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[[Instant Runoff Normalized Ratings|IRNR]] is related to STAR in the same way that [[IRV]] is related to [[Top-two runoff]].

Given that STAR is an automatic form of Score voting + Runoff, one can also create an automatic "[[Approval voting]] + Runoff" method by allowing voters to rank or score candidates, and then indicate an [[Condorcet//Approval|approval threshold]] for a particular rank or score such that they'd approve all candidates at that same rank or score or a higher rank or score, and then use the ranks or scores to figure out which of the two most approved candidates is preferred by a majority

Given that STAR is an automatic form of Score voting + Runoff, one can also create an automatic "[[Approval voting]] + Runoff" method by allowing voters to rank or score candidates, and then indicate an [[Condorcet//Approval|approval threshold]] for a particular rank or score such that they'd approve all candidates at that same rank or score or a higher rank or score, and then use the ranks or scores to figure out which of the two most approved candidates is preferred by a majority.

== Notes ==

STAR fails [[cloneproofness]], because adding a clone of the Score winner guarantees the original Score runner-up can never win. However, note that this means that at most one clone of each candidate has incentive to run, whereas many other clone-positive methods incentivize many clones to run. Further, some [[rated method]] advocates actually prefer that STAR fail cloneproofness in this way, since it means that it may give more [[Utilitarianism|utilitarian]] results as more candidates run.

==See also==