Weighted positional method: Difference between revisions

Rewrite notes, add part about criterion failures.
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(Rewrite notes, add part about criterion failures.)
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With more work, the examples can be generalized to any number of candidates greater then 3 by assuming every voter ranks all the other candidates in the same order.
 
== NotesGeneralizations ==
It is possible to view [[Approval voting]] and [[Score voting]] as a more general weighted positional method, akinwhere toeach pluralityvoter ([[FPTP]])has wheresome votersfreedom mayin rankwhat candidates<math>a</math> vector to equallychoose. [[ScoreFor voting]]Approval, isthe thenvoter's <math>a</math> furthervector generalizationhas ofvalue the1 entirefor weightedevery positionalapproved methodcandidate categoryand where0 votersotherwise are- allowedi.e. 1 down to givethe differingvoter's amountsapproval ofcutoff supportand tothen 0 below - while for Score voting, the candidatesvoter theydirectly "rankspecifies 1st"<math>a</math>.
 
As a result, [[Score voting]] fails every criterion that at least one weighted positional method fails, because the voters could just happen to rate the candidates the same way a weighted positional method would score them.
 
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