Wasted votes: Difference between revisions
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For voting methods that pass the participation criterion, one possible way to define the number of wasted votes in an election under that voting method is fallowing:
The number of wasted votes is equal to number of votes in the largest possible set of votes such that for any possible subset of votes in this set, removing those votes cannot change the election result. (footnote 1)
When this mathematical definition of the number of wasted votes in an election is applied to FPTP, it produces the same count for the number of wasted votes the procedure above produces.
However this definition does have it's limitations: in voting methods that do not pass the participation criterion, such participation failures can drastically deflate the tally of the number of wasted votes. Example: consider the fallowing voting method: voters cast single preference votes and if there are an odd number of votes cast, the candidate with the most votes wins, otherwise the candidate with the 2nd most votes wins. Under this definition of wasted votes, there are no wasted votes under this method because every vote changes the winner. However not every vote changes the winner in a way that benefits the voter who casted it, and if a voter casts a vote that worsens the election result from their perspective, then they might as well not even
== 2nd extension: Calculating the number of wasted votes under other voting methods that pass the participation criterion ==
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The number of wasted votes is equal to number of votes in the largest possible set of votes such that for any possible subset of votes in this set, removing those votes cannot change the election result to one that is preferred by all the voters who's votes are in the subset.
Note that for methods that allow voters to omit preferences between candidates, calculating this metric exactly (footnote
== Footenotes ==
Footnote 1: An election result in which 2 possible election outcomes are tied is a different election result then one in which there is only one winning election outcome (one winning candidate in a single winner election).
Footnote 1: It can still be approximated by making assumptions about for any two candidates A and B, the probability that a voter that rates/ranks them equally prefers A over B vs. B over A)▼
▲Footnote
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