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Wasted votes: Difference between revisions
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The concept of a wasted vote is related to [[Vote splitting]] and other similar
== Calculating the number of wasted votes in a FPTP election ==
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Additionally, since in order to win an election the winner need only have more votes then their opponent (and as FPTP elections are winner take all, they cannot win extra seats for beating their opponent by a large margin) the number of votes cast for the winning candidate above the threshold of votes needed to surpass the candidate with the 2nd most votes are also considered wasted.
Finally, in an uncontested election where there is only one candidate, that threshold becomes 1 (thus all but a single vote are wasted) since as long as at-least one person votes for the single candidate, it does not matter how many additional votes they receive in order to win the election
== 1st generalization: Calculating the number of wasted votes under deterministic non-delegated voting methods that pass the participation criterion ==
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 as follows:
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)
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== 2nd generalization: Calculating the number of wasted votes under all deterministic non-delegated voting methods ==
A 2nd possible generalization of the previous generalized definition of wasted votes to methods that do not pass the [[
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 if none of the voters who's votes are in that subset prefer the new election result to the old one.
Note that for methods that allow voters to omit preferences between candidates, calculating this metric exactly (footnote 2) requires knowing not just all of the votes used in the election to calculate, but also the preferences of all of the voters casting those votes. This means that this metric is no-longer defined by just the raw votes, as under such methods, multiple elections in which the exact same votes are cast can have different numbers of wasted votes depending on the voters casting those votes.
== Wasted votes in weighted-vote multi-winner systems ==
Some voting systems, like Chamberlin-Courant and [[Evaluative Proportional Representation]], return an assembly (i.e. multiple winners) with each winner having a weight. Each winner has a weighted vote in decisions made by the assembly - a generalization of having an integer number of seats. If each voter's ballot influences the weights of the winners to some slight degree, then it can be argued that no vote is wasted because all of them have an effect on the outcome.
However, such changes need not alter the outcomes of the assembly's votes. For instance, if changing a ballot changes the weights in a two-winner assembly from (0.49, 0.51) to (0.48, 0.52), and the assembly uses majority rule, the second winner can force the outcome in both cases.
== Footnotes ==
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==See also==
*[[Vote splitting]]
*[[Exhausted ballot]]
[[Category:Voting theory]]
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