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Approval voting
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==== Dichotomous preferences ==== Approval avoids the issue of multiple sincere votes in special cases when voters have [[dichotomous preferences]]. For a voter with dichotomous preferences, approval is [[Strategyproofness|strategyproof]].{{sfn|Brams|Fishburn|1983|p=31}} When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval is guaranteed to elect a Condorcet winner.{{sfn|Brams|Fishburn|1983|p=38}} However, having dichotomous preferences when there are three or more candidates is not typical. It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters.<ref name=probstrat/> Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group.{{sfn|Brams|Fishburn|1983|p=16–17}} A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences. Being strategy-proof for a voter means that there is a unique way for the voter to vote that is a strategically best way to vote, regardless of how others vote. In approval, the strategy-proof vote, if it exists, is a sincere vote.{{sfn|Brams|Fishburn|1983|p=29}}
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