Approval voting: Difference between revisions

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==== Indeterminacy of Outcome ====

In certain elections, honest voters merely varying the cut-off where they give approval can lead to any particular candidate winning.<ref>{{Cite journal|last=Saari|first=Donald G.|last2=Jill|first2=Van Newenhizen|year=1988|title=The problem of indeterminancy in approval, multiple, and truncated voting systems|journal=Public Choice|volume=59|issue=2|pages=101–120|doi=10.1007/BF00054447|jstor=30024954}}</ref> Consider an election with 15 voters deciding among three candidates (A, B, C). The voters have the preferences

{|

{A: 2, B: 1, C: 0} × 6

|{A: 2, B: 1, C: 0} × 6

|-

⚫

{B: 2, C: 1, A: 0} × 5

{C: 2, B: 1, A: 0} × 4.

|{B: 2, C: 1, A: 0} × 5

|-

⚫

|{C: 2, B: 1, A: 0} × 4.

|}

Even if all voters vote honestly, any candidate can win, dependent on which voters choose to approve a second candidate. If no voters approve of a second candidate, A wins. If CBA voters approve of C and B, and the other voters only approve their favorite, then B wins. If all BCA voters approve of B and C, and the other voters only approve their favorite, then C wins. Thus, as noted above, in such elections, voters have an incentive to strategically vary the number of candidates they approve of.