Approval voting: Difference between revisions

==== 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

{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.

Approval voting advocates say this is a positive feature of approval voting, saying that the above example "demonstrates that AV responds positively to distinctions voters make among candidates that ordinal preference rankings do not mirror".<ref>{{Cite journal|last=Brams|first=Steven J.|last2=Fishburn|first2=Peter C.|last3=Merrill|first3=Samuel|author-mask3=Merrill, Samuel, III|year=1988|title=The responsiveness of approval voting: Comments on Saari and Van Newenhizen|journal=Public Choice|volume=59|pages=121–131|doi=10.1007/BF00054448}}</ref> That is, approval voting allows voters to better express their degree of approval. One example of such a situation is where we replace the CBA voter preferences with {C: 2.1, B: 2, A: 0}; in this case, it would be appropriate for B to win, as the CBA voters think C and B nearly equivalent.