Editing Approval voting (section)

== Compliance with voting system criteria ==
{{Incomplete table|date=October 2024}}
Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval satisfies different sets of criteria.

There is no ultimate authority on which criteria should be considered, but the following are criteria that many voting theorists accept and consider desirable:
{| class="wikitable" style="text-align:center"
|- style="font-size:90%;"
! '''Voting model:'''!! [[Majority winner criterion|Majority]]!! [[Monotonicity criterion|Monotone]] and [[Participation criterion|Participation]] !! [[Condorcet criterion|Condorcet]] and [[Smith set|Smith]] !! [[Independence of irrelevant alternatives|IIA]] !! [[Clone independence]] !! [[Reversal symmetry]]
![[Sincere favorite criterion|Sincere favorite]]
![[Gibbard's theorem|Strategyproof]]
|-
! [[Impartial anonymous culture|Zero information]]<ref name=":2" />
|{{No}} 
|{{Yes}} 
|{{No}} 
|{{No}} 
|{{No}} 
|{{Yes}}
|{{Yes}}
|{{No}}
|-
!Leader rule<ref name=":3" />{{Explain|date=May 2025}}
|{{Yes}}
|{{Yes}}
|{{Yes}}
|{{No}}
| 
| |
|{{Yes}}
|{{No}}
|-
![[Trembling hand perfect equilibrium|Trembling ballots]]<ref name=":4" />
|{{Yes}}
|{{Yes}}
|{{Yes}}
|{{No}}
|
| |
|{{Yes}}
|{{No}}
|-
! [[Dichotomous preferences|Binary preferences]]<ref name=":0" />{{NoteTag|Assuming voters have only two categories of preference ("approve" and "disapprove"). Voters are indifferent between any two candidates they approve, and between any two they disapprove.{{sfn|Brams|Fishburn|1983|p=16–17}} As a result, a voter's approval of a candidate does not depend on what the other alternatives are.}}
|{{Yes}} 
|{{Yes}} 
|{{Yes}} 
|{{Yes}} 
|{{Yes}} 
|{{Yes}}
|{{Yes}} 
|{{Yes}}
|}