Mutual majority criterion: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 1:
The '''Mutual majority criterion''' is a criterion for evaluating [[voting system]]s. Most simply, it can be thought of as requiring that whenever a [[majority]] of voters prefer a set of candidates (often candidates from the same political party) above all others (i.e. when choosing among ice cream flavors, a majority of voters are split between several variants of chocolate ice cream, but agree that any of the chocolate-type flavors are better than any of the other ice cream flavors), someone from that set must win (i.e. one of the chocolate-type flavors must win).
It is an extension of (and also implies) the [[Majority criterion|majority criterion]] for sets of candidates.
{{definition|If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.}}▼
The mutual majority criterion is implied by the [[Smith criterion]].
[Merge: The mutual majority criterion says that if a majority of voters unanimously vote a given set of candidates above a given rating or ranking, and all other candidates below that rating or ranking, then the winner must be from that set.]▼
▲; Systems which pass:
: [[Borda-Elimination]], [[Bucklin voting|Bucklin]], [[Coombs]], [[IRV]], [[Kemeny-Young]], [[Nanson (original)]], [[Raynaud|Pairwise-Elimination]], [[Ranked Pairs]], [[Schulze method|Schulze]], [[Smith//Minimax|Smith//Minmax]], [[Descending Solid Coalitions]], [[Majority Choice Approval]], any [[:Category:Smith-efficient Condorcet methods|Smith-efficient Condorcet method]], [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]]
; Systems which fail
: [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]]
==
▲It can be stated as follows:{{definition|If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.}}
Voting methods which pass the majority criterion but not the mutual majority criterion (some ranked methods) possess a spoiler effect, since if all but one candidate in the mutual majority drops out, the remaining candidate in the mutual majority is guaranteed to win, whereas if nobody had dropped out, a candidate not in the mutual majority might have won. ▼
▲
== Notes ==
The mutual majority criterion doesn't apply to situations where there are two largest "sides" if enough voters are indifferent to the two sides. <blockquote>51 A>C▼
▲Voting methods which pass the majority criterion but not the mutual majority criterion (some ranked methods fall under this category, notably [[FPTP]]) possess a spoiler effect, since if all but one candidate in the mutual majority drops out, the remaining candidate in the mutual majority is guaranteed to win, whereas if nobody had dropped out, a candidate not in the mutual majority might have won.
▲The mutual majority criterion doesn't apply to situations where there are
49 B
10 C(>A=B) </blockquote>The last line "10 C(>A=B)" should be read as "these 10 voters prefer C as their 1st choice and are indifferent between A and B."
Even though candidate A is preferred by the (same) majority of voters in [[Pairwise counting|pairwise matchups]] against B (51 vs. 49) and C (51 vs. 10), candidate A technically is not preferred by an absolute majority (i.e. over half of all voters), and C would beat A in some mutual majority-passing methods, such as [[Bucklin]]. A "mutual plurality" criterion might make sense for these types of situations where a [[plurality]] of voters prefer a set of candidates above all others, and everyone in that set [[Pairwise counting|pairwise beats]] everyone outside of the set; this mutual plurality criterion implies the mutual majority criterion (because a majority is a plurality, and anyone who is preferred by an absolute majority over another candidate is guaranteed to pairwise beat that candidate, thus all candidates in the mutual majority set pairwise beat all other candidates). The [[Smith criterion]] implies this mutual plurality criterion (because the Smith criterion implies that someone from the smallest set of candidates that can pairwise beat all others must win, and this smallest set must be a subset of any set of candidates such that that anyone in the set of candidates can pairwise beat all candidates not in the set).
25 B
49 C</blockquote>Despite B being preferred by an absolute majority over C, and the only candidate preferred by any voters in that absolute majority over or equally to B being A, the mutual majority criterion doesn't guarantee that either A or B must win. It has been argued that to avoid the [[Chicken dilemma]], C must win here
[[Category:Voting system criteria]]
| |||