Majority: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 12:
There will not always be a majority winner, depending on the context and definition that's used.
== Majority rule/Majority winner - Four Criteria ==
Many methods claim to elect the "majority winner" or work by "majority rule" (See, for example, the [[Center for Voting and Democracy|CVD]]'s talking points re: IRV: [http://www.fairvote.org/irv/talking.htm]). However, [[Condorcet's paradox]] raises an issue: with some groups of voters, no matter which candidate wins, ''some'' majority of the voters will prefer a different candidate.
<div class="blist">
Line 37 ⟶ 35:
</div>
In pseudo-majority methods (like [[Plurality voting|plurality]] and [[range voting]]), a given majority of the electorate '''can''' coordinate their intentions and decide the winner, but this merely postpones the question of how they do this. The stronger majority methods not only enable firmly coordinated majorities to assert themselves, but they allow un-coordinated majorities to '''reveal''' themselves, without any need for prior coordination. Voting methods that facilitate this process of revelation are considered superior to those that do not by majoritarian advocates.
The remaining three categories allow mutual majorities to reveal themselves (in the absence of a self-defeating strategy by supporters of this majority, or something like a [[chicken dilemma]]). Strong majority rule methods not only reveal mutual majorities, but they reveal [[minimal dominant set]]s and [[Condorcet winner|Condorcet winners]] (in the absence of a severe [[Burying|burying strategy]]). This is considered especially valuable because it means revealing possible compromises on divisive issues, thus avoiding a lot of political polarization and strife.
=== Criterion 1 only - Pseudo-Majority Rule Methods===
Line 50 ⟶ 48:
:20 C > A > B</div>
In a plurality election, a clear majority (60-40) prefer both A and B to C. But unless A and B voters know whether to vote for A or whether to vote for B, C may win a plurality of votes. In addition, voters for A and B may play a game of "[[Chicken dilemma|chicken]]", refusing to vote for the other, because they believe their candidate should win.
===Criteria 1 and 2 - Weak Majority Rule Methods===
[[Instant-runoff voting]] (aka IRV, Single-winner [[STV]]) passes the mutual majority criterion. In the example above, IRV enables A and B to coordinate. If all voters voted their sincere preferences, B would be eliminated first, but their votes would transfer to A, resulting in a majority for A.
However, IRV doesn't pass the [[Condorcet criterion]]. In an election with preferences as follows:
Line 62 ⟶ 60:
:40 C > B > A</div>
Looking at this election [[Pairwise counting|pairwise]], there are three majorities: a majority (69 to 31) prefer B to A, a majority (69-31) prefer C to A, and a majority (60-40) prefer B to C. If you were to award the title "majority winner" to any candidate, B has the fairest claim to that title, as (different) majorities of voters prefer B to each other candidate. However, in IRV, B is eliminated first and does not win.
=== Criteria 1,2, and 3 - Intermediate Majority Rule Methods===
Line 72 ⟶ 70:
=== Criteria 1,2,3, and 4 - Strong Majority Rule Methods===
[[
''Derived from an e-mail by James Green-Armytage''
Line 98 ⟶ 96:
== Majority rule criteria based on beatpaths ==
If more voters prefer candidate A to candidate B, then A ''[[Pairwise beat|pairwise beats]]'' B, and the ''strength'' of this pairwise win is equal to the literal number of voters who rank A above B. (It is possible to define ''strength'' in [[Defeat strength|other ways]], but not for this purpose.)
Candidate A has a ''[[beatpath]]'' to candidate B if there is some sequence of candidates such that A is the first candidate, B is the last candidate, and for every pair of adjacent candidates in this sequence I followed by J, I pairwise beats J. The strength of this beatpath is equal to the strength of the weakest pairwise win in this sequence (that is, of one candidate over the following candidate).
A pairwise win or a beatpath is of ''majority strength'' if its strength is equal to more than half of the voters.
Line 114 ⟶ 112:
The most popular method which satisfies these properties is the [[Schulze method]].
== Notes ==
The most common, simple alternative to majority rule is [[utilitarianism]] i.e. in the two-candidate case, rather than electing the majority's preference, elect the candidate that makes voters "happier". Note that while in the two-candidate case, a majority can force its preference with no coordination (i.e. each voter can vote strategically according to their own preference) in utilitarian methods by saying that they get maximal utility from their preferred candidate and no utility for their less-preferred candidate (i.e. [[normalization]]), this doesn't hold when there are more candidates. However, a "utilitarian" [[rated method]] like [[Majority Judgement]] passes the [[majority criterion for rated ballots]], ensuring that a normalizing majority can get their preference.
The most basic criterion for majority rule is that a voting method must pass the [[majority criterion]] in the two-candidate case. However, this means that all majoritarian methods must fail [[Independence of irrelevant alternatives]], because when there is a [[Condorcet cycle]] of more than two candidates, no matter who the voting method elects, all candidates except one that [[Pairwise beat|pairwise beats]] the winner can be eliminated to change the winner i.e. the pairwise-beating candidate who was a loser now wins as a majority's 1st choice. Note that this means that while certain voting methods may nominally pass IIA (i.e. [[Approval voting]], [[Score voting]]) because they fail the majority criterion, they will still fail it if the majority of voters would strategically vote in a two-candidate election to elect their preferred candidate.
Almost all (all?) extensions of majority rule involve the winner of the election [[Pairwise beat|pairwise beating]] at least one other candidate. This can easily be seen by how many majoritarian methods involve [[Runoff|runoffs]], and explains why most such methods pass the [[Condorcet loser criterion]] (with the notable exception of some methods like [[Minimax]]).
Sometimes excluding voters with no preference among any of the named candidates can make a plurality become a majority. Example:<blockquote>49 A>B
48 B>A
3 A=B</blockquote>If ignoring the A=B voters (who have no preferences between any of the candidates marked on at least one ballot), then A is a majority's 1st choice, but otherwise, is simply a plurality's 1st choice.
[[ISDA]] implies several of the criteria mentioned above. When there is a [[Mutual majority criterion|mutual majority]] and a minority with a preference among the mutual majority's preferred candidates, the ISDA-based reasoning for deciding who to elect can be thought of as eliminating everyone not in the mutual majority, checking if there is a new mutual majority set, and then repeating. Taking the above example:
Line 128 ⟶ 136:
40 C > B</blockquote>The 31 A>B>C and 29 B>C>A voters fuse into one coalition with A gone, and so there is now a majority who put B as their 1st choice, and because ISDA implies the [[Majority criterion|majority criterion]], B wins.
A majority is a
See [[:Category:Majority rule-based voting methods|Category:Majority rule-based voting methods]].
[[Category:Voting theory]]
[[Category:Majority-related concepts]]
| |||