Plurality criterion: Difference between revisions
m
no edit summary
imported>KVenzke No edit summary |
mNo edit summary |
||
| (4 intermediate revisions by 2 users not shown) | |||
Line 1:
<p>[[Plurality voting|First-Preference Plurality]], [[Approval voting]], [[IRV]], and many [[Condorcet method|Condorcet methods]] (using [[winning votes]] as defeat strength) satisfy the Plurality criterion. [[Condorcet method|Condorcet methods]] using margins as the measure of defeat strength fail it, as does [[Raynaud]] (using either winning votes or margins as the measure of defeat strength), and also [[Minmax|Minmax(pairwise opposition)]].
When the Plurality criterion requires that ''B'' not be elected, it means that even if all the voters who gave ''B some'' ranking were to elevate him to the top position, he would still not be the [[Plurality voting|First Preference Plurality]] winner.
Line 14:
It is conceivable that if ''B'' were elected, voters might not consider this a legitimate result.
One connection the Plurality criterion has to most voting methods is that it implies that when all voters bullet vote (in Score voting, also max-scoring the bullet-voted candidate), the candidate bullet voted by the most voters (i.e. the [[FPTP]] winner) will win. Most voting methods do this. An extension of this is to check whether, for a given voting method, when all voters vote some candidates 1st and all other candidates last (and [[Min-max voting|Min-max vote]] in Score), then the candidate marked 1st on the most ballots (the [[Approval voting]] winner) wins. This isn't passed by all voting methods; for example, [[IRV]] with its most common equal-ranking implementation, [[Equal-ranking methods in IRV|fractional equal-ranking]], doesn't necessarily elect such a candidate.
== Plurality criterion for rated ballots ==
<p>Example where [[Score voting]] fails if the definition of the criterion is extended to scored ballots:</p>
<p>3 A:1</p>1 C:5 B:4
1 D:5 B:4
Scores are A 3, C 5, B 8, D 5, making B the winner. Yet when looking at the rankings:
3 A
1 C>B
1 D>B
B is preferred on 2 ballots, while A is preferred 1st on 3 ballots. However, Score voting passes a related criterion: "If the number of ballots giving A maximal support is greater than the number of ballots on which another candidate B is given any support, then B must not be elected." This is because candidate B can't get more points than A, since even if all voters who score B give B the maximum score, candidate A will have more ballots giving them the maximum score than B, and thus more points.
[[Category:Voting system criteria]]
| |||