[EM] Deconstructing the Majority Criterion

[Juho Laatu]

On 17.6.2013, at 18.26, Benjamin Grant wrote:

> Majority Criterion

My definition of Majority Criterion is simply something like "if more than 50% of the voters prefer candidate A to all other candidates, then A shall win". There are methods that aim at respecting the wishes of the majority ("majority oriented"). Range/Score is not one of them. It rather aims at electing the candidate that has the highest sum of utility among the voters. This is a different need than the idea of letting the majority decide.

Majority oriented methods can give poor results from the range point of view. For example sincere votes 51: A=10, B=9, C=9 ; 26: B=10, C=9, A=0 ; 25 C=10, B=9, A=0 tell us that B and C have clearly higher average utility among the voters than A, although majority of the voters consider A to be the best candidate. A would not be a good winner according to the Range philosophy.

One could say that majority oriented methods are typically used in competitive environments since majority rule seems to make sense in environments where we expect voters to take position strictly in favour of their "own" candidate and against the other candidates and vote accordingly. In Range such thinking may lead to exaggeration. Maybe we will get votes like 51: A=10, B=0, C=0 ; 26: B=10, C=0, A=0 ; 25 C=10, B=0, A=0 although the sincere preferences are as above, With this kind of maximally exaggerated votes Range will also respect the majority rule (but it loses its expressiveness and its ability to elect the candidate that has highest sum of utility among the voters).

In summary, Range is not a majority oriented method, and not really a method for competitive environments (since it may become just "approval with fractional votes"). It should not follow the majority rule since that would ruin its intended other good properties. Majority oriented methods are often good for competitive environments. Range is good when the election organizer and the voters sincerely want to elect the candidate with highest sum of utility.

Juho


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