Social utility efficiency

Social utility efficiency (SUE) is a measurement of the utilitarian performance of voting methods—how likely they are to elect the candidate who best represents the voters' preferences.[2]

Efficiency of several voting systems with an impartial culture model and 25 voters[1]

It is also known as Voter Satisfaction Index (VSI)[3] or Voter Satisfaction Efficiency (VSE).[4] Bayesian Regret measures the same property, but inverted and non-normalized.[3][5][6][7][8]

Social utility efficiency is defined as the ratio between the social utility of the candidate who is elected by a given voting method and that of the candidate who maximizes social utility, where ${\displaystyle E[]}$is the expected value over many iterations:[9]

${\displaystyle {\mathit {SUE}}={\frac {E[{\text{selected candidate}}]-E[{\text{random candidate}}]}{E[{\text{maximizing candidate}}]-E[{\text{random candidate}}]}}}$

A voting method with 100% efficiency would always pick the candidate that maximizes voter utility. A method that chooses a winner randomly would have efficiency of 0%, and a (pathological) method that did worse than a random pick would have less than 0% efficiency.

SUE is not only affected by the voting method, but is a function of the number of voters, number of candidates, and of any strategies used by the voters.[1]

The concept was originally introduced as a system's "effectiveness" by Weber in 1977,[2] using a random society (impartial culture) model, but it has since been extended to the more realistic spatial model of voting[1] and a hierarchical clusters model.[4]