# Utilitarian winner

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In an election, the utilitarian winner (UW) is the candidate who would maximize the utility of the voters (the utilitarian welfare function) if they won.[1]

Cardinal voting systems are based on the concept of maximizing cardinal utility, having voters express their estimated utility by scoring the candidates. In this case it is simply the candidate with the highest sum of score.

In most cases, the utilitarian winner and the Condorcet winner (CW) are the same, though it's possible for them to be different. However, Marcus Pivato mathematically demonstrates that "if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function."[2]

## Notes

In a two-candidate election (or more generally, any time one more candidate is running than the number of seats to fill), utilitarian voting and majority rule will give the same outcome when all voters are strategic. This is because utilitarianism allows each voter to be maximally important in at most one pairwise matchup (i.e. a person who thinks their 1st choice is maximally better than their 2nd choice is allowed to feel that way utility-wise, but then is assumed to not gain or lose any utility when going between their 2nd choice and any other candidate), and majority rule assumes that any slight preference the voter expresses in a pairwise matchup ought to be treated as maximally important. This is the reason utilitarianism can't have Condorcet cycles.

Note that one rationale for utilitarianism being superior to rankings is "based on the view that no justification exists for restricting voters’ freedom to rank the alternatives on a given scale."[1] However, this avoids one feature of ranking which is not possible with ratings, which is that it allows a voter to express maximal preferences between several transitive pairs of candidates i.e. a voter may say that A is maximally better than B, B is maximally better than C, etc. See Ballot#Notes for discussion on this. So arguably, giving voters freedom to either rank the candidates on a scale or rank them in a way where they can express maximal transitive pairwise preferences, such that all of this information is used simultaneously by the voting method (i.e. using pairwise counting in Category:Pairwise counting-based voting methods) is better justified by this type of argument.