Majority: Difference between revisions
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== Comparison to Utilitarian systems ==
Mathematically, [[w:Majority_criterion#Majority_rule_as_an_approximation_of_utilitarianism|majoritarianism is a necessary approximation of utilitarianism]] under the assumption that satisfying any of a voter's preferences has the same utility as any other voter. Any voter's utility towards A>B exactly cancels any other voter's utility towards B>A, so the favoring the majority maximizes net utility. It is, effectively, a rule of thumb under the assumption of strict utilitarian equality of all voters.
All utilitarian systems are [[Cardinal voting]] methods because other ballot structures do not contain enough informaiton. All such systems fail the majority criterion by design. Common examples of such as [[Approval voting|Approval]], [[Score]], and [[STAR voting]]. Following from Utilitarian theory it is argued that the [[Utilitarian winner]] is preferred in situations where they are well-liked by all voters rather than a candidate who is narrowly preferred by a majority but loathed by the minority.▼
[[Utilitarian winner|Utilitarian]] systems are based on not making such an assumption, by instead letting voters give their own estimates of utility for different scenarios. Since cardinal ballots are capped (there are no "[[w:utility monsters|utility monsters]]"), voters can effectively only express ''degrees of indifference'' between options, reducing the intensity of their preferences. Critics of utilitarianism claim this inherently penalizes voters who choose to do so, and therefore the assumption of equal intensity of preferences of majority rule is more "fair to all".
In contrast, under the philosophy of utilitarianism choosing a majoritarian winner when a [[utilitarian winner]] is available would be considered bad (according to the voters themselves), as in such scenarios the majoritarian rule-of-thumb has likely failed. For utilitarians, taking the indifferences into account allows voters to concede towards a greater good, ''if they choose to do so''. Under any utilitarian system, a majority can always [[bullet vote]] and get its way if they choose to do so. The point, according to utilitarians, is to grant them the choice of ''not'' doing so.
▲All utilitarian systems are [[
Note that a utilitarian winner need not have significantly more utility than the majoritarian winner to win, nor need satisfy significantly more people. See [[Smith//Score#Notes]] for some ideas on mixing the two philosophies.
If voters are considered imprecise judges of their own utilities (i.e. comparisons are not infinitely precise, so indifferences do exist whether voters express them in their ballots or not), then comparisons between candidates are based on slightly noisy utilities. This means even rankings may be regarded as probabilistically accurate. In this case, both utilitarianism and majoritarianism represent different philosophies of addressing this inherent noise. Ranked systems under majoritarianism assume all preferences are 100% accurate and there are no degrees of indifference, regardless of how closely the candidates may be perceived to the ranked voter. Cardinal systems would consider the ballot as a sample of the underlying distribution of utilities, such that their aggregation would reproduce the statistical likelihood of satisfying the individual distributions on an average election.
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