Implicit utilitarian voting

Part of the Politics series
Electoral systems
Majoritarian/plurality Plurality First-past-the-post Plurality at-large (plurality block voting) General ticket (party block voting) Multi-round voting Two-round Exhaustive ballot Majority at-large (two-round block voting) Ranked / preferential systems Instant-runoff (alternative vote) Contingent vote Coombs' method Condorcet methods (Copeland's, Dodgson's, Kemeny–Young, Minimax, Nanson's, ranked pairs, Schulze, Alternative Smith) Positional voting (Borda count, Nauru/Dowdall method) Bucklin voting Oklahoma primary electoral system Preferential block voting Cardinal / graded systems Score voting Approval voting Combined approval voting Unified primary Usual judgment Satisfaction approval voting Majority judgment STAR voting
Proportional representation Party-list (open lists, closed lists, local lists) Highest averages (D'Hondt, Sainte-Laguë, Huntington–Hill) Largest remainder (Hare, Droop, Imperiali, Hagenbach-Bischoff) Proportional forms of ranked voting Single transferable vote (Gregory, Wright) CPO-STV Schulze STV Proportional forms of approval voting Proportional approval voting Sequential proportional approval voting Biproportional apportionment Fair majority voting Weighted voting Direct representation Interactive representation Liquid democracy
Mixed systems By type of representation Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote (positive vote transfer) Scorporo (negative vote transfer) Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Other systems and related theory Multiple non-transferable vote Semi-proportional representation Single non-transferable vote Limited voting Cumulative voting Binomial voting Double simultaneous vote Proxy voting Delegated voting Random selection (sortition, random ballot) Comparison of electoral systems Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Public choice theory
Politics portal
v t

Implicit utilitarian voting (IUV) is a voting system in which the agents express their preferences by ranking the alternatives (like in ranked voting), and the system tries to select an alternative which maximizes the sum of utilities, as in the utilitarian social choice rule and utilitarian voting.^[1]

The main challenge in IUV is that the rankings do not contain sufficient information to calculate the utilities. For example, if Alice ranks option 1 above option 2, we do not know whether Alice's utility from option 1 is much higher than from option 2, or only slightly higher. So if Bob ranks option 2 above option 1, we cannot know which of the two options maximizes the sum of utilities.

Since a voting-rule that can only access the rankings cannot find the max-sum alternative in all cases, IUV aims to find a voting-rule that approximates the max-sum alternative. The quality of an approximation can be measured in several ways.

1. The distortion of a voting-rule is the worst-case (over utility functions consistent with the reported profile of rankings) ratio between the maximum utility-sum and the utility-sum of the alternative selected by the rule.^[2]
2. The regret of a voting-rule is the worst-case (over utility functions consistent with the reported profile of rankings) difference between the maximum utility-sum and the utility-sum of the alternative selected by the rule.^[1]

Some achievements in the theory of IUV are:

• Analyzing the distortion of various existing voting rules;^[2]
• Designing voting rules that minimize the distortion in single-winner elections^[3] and in multi-winner elections;^[1]
• Analyzing the distortion of various input formats for Preference elicitation in participatory budgeting.^[4]

Implementation[]

Implicit utilitarian voting rules are used in the RoboVote website.

See also[]

• Utilitarian cake-cutting - the utilitarian principle in a different context.

References[]