Implicit utilitarian voting


Implicit utilitarian voting is a voting system in which the agents express their preferences by ranking the alternatives, and the system tries to select an alternative which maximizes the sum of utilities.
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 ratio between the maximum utility-sum and the utility-sum of the alternative selected by the rule.
  2. The regret of a voting-rule is the worst-case difference between the maximum utility-sum and the utility-sum of the alternative selected by the rule.
Some achievements in the theory of IUV are:
Implicit utilitarian voting rules are used in the website.