Implicit utilitarian voting

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 (like in 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.

References
  1. Shah, Nisarg; Procaccia, Ariel D.; Nath, Swaprava; Caragiannis, Ioannis (2017-01-16). "Subset Selection Via Implicit Utilitarian Voting". Journal of Artificial Intelligence Research. 58: 123–152. doi:10.1613/jair.5282. ISSN 1076-9757.
  2. Procaccia, Ariel D.; Rosenschein, Jeffrey S. (2006). Klusch, Matthias; Rovatsos, Michael; Payne, Terry R. (eds.). "The Distortion of Cardinal Preferences in Voting". Cooperative Information Agents X. Lecture Notes in Computer Science. Springer Berlin Heidelberg. 4149: 317–331. CiteSeerX 10.1.1.113.2486. doi:10.1007/11839354_23. ISBN 9783540385707.
  3. Craig Boutilier, Ioannis Caragiannis, Simi Haber, Tyler Lua, Ariel D. Procaccia, Or Sheffet (2015). "Optimal social choice functions: A utilitarian view". www.sciencedirect.com. Retrieved 2019-04-05.CS1 maint: multiple names: authors list (link)
  4. Gerdus Benade and Swaprava Nath and Ariel D. Procaccia and Nisarg Shah (2017). "Preference Elicitation for Participatory Budgeting" (PDF). Proceedings of AAAI 2017.
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