Approval Compatible Voting Rules

27 Pages Posted: 19 Oct 2022

See all articles by Jérôme Lang

Jérôme Lang

Université Paris Dauphine

Zoi Terzopoulou

University of Amsterdam

William Zwicker

Union College


In a classical voting situation, each voter in a group is asked to report a ranking over a set of alternatives, and a voting rule is applied to determine a winning alternative. But voters may also hold approval preferences, giving rise to an approval winner. If voters with approval preferences are asked to report rankings instead, and assuming that voters are sincere, can an approval winner possibly win the election? Can an approval loser lose the election, or can all approval co-winners be co-winners of the election? These three types of questions lead to different notions of approval compatibility for voting rules, called positive, negative, and uniform approval compatibility. We find that negative approval compatibility is a very weak notion, while uniform positive approval compatibility is a very strong one. We also show that positive approval compatibility as well as uniform negative approval compatibility divide usual voting rules into two significant families: Borda, plurality, plurality with runoff, STV, and Condorcet-consistent rules satisfy these notions, while several positional scoring rules (with Borda and Plurality excepted) violate them.

Keywords: Social Choice Theory, Voting, Approval Voting, Rankings

Suggested Citation

Lang, Jérôme and Terzopoulou, Zoi and Zwicker, William, Approval Compatible Voting Rules. JME-D-22-00323, Université Paris-Dauphine Research Paper No. 4252553, Available at SSRN: or

Jérôme Lang

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, 75775

Zoi Terzopoulou (Contact Author)

University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB

William Zwicker

Union College ( email )

Schenectady, NY 12308-3151
United States

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