Llull Voting

Llull Voting is a single winner voting system that attempts to find a compromise between approval voting and the Condorcet criterion. There are two different versions. It is named in honor of Ramon Llull, a discoverer of the Borda Count and Condorcet Method.

Version 1: Llull-Smith Voting

Assume that there are m number of voters and n number of alternatives. Each voter submits a total preference order containing all n alternatives. Note that voters are allowed to express indifference between alternatives in their total preference order. If there exists an alternative that is approved by a majority of all m voters, then the alternative with the greatest number of approvals wins the election. However, if no alternative is approved of by a majority of voters, then the member of the Smith set with the greatest number of approvals is elected the winning alternative.

Version 2: Llull-Schwartz Voting

Assume that there are m number of voters and n number of alternatives. Each voter submits a total preference order containing all n alternatives. Note that voters are allowed to express indifference between alternatives in their total preference order. If there exists an alternative that is approved by a majority of all m voters, then the alternative with the greatest number of approvals wins the election. However, if no alternative is approved of by a majority of voters, then the member of the Schwartz set with the greatest number of approvals is elected the winning alternative.