Summary

DescriptionVoting Paradox example.png	English: 3 voters (blue circles) and 3 candidates (red circles) in a 2-dimensional political space. The voters prefer candidates closest to themselves, leading to a circular societal preference of A > B > C > A... and no Condorcet winner. Voter locations: 1: (1, 1) 2: (6, 3) 3: (1, 7) Candidate locations: A: (2, 3) B: (5, 1) C: (4, 6) Distances from voters to candidates: 1: A = 2.2, B = 4.0, C = 5.8 2: B = 2.2, C = 3.6, A = 4.0 3: C = 3.2, A = 4.1, B = 7.2 Note that the distances are not equal/symmetrical. A score voting system with honest voters would select A as the winner, since A is closest to the centroid of the voters. See below.
Date	8 January 2017
Source	Own work
Author	Votingstuff
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Score voting

Under Score voting, candidate A would win, as they are the closest to the centroid of voters. For instance, if the largest distance (7.2) is assigned a score of 0, and all voters vote proportionally to that distance on a scale of 0 to 6, the scores would be:

If instead the voters normalize their votes based on their own maximum and minimum distance, with the middle candidate scored proportionally, the results are:

Other ways of normalizing the scores also lead to A winning.

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