User:Psephomancy/CW vs UW

Here are 3 voters (X, Y, Z), and three candidates (A, B, C) in a two-dimensional political space. The faint circles show the distance from each voter to each candidate, so you can see that B is slightly closer to Z than C is, for instance.

Candidate C is the Utilitarian Winner: They are the best representative of the entire population (X, Y, Z), and make the population happiest overall.

Candidate A is the Condorcet Winner and the Majority Winner: They are a (slightly) better representative of a majority faction (X, Y), even though they make the minority faction (Z) very unhappy.

Condorcet and majoritarian systems choose A, because 2 voters slightly prefer A over C, but C is the best match for all voters. The fundamental problem with ranked-choice ballots is that they can't capture intensity of preference, so X/Y's slight preference for A over C is given equal weight to Z's strong preference for C over A.

(Borda also chooses A, since it weights all relative preferences equally when assigning point values, even though the preference strengths are not equal. Borda results in A getting 4 points, C 3 points, and B 2 points.)