Eric Gorr wrote:
Condorcet did not elect the wrong candidate. The voters were clearly split, but both of the larger groups preferred the third option over the primary opposition. As such, the highest utility candidate was elected by Condorcet.
Why do you believe that the first place preferences matter more then the middle or final preferences? What is the basis for this assumption?
There are 3 candidates in an election A,B and C. The votes and relative utilities are:
45 A1.0>B0.3>C0.1 8 B1.0>A0.6>C0.2 5 B1.0>C0.6>A0.2 42 C1.0>B0.4>A0.1
The Condorcet winner is B. Adding up the utilities of the candidates the winner we get
A: 45x1 + 8x0.6 + 5x0.2 + 42x0.1 = 55 B: 13x1 + 45x0.3 + 42x0.4 = 43.3 C: 42x1 + 45x0.1 + 8x0.2 + 5x0.6 = 51.1
A has the highest total utility, A is not the Condorcet winner.
Yes, I can invent numbers that show just the opposite.
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