4. What is a Condorcet Candidate?

In voting theory, a Condorcet candidate is a candidate who always wins in a 2-person election but loses in larger election. For example, consider the 6-tuples of 6-sided die rolls A = (1,1,1,4,7,7), B = (2,2,5,5,5,5), and C = (3,3,3,3,3,6).

Represent a two-person election by considering all 36 outcomes for rolling these two dice. Then B beats A 22 to 14, and beats C 20 to 16. In a three way election, A wins with 82, B is second with 80, and C is last with 54.