This is Chance strategy and choice problem 21-8

21.8 We introduce a "fairness" criterion for social choice methods that we call the Invariance Criterion, defined as follows: given a preference table, construct the social preference graph that is a tournament 7. We say that a voting method satisfies Invariance if every preference table with the same candidates resulting in the same preference table 7 produces the same social choice by the voting method. Prove by example that each of the voting methods Plurality, Borda Count, Hare, Coombs, and Dictatorship violate the Invariance Criterion. Can you think of a voting method that satisfies the Invariance Criterion