Question

Consider the following voting method: If there is a Condorcet winner, he is

selected. Otherwise, plurality is used. Clearly this satisfies the Condorcet

winner condition. Give an example with four candidates where it doesn’t

satisfy the Condorcet loser criterion.

Answer 1

The approval method which is shown below violates the Condorcet Loser criterion. This is an example in which the concordet loser is selected at last. So, I will explain the approval method now. In the approval method, There are four candidates- A, B, C and D. Suppose the preference by three different voters be given as follows:

A>B>D>C

C>A>D>B

B>C>D>A

So, here we can see that all the candidates other than D is preferred 2 out of 3 votes. So, D is the concordent loser here.

But when we consider the disapprovals, we can see that D has no disapprovals while A,B and C are disapproved by any one of them. So, ultimately D is selected.

This vkiolates the concordet loser criteria.