|Some relationships are transitive , such as `if A> B and B> C then it follows that A> C', but some relationships are intransitive , for example if A likes B and B likes C it does not necessarily follow that A likes C.|
A beats B by 2 choices to 1.
B beats C by 2 choices to 1
but A loses to C, again by 2 choices to 1.
Three voters go to vote in this election and have to rank the candidates. First, check you agree that each voter has six possible ways in which they can do this.
Assuming the voters are just as likely to rank them in one order as another, what is the probability that they all vote in a way that results in a paradoxical (intransitive) outcome?