Intransitive votes

In the previous post I gave an example of students deciding who best guessed some lecturers’ ages.

I chose the numbers carefully so that under three reasonable methods of measuring:

Method	First place	Second place	Third place
Method a	Adam	Beth	Charlie
Method b	Beth	Charlie	Adam
Method c	Charlie	Adam	Beth

This is actually almost identical to Condorcet’s voting paradox:

Voter	First preference	Second preference	Third preference
Voter 1	A	B	C
Voter 2	B	C	A
Voter 3	C	A	B

If three people in an election vote for candidates A, B, and C this way, then even using a method that takes account of all the preferences in one of the Condorcet voting system leads to a deadlock.