Tag Archives: intransitivity

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.  Continue reading

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