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 **