Find the Run-off Flaw

[donald at mich.com]

>
>Dear Methods List,
>
>     The foundation of the Condorcet method is based on two claims.
>One - the Condorcet people claim that run-off methods have a flaw of not
>always electing the majority wish of the people.
>The second claim is that Condorcet does always elect the majority wish of
>the people.
>
>     I am going to consider only the first claim in this message.
>If claim one is true then it would be true for all run-off methods and
>also be true even if no one knew anything about Condorcet - not even you.
>
>     So - I am asking you Condorcet people to prove claim one. Forget
>about Condorcet for a moment and prove that one of the run-off types has
>this flaw. Any type of run-off should do - they all should have the flaw -
>if it exists.
>
>     This is your assignment - "if you care to accept" - find the claim
>one flaw in the following run-off example:
>
>A social club of one hundred members elects a president each year at their
>annual election dinner. They usually have from three to five candidates.
>Their method is to conduct a series of run-off ballots until they have a
>winner with a majority. On each ballot after the first they will drop the
>low candidate. The ballot returns of the last election are as follows:
>
>             Ballot One    27A   26B   24C   23D
>             Ballot Two    36A   34B   30C
>             Ballot Three  51A   49B
>
>Show the claim one flaw - prove that this election did not elect the
>majority wish of the voters.
>
>     If these results do not show the flaw then you are free to change the
>numbers in order to show a case in which a different series of run-offs
>shows the claim one flaw.
>
>     The reason I picked this type of run-off is because I want to avoid
>the ranking of candidates so that you will not slip and use Condorcet -
>remember, for this example Condorcet does not exist.
>
>I await your reply
>
>God Speed,
>
>Donald,