Find the Run-off Flaw

Mike Ossipoff dfb at
Tue Nov 19 12:38:33 PST 1996

donald at writes:
> >
> >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.

Nonsense. We've made neither claim. There isn't always a particular
alternative that is the "majority wish of the people". A BeatsAll
candidate, who has separate majorities over each one of other 
alternatives comes the closest to qualifying for Don'd term.
And yes, Condorcet's method will always elect a BeatsAll winner
when there is one, and IRO will often fail to, as has been often
demonstrated for Don.

> >
> >     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.

Ok, Don, here it is again: An example where IRO fails to elect
the BeatsAll alternative, the nearest thing to your "majorilty wish
of the people":

35: A,B,C
32: B
33: C,B,A

Figure it out, Don. B gets immediately eliminated in IRO, even
though 65% of the people would rather have B than A, and 67%
of the people would rather have B than C. B, having separate 
majorities over everything else, is the nearest thing to your
"majority wish of the people".

Of course if, by "majority wish of the people", you mean something
that is the 1st choice of a majority of all the voters, then
many methods, including even IRO will elect that majority
alternative. That isn't much of a test of a method. It's too
easy. And there usually isn't a majority winner of that type,
and when there isn't, IRO often will seriously violate majority
rule, as in the above example.

> >
> >     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.

1) As I said, I don't know what you're talking about when you say
"the majority wish of the voters".

2) How can we say anything about majority when you won't show
the voters' preferences? :-)

> >
> >     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.

And apparently, for you, people's preferences don't exist either.
If they didn't, then we wouldn't have a problem with IRO either.

> >
> >I await your reply
> >
> >God Speed,
> >
> >Donald,
> .-


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