[EM] "More often" (was: IRV and Condorcet operating identically)

[Markus Schulze]

Jan Kok wrote (25 Feb 2003):
> "(3)  The instant runoff count committee shall sort and count votes for
> candidates.  If, in the first round, no candidate received a majority of
> first choices, all candidates shall be eliminated except the two candidates
> with the greatest number of first choices.  Ballots which rank eliminated
> candidates and which indicate one of the final candidates as an alternate
> choice shall be counted as votes for whichever of the final candidates is
> ranked higher for that office on each ballot.  In each round, each ballot
> is counted as one vote for the highest ranked advancing candidate on that
> ballot."

Craig Carey wrote (28 Feb 2003):
> A note to Mr Schulze: I contradicted this wrong statement at my
> mailing list. It had algebra in it.
>
> ------------------------------------------------------------------
> > From:  Markus Schulze <markus.schulze at ...
> > Date:  Wed Feb 26, 2003  12:09 pm
> > Subject:  Re: [EM] Might IRV adoption be inevitable?
> >
> > Venzke Kevin wrote (25 Feb 2003):
> > > I wonder if the only reason IRV has more apparent
> > > backing than approval or Condorcet is because it would
> ...
> >
> > And in so far as there is no known version of proportional
> > representation by the [Alternative Vote method] that has been
> > proven to meet monotonicity,
> ...
> ------------------------------------------------------------------
>
> The method of Vermont, as described by Mr Kok in this
> message, seems to be perfectly monotonic, and it is a variant
> of the Alternative Vote.

Dear Craig, I wrote (26 Feb 2003) that "there is no known version of
proportional representation by the single transferable vote that has
been proven to meet monotonicity." The method in Jan Kok's 25 Feb 2003
mail is a single-winner method and not a method of proportional
representation by the single transferable vote. Furthermore, the
method in Jan Kok's 25 Feb 2003 mail violates monotonicity. Example:

   8 voters vote A > C > B.
   5 voters vote B > A > C.
   4 voters vote C > B > A.

The winner is candidate B. However, when 2 ACB voters change their
opinion to CAB, then this example looks as follows:

   6 voters vote A > C > B.
   5 voters vote B > A > C.
   4 voters vote C > B > A.
   2 voters vote C > A > B.

Now, candidate A is the winner. This is a clear violation of
monotonicity.

Markus Schulze

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