[EM] Blake's Margins Arguments

[Markus Schulze]

Dear Craig,

you wrote (4 March 2003):
> The IFPP method fails the MMC rule so the rule is almost certainly
> wrong by this fact alone
>
> ------------------------------------------------------------------
>      AD  25
>      B.  27
>      C.  24
>      D.  24
>
> The 1 winner IFPP method finds that candidate B is the winner.
> ------------------------------------------------------------------
>
> IFPP for 6 papers and 4 candidates and 1 winner, is shown
> here along with a derivation: ...

There is no need to read the derivation for IFPP for 4 candidates
since IFPP violates MMC already in the 3-candidate case.

MMC says:

  If there is a set of candidates such that a majority of the voters
  strictly prefers each candidate of this set to each candidate
  outside this set, then the winner must be a candidate of this set.

Here is a 3-candidate example showing IFPP fails MMC:

   30 ABC
   30 BAC
   40 CAB

In this example, a majority of the voters strictly prefers the
candidates A and B to the candidate C. Nevertheless, IFPP chooses
candidate C.

******

By the way: I believe that the strong opinion of some participants
on the "boring margins/winning-votes debate" (Rob LeGrand) is mainly
a relic from those times when only very few Condorcet methods
(e.g. MinMax method, Copeland method) were known to this mailing
list and when all of these Condorcet methods had serious problems.
In those times, it was necessary to put much weight in the
majoritarian argumentation to be able to justify the proposed
Condorcet method against the attacks e.g. of the IRV supporters.
However, the currently discussed Condorcet methods are so
sophisticated that it is not necessary anymore that the reader
agrees to a certain opinion of the "lesser-of-2-evils problem"
to see the beautifulness and the elegance e.g. of the Ranked Pairs
method or the beat path method.

Markus Schulze

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