[EM] Burlington dumps IRV; Immunity from Majority Complaints (IMC) criterion

[Markus Schulze]

Dear Steve Eppley,

the following criterion has been discussed several
times in the Election Methods mailing list:

    Suppose a majority of the voters prefers candidate A
    to candidate B. Then candidate B must not be elected,
    unless there is a sequence of candidates from
    candidate B to candidate A where each candidate beats
    the next candidate with a majority that is at least
    as strong as the majority of candidate A against
    candidate B.

The above criterion was called e.g. "beatpath criterion"
or "immunity from binary arguments". The above criterion
is satisfied e.g. by the Schulze method.

Your "immunity from majority complaints" criterion has
the following problems:

(1) To guarantee that only the ranked pairs method
satisfies this criterion, you added the requirement
that each candidate of this sequence must be ranked
ahead the next candidate of this sequence according
to the social ordering.

(2) To guarantee that only the ranked pairs method
with "winning votes" satisfies this criterion, you
added the requirement that the strength of a pairwise
comparison must be measured by the number of voters
who prefer the winning candidate to the losing
candidate of this pairwise comparison.

These additional requirements are not justified
by the original motivation for this criterion:

 > Suppose a majority rank x over y but x does not
 > finish ahead of y (in the election's order of finish).
 > They may complain that x should have finished ahead
 > of y, using "majority rule" as their argument. (...)
 > So it is desirable to be able to turn their own
 > "majority rule" argument against them.

(3) Your criterion presumes that the purpose of an
election method is to create a social ordering.
However, most readers will argue that the purpose
of an election method is to find a winner and not
to create a social ordering.

Markus Schulze