[EM] Fixing IRV

[Anthony Simmons]

>> From: Richard Moore <rmoore4 at home.com>
>> Subject: Re: [EM] Fixing IRV

>> Anthony Simmons wrote:
>> > Therefore, it is possible (yes, "at least in principle") to
>> > prove that a given election method is or is not equivalent to
>> > a non-elimination method.  This does *not* mean there's a
>> > feasible method.
>
>> > Life is so easy with finite sets.

>> This certainly could be used "in principle" to prove things
>> about elections for N <= N1 and m <= m1, where N1 and m1 are
>> abritrary limits. But unless you can construct a
>> mathematical induction proof, this result doesn't apply for
>> N > N1 or m > m1, and you have to repeat the process with
>> these larger numbers. It then follows that the problem is
>> infinite in scope.

Fortunately for everyone who is eager to get started matching
them up, election methods have to be compared only with
others that have the same number of ballots.  N is an
arbitrary variable, and the proof says that for any N, the
result is true.  This amounts to having a separate proof for
each N, and for each proof, the number of possible
comparisons is finite.

"In principle" just means that the actual act of comparing
sets only has a finite number of steps, and implies that it
may not be practical.

>> Example: The method that says "elect the Borda winner unless
>> there are more than 1 million voters, in which case elect
>> the plurality winner" is equivalent to Borda as long as the
>> number of voters is less than or equal to 1 million.

>> In this light, of course, the number of methods is also
>> infinite.

>> Richard