Specific Failing of Copeland/Regular Champion

[Mike Ossipoff]

Rob Lanphier writes:
> 
> Could someone on this list point me to a specific failing of Copeland or 
> Regular Champion and provide a specific scenario (preferably a sample set of 
> ballots)?  Given what Mike has said so far, I'm assuming it would involve 
> voters expressing insincere ballots on a small scale and having a large effect 
> on the election, but I haven't worked it out.
> 


But it wouldn't even require insincerity, in the sense of falsification
of preference orderings. Mere truncation, something that's occurred
on a large scale in every rank-balloting election I've participated
in, would bring out the problems of Copeland & Regular-Champion.

These problems are of 2 main types:

1. Failure to meet lesser-of-2-evils & majority rule criteria
2. The Rich Parties problem

I've listed a number of criteria, 5 of them, relating to
lesser-of-2-evils & majority rule, which Regular Champion
& other Copeland versions fail, and which Condorcet's method
passes.

They are:

Generalized Majority Criterion (GMC)
Lesser-of-2-Evils Criterion #1 (LO2E-1)
Lesser-of-2-Evils Criterion #2 (LO2E-2)
Invulnerability to Mis-Estimate (IME)
Truncation Resistance Criterion (TRC)

I'm willing to post definitions of these criteria, & demonstrations
that Condorcet's method meets them.

1 or 2 examples will show that Regular Champion fails them.
Anyway, here's an example of Regular-Champion screwing up:

I've posted this example before, in case it seems familiar. 

Sincere rankings:

40%: Dole, Clinton, Nader
25%: Clinton
35%: Nader, Clinton, Dole

Dole voters truncate:

40%: Dole
25%: Clinton
35%: Nader, Clinton

This creates a circular tie in which Nader beats Clinton beats Dole
beats Nader.

In Regular-Champion, every candidate has the same Copeland
score, since each is beaten by 1 & beats 1. So there's
a Copeland tie, which is solved by Plurality. Dole wins.
Dole wins because his voters refused to rank Clinton.

That can't happen in Condorcet. The Dole truncation can't
change the fact that Dole has a majority against him, and can't
change the fact that Clinton doesn't have a majority againsts
him. Dole can't possibly win due to truncation. Clinton wins,
with only 35% against him in a defeat.

In this example, Regular Champion fails TRC, LO2E1, & GMC.

But, in any case, its undesirable result is plain enough to
the Clinton & Nader voters in the majority who prefer Clinton
to Dole.

***

The Rich Parties problem:

Steve has posted an example of how Copeland's choice
of which party gets one of its candidates elected depends
entirely on how many candidates the various parties run.
In Steve's example, a party loses because it doesn't run
as many candidates as the other parties. Any method that
would do that is completely unacceptable.

I'm sure that Steve will re-post his Rich Parties example
upon request.

***

Mike



> Thanks
> Rob Lanphier
> robla at eskimo.com
> http://www.eskimo.com/~robla
> .-
> 


--