[EM] RE: (crossposted) Revisiting Copeland

[Kevin Venzke]

Hello,

--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> At 10:52 AM 9/9/2005, Kevin Venzke wrote:
> >I couldn't support Copeland unless you use a tiebreaker that satisfies
> >minimal defense. Otherwise:
> >
> >49 A
> >24 B
> >27 C>B
> >
> >A could be elected, for instance with a plurality tiebreaker.
> 
> It is one thing to use an example like this for discussion purposes 
> on the Election Methods list; it is quite enough to use it on a list 
> which is moving toward (or is) a general public discussion. That 
> example is so unlikely in a public election that we might as well say 
> it is impossible.

I can't understand why you call this scenario unlikely. If you remove
"noise" votes that are too few to make much difference, this seems very
likely, if a third party (behind candidate C) gained enough strength.

> Take 101 random voters in a public election with percentages like 
> that . Given that almost fifty percent of this population strongly 
> supports A, strongly enough not to even rate the other candidates, 
> which is highly unlikely by itself, what is the probability that none 
> of the other 51 voters would likewise fail to rate A. What is the 
> chance that none of the other voters would actually prefer A over B or C?

The voters are partisan. Those that like A do not like B or C at all. Those
that like B best may prefer either A or C to the other, but it is not usually
strategically wise to rank both of the frontrunner candidates under Condorcet
methods. They do not rank C because this can give the election to C 
unnecessarily (that is, if they are confident that the C voters will not 
bullet-vote).

> Such an example may well be used to quickly show a characteristic of 
> an election method; and the writer doesn't want to take the time to 
> construct a more plausible scenario -- which is understandable -- but 
> no election method is perfect, probably, so it may well be enough 
> that harmful scenarios are very rare.

So you believe voters won't want to truncate? You envision Bush voters
wanting to rank "Bush>Kerry>Nader" because they can?

> No election method is going to produce great results with a highly 
> polarized electorate, as is shown in this example.

I don't agree with you. If B is elected in the above scenario, we have no
reason to believe that any voter regrets the way they voted.

> As I understand Copeland, truncated votes, as shown, would be 
> considered as equal ratings below the rated candidate(s), so the 
> complete description of the votes would be

Copeland doesn't use defeat strength, so it is irrelevant how you handle
equal rankings.

> 49: A>B=C
> 24: B>C>A
> 27: C>B>A

No, it would be:
49 A>B=C
12 B>A>C
12 B>C>A
27 C>B>A

This is the margins treatment (that is, pretend that the B voters split half 
and half on A vs. C).

> With Copeland, the number of pairwise victories are counted first. 
> This would be
> 
> A: 0
> B: 75
> C: 78
> 
> C is likewise the winner. What is this example supposed to show?

Copeland returns a three-way tie. By the way, did you not have a problem with
C supposedly winning?? C receives acknowledgment from only 27% of the voters!

The example shows that Copeland with a plurality tie-breaker can elect
candidate A, even when more than half of the voters preferred B to A and
didn't prefer A to anybody.

In my opinion, this is a majority rule issue.

Kevin Venzke


	

	
		
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