[EM] Clone proofing Copeland

[mrouse1 at mrouse.com]

Chris Benham wrote:
> I'm happy with its performance in this old example:
>
> 101: A
> 001: B>A
> 101: C>B
>
> It easily elects A. Schulze (like the other Winning Votes "defeat
dropper" methods) elects B.
>
> It meets my  "No Zero-Information Strategy" criterion, which means that
the voter with no idea how others will vote does best to simply rank
sincerely.
>
This is an interesting example, partly because it seems to me that C would
be a better winner. I ran through some possibilities on the Ranked-ballot
voting calculator at http://cec.wustl.edu/~rhl1/rbvote/calc.html, and got
the following:

101: A
001: B>A
101: C>B

A:   Baldwin, Nanson, Raynaud
C:   Black, Borda
(Other methods required a random tiebreaker).

Strangely, if you reverse all the rankings, you get:

101: C=B>A
1: C>A>B
101: A>B>C

A    Baldwin, Nanson, Raynaud
B    Black, Borda

Which means it made no difference to Baldwin, Nanson, or Raynaud. Black
and Borda gave different answers for the reverse order, which seems
logical.

Now let's look at some possibilities for the second and third choice for
those who picked A.

101: A>B>C
1: B>A>C
101: C>B>A

A: Carey, Hare
B: Baldwin, Black, Borda, Bucklin, Coombs, Copeland, Dodgson, Nanson,
Schulze, Simpson, Small

B looks like a good choice. Carey and Hare give a rather bizarre result,
and strangely enough, if you reverse the rankings, you get every method
picking C as the winner.

If you pick C as the second choice for those that prefer A, you get:

101: A>C>B
1: B>A>C
101: C>B>A

A: Baldwin, Carey, Hare, Nanson, Raynaud
C: Black, Borda, Bucklin

And yet reversing the order, you get

A: Baldwin, Carey, Hare, Nanson, Raynaud (again!)
B: Black, Borda, Bucklin

Finally, if the votes are split as close to 50-50 as possible, you have

50: A>C>B
51: A>B>C
1: B>A>C
101: C>B>A

A: Baldwin, Carey, Hare, Nanson, Raynaud
B: Bucklin
C: Black, Borda, Coombs

Moving one vote from A>B>C to A>C>B makes Bucklin undefined but does not
affect the others. Reversing the order still lets A win under Baldwin,
Carey, Nanson, and Raynaud. Hare changes to candidate C, and Black, Borda,
Coombs all change to B.

The upshot is, with this example it looks like Borda and Black act the
most logically through the range of possible rankings for B and C when
voters pick candidate A for their first choice.

(Of couse, right now I'm kind of punchy from pain pills, so I could be
missing something. :D )


Michael Rouse