[EM] Clone proofing Copeland

[Brian Olson]

If I understand this, it's a Condorcet cycle resolution system based  
purely on who was 1st pick on each ballot. So, count up the virtual  
round robin matrix, and count 1st place votes separately for later if  
needed.

It's incomplete. A Condorcet method can elect someone no one put in  
for first place. It can even have a cycle of people no one voted for  
first place.

choices A, B and C exhibit a cycle of being voted for in 2nd, 3nd and  
4th place. Eight other choices split the first place vote evenly and  
are otherwise always ranked 5th or lower. There is now a cycle  
between prospective winners A, B and C and none of them has any first  
place votes.

D>A>B>C>E>F>G>H>I>J>K
E>A>B>C>F>G>H>I>J>K>D
F>A>B>C>G>H>I>J>K>D>E
G>B>C>A>H>I>J>K>D>E>F
H>B>C>A>I>J>K>D>E>F>G
I>B>C>A>J>K>D>E>F>G>H
J>C>A>B>K>D>E>F>G>H>I
K>C>A>B>D>E>F>G>H>I>J

http://betterpolls.com/et?vrr=-clist&if=-cname&cand=11&seats=1&data=D% 
3EA%3EB%3EC%3EE%3EF%3EG%3EH%3EI%3EJ%3EK%0D%0AE%3EA%3EB%3EC%3EF%3EG%3EH 
%3EI%3EJ%3EK%3ED%0D%0AF%3EA%3EB%3EC%3EG%3EH%3EI%3EJ%3EK%3ED%3EE%0D%0AG 
%3EB%3EC%3EA%3EH%3EI%3EJ%3EK%3ED%3EE%3EF%0D%0AH%3EB%3EC%3EA%3EI%3EJ% 
3EK%3ED%3EE%3EF%3EG%0D%0AI%3EB%3EC%3EA%3EJ%3EK%3ED%3EE%3EF%3EG%3EH%0D% 
0AJ%3EC%3EA%3EB%3EK%3ED%3EE%3EF%3EG%3EH%3EI%0D%0AK%3EC%3EA%3EB%3ED%3EE 
%3EF%3EG%3EH%3EI%3EJ

On Dec 30, 2006, at 5:52 PM, Simmons, Forest wrote:

> Here's a version that is both clone proof and monotonic:
>
> The winner is the alternative A with the smallest number of ballots  
> on which alternatives that beat A pairwise are ranked in first  
> place. [shared first place slots are counted fractionally]
>
> That's it.
>
> This method satisfies the Smith Criterion, Monotonicity, and Clone  
> Independence.
>
> I'll leave it up to Chris to tell us which of Woodall's criteria  
> are not respected by this method.
>
> I also like the stochastic version that chooses by random ballot  
> from the set of alternatives  S, such that for each  A in S,  at  
> most fifty percent of the first place slots are taken up by  
> alternatives that beat A pairwise.