[EM] criteria questions

[Juho Laatu]

Hello Jobst, James,

On Aug 10, 2005, at 14:02, Jobst Heitzig wrote:
> James:
>>> 2. Does the Condorcet criterion plus the independence of
>>> clones criterion imply the Smith criterion?

> Rule a: Picks the Condorcet Winner if it exists, otherwise determine
> which candidates are defeated *most* often and pick one of them at
> random. Fulfils Condorcet Criterion and Independence of Clones, but
> certainly not the Smith criterion.

Does this algorithm meet the Independence of Clones criterion? I'm not 
sure if I got the definitions right, but here is an example that shows 
what I was thinking. The idea is that the most defeated candidate is in 
the d-e-f clone set, but if one of the a-b-c clone set candidates is 
removed, we have a Condorcet winner in the a-b-c clone set.

11:  abcdef
11:  bcaefd
11:  cabfde
10:  defcba
10:  efdbac
10:  fdeacb



Here is also another counterexample algorithm candidate.

Find the largest clone sets (genuine subsets of the set of candidates). 
Replace the clone subsets in the ballots each with one symbolic 
candidate representing the whole clone set. Find the MinMax winner. If 
the winner is a symbolic candidate representing a clone set, take the 
original ballots, eliminate all other candidates than the members of 
this clone set and start again from the beginning.

This modified MinMax should still be Condorcet compliant and 
non-Smith-compliant. And the modifications should make it independent 
of clones.

BR, Juho


((P.S. Some time ago I brought up the idea of using "voluntary and 
manually generated clone wannabe sets" (=parties) on this list (April 
28th). The algorithm above finds the clone sets automatically but it is 
quite rough. It would be quite possible to enhance it so that the 
border line between clone sets and "close to clone sets" would be 
smooth (strengths of defeats would be weighed based on the 
strength/weakness of clone relationship between the candidates).))