Circular Stand-Off

[Markus Schulze]

Dear Steve,

you wrote (17 Mar 1999):
> > The following is Schulze's Example:
> >    40 voters prefer A > B > C.
> >    35 voters prefer B > C > A.
> >    25 voters prefer C > A > B.
> >    Candidate A prefers candidate B to candidate C.
> >    Candidate B prefers candidate C to candidate A.
> >    Candidate C prefers candidate A to candidate B.
> > 
> > Donald writes: I would call this a Circular Stand-Off. All three 
> > candidates are still contenders - any one of them could be the 
> > winner if only the "correct" candidate would withdraw. 
>
> There is no "correct" candidate to withdraw (or to elect) when there 
> is a sincere circular tie.  See the discussion in this list regarding 
> the merits of the Smith//Random method, which randomly elects one of 
> the top cycle.
>
> > It is merely a question of which candidate gives in first. This 
> > stand-off could last long after "Schulze is Dead". (punch line 
> > of a famous joke).
>
> No, it can't last long because the JITW procedure provides candidates 
> only a short period of time (a few days, maybe a week) to withdraw 
> before the final result is tallied.

You will have to explain why you think that JITW is an improvement.
When you write that "there is no 'correct' candidate to withdraw (or
to elect) when there is a sincere circular tie," you admit that JITW
doesn't lead to a "better" election result than every other Smith
Criterion election methods (since every candidate of the top set is
equally qualified). And the claim that JITW guarantees that no
candidate will regret having competed, is simply not true.

Example: JITW//Smith//Condorcet[EM] is used.

   A:B=48:52
   A:C=53:47
   A:D=43:57
   A:E=44:56
   B:C=45:55
   B:D=42:58
   B:E=62:38
   C:D=54:46
   C:E=41:59
   D:E=40:60
   A, B, and C won't withdraw under any circumstances.
   Candidate D prefers B to C to E to A.
   Candidate E prefers C to B to D to A.

If no candidate withdraws, candidate A is elected.
If only candidate D withdraws, candidate B is elected.
If only candidate E withdraws, candidate C is elected.
If both candidates, D and E, withdraw, candidate A is elected.

Markus Schulze