Circular Stand-Off

[Steve Eppley]

Markus wrote:
> Paul wrote (20 May 1999):
> > Markus Schulze wrote:
-snip-
> > > 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.
> >
> > How do you get this? When A is compared to every other
> > candidate, it loses more than any other. Let me be more 
> > rigorous. Let us define a vote for candidate A as being an 
> > instance where A is ranked higher than another candidate. 
> > So if we add up all the votes, A gets the least amount of 
> > votes (188 out of a possible 400).  
-snip-
>
> The example above demonstrates that JITW//Smith//Condorcet[EM]
> doesn't meet Steve Eppley's criterion that no candidate will regret
> having competed. If you want to demonstrate that a given criterion
> is violated, you cannot expect that the same example can be used
> for every election method. 

Apparently Markus didn't realize that Paul doesn't know how  
to tally Condorcet[EM], also known as Condorcet(VotesAgainst). 
There's no reason to think that Paul was trying to tally a 
different method, in this context.

As for the "criterion":  Markus has indeed proven there is 
a scenario where a candidate might regret having competed.  
(The scenario is implausible, though, because no reasons are 
given why A, B, and C would never withdraw.)  

But my point is the effect on potential candidates when they 
are deciding whether or not to compete.  My real criterion is 
to minimize incentives which will deter potential candidates 
from competing.  JITW should effectively eliminate the fear of 
spoiling.


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)