The "problem" with circularity (was Re: Reply to Blake Cretney)

[David Catchpole]

I'm afraid we can't take such a nihilist approach to "spoiler candidates."
The thing though is that the entrenchment of such candidates as a
possibility in any type of (non-stochastic) election does provide us with
an obstacle which cannot be simply pushed down. This doesn't mean we
simply give up on those norms we cannot always satsfy, though, as some
members of this list have suggested (especially as regards "Independence
from Irrelevant Alternatives"). A useful analogy was Arrow's of his
possibility theorems and Carnot's laws for thermal engines- they tell us
none of our constructions will be "perfect," but they also allow us to
compare the extent of imperfection.

On Wed, 17 Mar 1999, Steve Eppley wrote:

> Markus Schulze wrote:
> > Steve Eppley wrote:
> >>  JITW guarantees that no candidate can be
> >>  made into a spoiler against his/her will.
> > 
> > The Condorcet Paradox says that there are situations in
> > which _independently on who is elected_ there is always
> > a spoiler. These are the so-called "cyclic" situations.
> > 
> > JITW cannot get rid of this problem.
> 
> Sure it can.  Any candidate who believes s/he will spoil the outcome 
> by being included in the voters' orders of preference can simply 
> withdraw so the pairings involving him/her will not be counted.
> 
> Markus needs to reflect further on the meaning of the word "spoiler." 
> The "spoiler dilemma" is what deters candidates from competing: given 
> that voting methods are all flawed--some much more than others--they 
> have a reasonable fear that the outcome will be worse if they compete 
> than if they don't.  JITW allows them to compete and be certain the 
> outcome will be no worse than if they hadn't competed.  (This assumes 
> the voters won't goof by forgetting to rank their second choice ahead 
> of their third choice, when extra candidates on the ballot make 
> voting somewhat more tedious.)
> 
> > 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.
> > 
> > Independently on who is elected, there is always
> > a spoiler. JITW cannot guarantee that no candidate
> > can be made into a spoiler against his will.
> 
> The key phrase is "against his will."  Markus hasn't identified 
> which, if any, of the candidates in his example is forced to be a 
> spoiler against his will.  None of them can be.
> 
> There's no reason why any of the candidates would be deterred from 
> competing, since any can withdraw if that improves the outcome (from 
> his/her point of view).
> 
> Let's suppose that in Markus' example, if no one withdraws then A 
> will be elected.  Obviously, A is not a spoiler.  
> 
> If B hadn't competed, then C would have been elected.  So if B 
> wishes, B may voluntarily withdraw in order to avoid spoiling C's 
> election.
> 
> * *
> 
> I presume Markus' point has something to do with the fact that since 
> A has a reason to believe B will withdraw, then A would have an 
> incentive to offer to withdraw instead, producing an outcome 
> (electing B) which both A and B would prefer more than electing C.
> 
> And since C would have a reason to believe that A will offer to 
> withdraw, then C would have an incentive to offer to withdraw 
> instead, producing an outcome (electing A) which both C and A would 
> prefer more than electing B.  
> 
> But just because all the candidates have an incentive to withdraw 
> (though only one will, depending on the results of their 
> negotiations) that does NOT refute my claim about JITW.
> 
> 
> ---Steve     (Steve Eppley    seppley at alumni.caltech.edu)
> 
>