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

[Steve Eppley]

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)