[EM] non-determinism and PR.

[Bart Ingles]

Forest Simmons wrote:

> 
> And the obvious PAV solution would be 60 A's and 40 C's.  Membership
> in the cycle didn't guarantee B any positive probability.
> 
> It is interesting to me that in my other example
> 
> 34 ABC
 > 33 BCA
 > 33 CAB
> 
> some respondents thought it was obvious that A, B, and C should have
> nearly equal chances, while others thought it was obvious that the
> deterministic winner A should be chosen 100 percent of the time.
> 
> Some thought my hypothetical coin toss was way out of line in one
> direction, while others thought it was way out of line in the other.


What I meant by my earlier question is, suppose the above ballot example 
is the result of strategic voting in which the CAB voters' sincere 
preference order was really CBA, where C is the sincere Condorcet loser. 
  Any deterministic or non-deterministic method that gives C a nonzero 
probability of winning also gives this faction incentive to create a 
cycle.  It's possible that the nonzero probability of an A win would be 
enough to counter this incentive, but probably not if this faction 
preferred B only slightly to A.

OTOH, the sincere CW might have been A, and the BCA ballots the result 
of an insincere BAC faction attempting to create a cycle.  In this case 
any method that gives B a nonzero probability of winning also provides 
incentive for this behavior.

The same for the ABC ballots, if C was the sincere CW.

Of course this is not solely a problem for non-deterministic methods, 
but I don't see how non-determinism provides the solution.

Sorry if this rehashes questions that have already been covered.  I 
haven't been following the "sprucing up" thread closely; I'm mainly 
thinking about general three-candidate examples like the one above.

Regards,
Bart