Probabilistic criteria (was Re: [EM] Participation & SARC)

[Steve Eppley]

Mike O wrote:
> Markus S wrote:
-snip-
>> Suppose that you are in a public discussion outside the
>> internet. Suppose that one of your opponents says that all
>> those problems that you are talking about can be circumvented
>> simply be using a random tie breaker. What will your answer?
> 
> My answer would be: "Go for it!" I wouldn't take such a
> proposal seriously as a rival to the methods that I propose. 
-snip-

But almost everyone employs a random tie-breaker, because that's 
more acceptible democratically than other solutions to ties: a 
non-random dictator, or non-random unequal treatment of the 
alternatives.  Tie-breakers which aren't totally deterministic 
must be taken seriously, even though overall procedures which 
are often random do not need to be taken seriously.

If a criterion says the outcome must be unaffected if a 
particular portion of the scenario is varied, and there's a 
(possibly rare) scenario where we can't tell for sure what the 
outcome will be given some so-called "single-winner" procedure 
which by its definition selects more than one winner in that 
scenario, does the procedure satisfy the criterion or not?

Deterministic procedures are *never* random.  I define a 
probabilistic procedure as a procedure which is not 
deterministic.  This means a procedure which on rare occasions 
employs a random tie-breaker is considered probabilistic, not 
deterministic.  As I interpret Mike's history of advocacy, he 
(and most of us, including me) advocates probabilistic 
procedures.

Yes, we can argue that a procedure "practically" satisfies a 
criterion by pointing out that its failures would be rare and/or 
unimportant.  But it seems to me that we will be better off if 
we can demonstrate "complete" satisfaction.


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