Probabilistic criteria (was Re: [EM] Participation & SARC)
SEppley at alumni.caltech.edu
Tue May 9 09:20:27 PDT 2000
Mike O wrote:
> Markus S wrote:
>> 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.
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
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)
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