By the way, from what Kevin said, AERLO is nonmonotonic. That's ok.
Advantages come at a price, and a big gain can have price that some would
regard as an embarrassment. But I'll take an embarrassment instead of a
strategy problem anytime.
Kev in's objections to SOACC & Strong FBC apply also to SPCA & ASPCA.
Deviating from sincere ranking of the acceptables could change your effect
on other people's AERLO activation in a way favorable to you--in the case of
SPCA, a way that changes the winner to someone in your acceptable set.
But it's obvious that enhanced MMPO brings a lot of benefit, and so it's
just a matter of describing it.
All of us, including me, criticize criteria that are contrived so that some
particular method will pass. But that's the kind of criteria that I'm
writing now. That's because I want to describe what it is that enhanced MMPO
offers.
Here are a few approaches:
1. Probabilistic criteria, conditional complaince
2. Breaking it down to a ballot-specific guarantee and a nonmonotonic
exception
The 1st approach is simpler, though it results in a criterion that is
unmeetable. But enhanced MMPO meets those criteria provided that the voter
doesn't know if his ranking will affect other people's AERLO activation to
his benefit or antibenefit. That's what I meant by conditional compliance.
The 2nd approach results in a criterion met by enhanced MMPO. But it's a
method-specific-sounding criterion, an elaborate criterion that has wording
that matters because of what method we're talking about. So maybe the
resulting criteria should just be called enhanced MMPO properties instead of
criteria.
1. Probabilistic criteria, conditional compliance:
MMPO with AERLO meets SPCA, as defined, if the voter dosn't know if his
ranking will make things better or worse for him by its affect on other
people's AERLO activation. That's what I mean by conditional compliance.
MMPO with AERLO and power truncation meets ASPCA conditionally.
A stronger version could be written:
Completely Sincere Protection of Candidates who are Acceptble (CSPCA):
If, for a particular voter, the election is an acceptable/unacceptable
situation, then that voter should be able to maximize the probability that
the winner will come from his acceptable set, while sincerely ranking all of
the candidates.
[end of CSPCA definition]
MMPO, with AERLO, ATLO, and power truncation conditionally meets CSPCA.
Might as well use the stronger CSPCA, when sufficiently enhanced MMPO meets
both. But of course there's no reason to bother ranking the unacceptables,
and using ATLO to truncate them. Easier to just not rank them.
That's the 1st approach, probabilistic criteria, conditional compliance.
SOACC and Strong FBC could likewise be defined probabilistically, with the
goal being to maximize the voter's expectation instead of to get the voter's
best outcome. With the unknown effect on other people's AERLO activation,
those 2 things are not the same.
If SOACC and Strong FBC are defined probabilistically in that way, in terms
of maximizing expectation instead of getting the voter's best outcome, then
MMPO with AERLO meets them conditionally.
This conditional compliance means something. With other methods, you know
that burying your favorite to help a compromise will definitely help that
compromise, or at least won't hurt him. In MMPO, with the unknown effect on
other people's AERLO activation, you know no such thing.
SOACC could be strengthened by requiring that expectation can be maximized
while sincerely ranking the acceptables, and not falsifying a preference--a
counterpart to ASPCA. I'll call that ASOACC ("A" for augmented).
SOACC could be further strengthened by requiring that the voter be able to
maximize expectation while ranking all the candidates sincerely--a
countgerpart to CSPCA. I'll call that CSOACC ("C" for completely).
This has been about the first approach: probabilistic criteria, conditional
compliance.
In a subsequent posting, probably not tonight, I'll describe the 2nd
approach: Breaking it down, ballot-specific guarantee and nonmonotonic
exception.
Mike Ossipoff
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