# [EM] voting equilibrium only sketched

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Apr 29 23:09:31 PDT 2000

EM list--

I want to add that my brief description of a simplified voting
equilibrium definition was only a sketch, and that there are
details that would have to be clarified to make it complete.
I wrote it in that form for brevity. The details have been
written down. With all the necessary details, it is an
exceptionally wordy criterion, but when I use it I'll just
sketch it even more briefly than I did here, noting somewhere
that the details are available upon request.

The UUCC definition seems to me to be complete as written
in my letter here.

***

Well, in case someone will have an opinion about my attempt at
a complete definition of a simpler & more widely-applicable
voting equilibrium, why not state the details here.
Obviously, with something this wordy, there's plenty of opportunity
for errors, omissions, and things unintentionally left vague:

***

By a "comparison", I mean the magnitude-order comparison
between 2 vote totals. They could be the absolute vote-totals
used in point systems such as Plurality, Approval & Borda, or
in IRV. Or they could be the scores that determine the winner
or the outcome at some step of a circular tie solving method,
such as votes-against or margin scores.

By "crucial comparison", I mean a comparison whose order, if
it were reversed, would change who wins.

By "closest crucial comparison", I mean the crucial comparison
that is closest to a tie.

To vote between a certain candidate-pair means, in a point
system, to vote for one but not the other, or to vote so as to
give more points to one than to the other. In a rank method it
means to rank one of the 2 candidates higher than the other.

Of course, the way a voter can affect a comparison in a way
favorable to him involves voting between some candidate-pair.
For instance, in Plurality or Approval, it involves voting
between the 2 expected frontrunners, the candidates whose
vote totals are in the closest crucial comparison (the only
crucial comparison in this case). In Condorcet, it involves
voting to give one candidate a greater votes-against than
another, or voting to make one candidate pair-beat another.

The voters' strategy decisions are based on the assumption that
the strategy is for an individual voter, or for a faction that
is so small that the only crucial comparison that it can affect
is the one that would be the closest one if that faction didn't
vote. That assumption is standard in most strategy discussion.

All the voters share the same predictive beliefs, and they all
vote to get their most preferred outcome that they can.

It's assumed to be nearly certain that a certain comparison will
be the closest crucial comparison. By "nearly certain", I mean
that it's so certain that each voter feels sure that there's a
certain candidate-pair that he should vote between, no matter
what other candidate-pair that would prevent him from voting between.
But no so certain that he wouldn't improve his expectation some
by voting between other candidate-pairs, provided that doing
so wouldn't prevent him from voting between that more important
candidate pair, the one that would affect the likely closest crucial
comparison.

How the voter decides which other candidate-pairs to vote
between isn't relevant to this definition, or so it seems to
me now. In Approval, only improbably inconsistant frontrunner
probabilities would make it to a voter's advantage to not
vote, additionally, for every candidate that he likes better than
the one that he voted for in order to vote between that most
important candidate-pair. But it seems to me that this
definition doesn't have to talk about how voters determine which
other candidate-pairs to vote between.

So a simplified & extended voting equilibrium is an outcome,
including the officially reported & recorded count results, that
is consistant with the belief that a certain comparison is
the closest crucial comparison.

***

Maybe this isn't of interest, and I don't mean to waste anyone's
time, but I post it on the chance that someone might suggest
a better approach. But even if no one's interested, I haven't
wasted my time, because this is the 1st time that I've typed
all this out, to be printed out.

***

All I know about compliance is that Approval passes and
Plurality, Borda, & IRV fail.

***

Mike Ossipoff

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