[EM] More comments re: few voters, 0-info
MIKE OSSIPOFF
nkklrp at hotmail.com
Tue Mar 13 17:05:08 PST 2001
Though there must be a good mathematical strategy for few voters &
0-info, it might be quite a job.
Fist of all, since, as Richard pointed out, your other votes
affect the worth of voting for i, or even the worth of voting i over j,
then, except with 3 candidates, we must evaluate the worth to you
of every combination of candidates that you could vote for.
The obvious thing to do is use a computer program to evaluate the
worth to you of every combination of altenatives that you could vote
for, with every possible equiprobable combination of ways the other
people could vote. I guess "permutation" is a more accurate word
than "combination" here.
The trouble with that is that it quickly becomes prohibitively
time-consuming.
One very rough estimate would be to just use above-mean when the
voters & candidates are numerous enough to render that exhaustive
computer study too time-consuming.
But I'd expect that something less time-consuming is possible.
A few days ago Richard posted suggestions for symbols to represent
the various kinds of ties possible with 3 candidates. It could of course
be extended to more candidates.
He pointed out that each type of tie is equally likely no matter which
candidates are which in that tie. That kind of equality is enough when
there are lots of voters, and only one kind of tie is likely. But when
all sorts of ties can happen, we have to consider the actual probability
of the various kinds of ties.
That could be calculated, but, just as with the exhaustive computer
approach, we have to be able to say how people can be assumed to vote
in a 0-info election.
Can we assume that each voter is equally likely to vote for 1 candidate,
2 candidates, 3 candidates...or N candidates (other than voting for
favorite and not voting for last choice)? Richard suggested such an
assumption if voters are assumed to be using above-mean strategy. But
if other people are voting that way, then above-mean strategy is
surely not what you want to use. In that case, they know that and
we shouldn't expect them to use it. Does that mean that we shouldn't
expect them to be equally likely to vote for 1, 2, 3...N candidates
aside from favorite (which they vote for) and last choice (which they
don't vote for)?
What then, assume that for each voter every possible ballot is
equiprobable? For instance, with 3 candidates, these are the
possible ballots:
A, B, C, AB, AC, BA, BC, CA, CB
So I don't even know what kinds of ballots should be considered
equally likely for a voter in a 0-info election. That's the 1st
thing to decide, before strategy can be calculated.
Mike Ossipoff
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