[EM] Maximum Consent

[Anthony Simmons]

>> From: Richard Moore <rmoore4 at home.com>
>> Subject: Re: [EM] Maximum Consent

>> Anthony Simmons wrote:

>> > Ideally, if we wanted each vote to contain
>> > as much information as possible, we should try to create the
>> > system so that half of the votes are "yes" and half "no".

>> That's actually possible. Set a rule that any voter voting
>> for fewer than half of the candidates will have his ballot
>> augmented until it is half-full by randomly selecting from
>> the unvoted candidates, and if he votes for more than half
>> of the candidates his ballot will be diminished until it
>> is half-full by a similar process. Adding or subtracting
>> from a ballot in this way doesn't improve the information
>> content of the ballot, but it does create a negative
>> incentive for voting any ballot that isn't 50/50.

Well, that's not quite what I was thinking of.  I meant half
of votes overall.  Thus, one ballot might have most votes
"yes" and another mostly "no", but there's more information
if the total number of "yes" and "no" votes is roughtly equal
across all ballots.  Actually requiring half and half (and
even numbers of candidates) on each ballot would offer fewer
possibilities and therefore less information per ballot.

Actually, I didn't state it right anyway.  What I should have
said was that the amount of information in the ballots is
greater when the odds of a randomly chosen box on a randomly
chosen ballot has closer to 50/50 chance of being checked.
Plurality obviously doesn't come close to this.  Approval
may or may not; if it did come close, it would indicate that
most candidates are roughly equally popular, which is
obviously something that can't be enforced as part of an
election procedure.

Offhand, it seems like the chance of a voter being critical
(being in a position to turn the election one way or another)
is greatest when the information in the ballots is greatest,
so perhaps entropy (sometimes very nicely described as the
amount of surprise in a piece of information) is a measure of
power, similar to Banzhaf index.  I don't know if there's any
connection; it's just a wild thought.

>> Or simply throw out any ballot that isn't 50/50 (+/- 1/2,
>> if the number of candidates is odd). If that's
>> objectionable, it shouldn't be any more so than throwing
>> out Plurality ballots that have multiple candidates marked
>> on them (e.g., Palm Beach butterfly ballots).

>> Whether forcing 50/50 ballots really is a desirable goal,
>> outside the information-theoretical considerations, is
>> debatable. It discourages strategic voting but replaces it
>> with something that might be worse: excessive constraints.
>> I think many of us feel strategy in Approval is not a bad
>> thing, and that Approval has about the right constraints
>> as is.

>> Richard