[EM] Maximum Consent

[Anthony Simmons]

>> From: Forest Simmons <fsimmons at pcc.edu>
>> Subject: Re: Responses to some of Forest's ideas

>> On Sat, 28 Jul 2001 DEMOREP1 at aol.com wrote:

>> > Consensus (100 percent agreement) is in utopia-land.

>> From the point of view of maximum possible consent, the
>> Approval Winner is closer to the 100 percent ideal than
>> the 50 percent plus one winner when the two are not the
>> same.

>> The 50 percent plus one winner may be superior by some
>> other standard.

>> Forest

Perhaps we should take into account the fact that different
questions are being asked:

    (1) Is candidate A okay?  (Approval)
    (2) Is candidate A the best alternative?  (plurality)

We could get very high concensus numbers by asking voters to
(3) select the worst candidate, and then consider each
candidate's approval rating to be the percentage of voters
who didn't choose him/her/it as the worst.

I notice that when there is a large field of candidates, (2)
and (3) reduce the amount of information in each ballot, in
the information theoretic sense (the information being in the
way the ballot was voted).  That is, there's less uncertainty
about how each voter will vote on a particular candidate.
I'm looking at this in terms of each voter voting "yes" or
"no" on each candidate.

In (2) -- plurality, where each voter votes yes on one
candidate and no on all the others -- for example, most votes
are "no", so we can assume that a voter will vote "no" on a
randomly chosen candidate, and be right most of the time.
Same for (3), where most votes are "yes".

In (1), however, there is no constraint that forces most
votes to be "yes" or "no", so random guessing is less likely
to be successful.  Thus, votes in (1) -- Approval -- carry
more information.  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".
(If we wanted to be thorough, we would also have to take into
account the fact that votes on different candidates are not
independent, which would reduce the information per ballot,
but we are probably better off leaving those particular worms
in the can.)

Therefore, it would appear that Approval wins again.  But:

Ranking the candidates offers more possibilities -- different
ways to mark a ballot -- than simply checking off "yes" or
"no" for each.  From this, it seems to follow that IRV does
better according to this criterion than (1), (2) or (3), but
this violates a principle of logic that says that any
argument that shows IRV to be better than Approval is
invalid.

On the other hand, IRV doesn't use all of the information in
each round.  In the first round, it's the same as Plurality.
Then a candidate is dropped.  Though I haven't thought it
through, it seems reasonable to expect this to drop less
information from the ballot than if any other candidate were
dropped, since the votes for/against this candidate are most
predictable.  It seems like IRV starts as Plurality, and then
slowly drops information about some candidates, while
increasing information about others until it gets a winner,
using the least information that produces a majority.