[EM] Efforts to improve on CR's strategy

[Forest Simmons]

On Tue, 18 May 2004, Ken Johnson wrote:

>
> >Message: 2
> >From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
> >
> >Ken,
> >...
> >I did not test Plurality.  I think it is very strange that you found it to
> >be better than Approval.  ...
> >
> >Kevin Venzke
> >stepjak at yahoo.fr
> >
> >
> >Message: 3
> >From: bql at bolson.org
> >...
> >That's odd. Approval turned out pretty well in my sims.
> >...
> >Brian Olson
> >http://bolson.org/
> >
> >
> >
> Here's an example of the kind of Bad Thing that can happen with
> Approval. There are 3 candidates (A, B, C) and 10 voters. I am using
> signed CR's in the range -1 to 1 (CR>0: approve, CR<0: disapprove).
> Following are the sincere CR's:
> 9 voters: A(-1), B(0.1), C(1)
> 1 voter: A(-1), B(1), C(-0.1)
> avg CR: A(-1), B(0.19), C(0.89)
> approval: A(0), B(10), C(9)
> plurality: A(0), B(1), C(9)
>

It is interesting that when we measure CR, we always assume that it is
average or total CR that is relevant.

If we were to erase the "avg CR" line in the above tally and replace it
with "min CR" or "lowest percentile CR" we would get

          A(-1), B(.1), C(-.1)

and then declare that B does "best with respect to CR," since B sports the
largest number on the "min CR" line, the only line dealing with CR.

In fact, arguably "consensus" is more about finding the candidate that
maximizes minimum CR than about finding the candidate that maximizes the
average CR.  That's why getting consensus is so difficult: if one voter
holds out, then the consensus isn't perfect.

Approval is a kind of compromise between perfect consensus (which gives
too much control to the picky, and may be impossible) and average CR
maximization, which gives too much credence to the idea that one voter's
satisfaction completely makes up for another voter's dissatisfaction.

Approval tends to elect the alternative that is tolerable for the greatest
number of voters (at least in the zero info case), which is more in the
spirit of consensus (where the concerns of minorities cannot be ignored).

Digression***********

"One man's good fortune compensates for another's misery" might make more
sense in a country where goods and burdens were distributed equally
throughout society, but not in any actual capitalist, socialist, or
communist country of modern history.

If there were such a country, then in that society it would make sense to
try to maximize total or average CR.  Such a society would also ameliorate
the "tyranny of the majority" problem.

NAFTA has raised the GNP of both the USA and Mexico, as predicted.  But
within both countries the rich have gotten richer, and the poor have
gotten poorer, because the leaks that used to give some trickle down have
all been efficiently caulked.

In neither country has a majority of citizens increased in prosperity, but
note that it would be possible for the majority to increase in prosperity
while the lowest quartile of the poor moved downward.

**********end of digression

Approval does best at maximizing the number of voters that can live with
the winning result in the zero info case.

As information increases, Approval moves away from this kind of consensus
winner towards the CW if there is one.

If that were the whole story, then (in my opinion) Approval would be
better than Condorcet, since Approval would always give a result between
the Condorcet Winner and the consensus winner (in the above sense) which
is the kind of consensus winner most needed in actually existing societies
(in my opinion: see above digression).

Unfortunately, at least in the USA, moving away from zero information
means moving in the opposite direction ... the direction of decreasing
information towards more disinformation. "The more you watch, the less you
know."

As far as I'm concerned, that's the only reason that Condorcet might give
a more satisfactory result than Approval in the USA presidential election.

But is that possibility worth the extra baggage of ranked ballots?

When answering this question keep in mind that Approval elections tend to
correct the disinformation, so the dynamics of Approval tend to be self
correcting in the long run.

Forest

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