Approval and LO2E

Mike Ositoff ntk at
Tue Nov 3 23:53:44 PST 1998

Blake said:

Anyway, my problem is this:  Consider an election with
> a united but minority totalitarian movement and a fragmented
> democratic movement.  A and B will be the democrats.  C will
> be the totalitarian.  The public will be 55% democratic, 45%
> totalitarian.  The totalitarians will likely all vote for C
> alone.  Voter preferences are as follows:
> 30 A B C
> 25 B A C
> 45 C A=B
> Now if not enough A and B voters compromise the result could be 
> like this
> 25 A
> 10 A B
> 20 B
> 45 C
> A 35
> B 30
> C 45
> With C winning easily

I believe that the best rank methods, by which I mean the VA
methods, are better than Approval. Of course one can't expect
Approval to have the full strategy advantages of the best rank

This kind of example has been used before. Typically, either
A or B would be more of a middle alternative, in which case
it would be CW unless one extreme has a majority. That makes
it easy for A & B voters to know whom to vote for. If B is
middle, then its voters have no reason to vote for anything
else, and A voters know that B is the best they can get, and
so vote for B.

Or, if neither A or B is more middle than the other, maybae
one is known or strongly suspected to be significantly bigger
than the other. Then, too, it wouldn't be hard for A & B voters
to know which to vote for. The bigger one is the obvious place
for A & B votes to come  together. Its voters vote for it only
and the other alternative's voters vote for it too.

If neither of those things is true, and A & B are equally
distant from C, and seemingly equal in size? What would
happen would depend of whether trust exists and is justified.

Not satisfactory? You can't have everything with such a simple
method. As an A or B voter, I'd vote for the other in that
situation, without either of the above-described helpful
conditions. I'd vote for both. Of course, if the other
voters defected, then I'd do the same next time, and they'd
know to expect that. That's why they'd be foolish to defect
under those conditions. With neither A nor B seeming bigger
or more middle than the other, it would be quite obvious that
both groups of voters need to co-operate to beat C. Consider
how it would make the A voters look if they defected and caused
the election of the totalitarian. The fact that there then
might not _be_ a next election would be all the more reason
why defection would be out of the question.
> On the other hand, one of the A or B groups could stare down the other
> side, using its fear of C to force it to compromise.
> 35 A B
> 20 B
> 45 C
> A 35
> B 55
> C 45
> Here B won because the C voters panicked.  This is what I mean by
> government of the stubborn.

Not plausible. If it looked as if A is likely to have 75% more
voters than B, the A voters would have reason to expect the
B voters to vote for A. The A voters would be in a better
position to exxpect that. Whether they'd refuse to vote for
B would depend on what degree of amity or enmity exists between
A & B voters. If they get on very well, then of course both
would vote {A,B}. If not, then the A voters would vote {A}
and the B voters would know that, and would vote {A,B}, if
we're assuming that they want to optimize the outcome.

> If both A and B compromise the results could look like this
> 50 A B
> 3 A
> 2 B
> C 45
> A 53
> B 52
> C 45
> See how compromise can result in the election between A and B being
> made by a few people who don't compromise.

The A voters, in your above example, defected in smaller numbers,
percentage-wise, but A still won. If A & B voters aren't 
on the best of terms, and defection by either side is considered
possible, and A voters are determined not to let B voters steal
the election, then the A voters would make it clear, before
the election, that they were just voting for A, because A has
probably about 75% more voters than B and is therefore the natural
choice to beat C.

By the way, if voters were using the mathematical strategy
that I described the other day, then, if A is expected to
be about 75% bigger than B, and it were known that both
A & B votes know that, then it would be obvious that A
has a higher probability of being the other frontrunner with
C. The psycological strategic considerations would make
it look like a virtually zero chance that B could be a frontrunner
with C. A would win for sure. Just the fact that A is 2nd biggest
and B is smallest would make A look more like a frontrunner,
and then the consideration of what the other voters are
doing would make it pretty much a sure than that B can't
be a frontrunner.

> This is in contrast to Smith//Condorcet, Tideman, Schulze (VA and Margins) 
> and AV/IRO, where the democratic voters can prevent the election of C 
> just by ranking C last.  And the C voters have no way to use insincere 
> voting to get C elected.

I'll check that claim out.

> This is of course related to my problems with Approval and Clones,
> since A and B are clones as far as their sincere rankings in this
> example.

Clones are a special case. Approval doesn't _automatically_
do the right thing in this clone example, but it doesn't
have Margins' tendency to require complete abandonment of
favorites as can happen in Margins if its poorly-deterred
order-reversal happens.

Rankings provide much opportunity for a method to screw up,
which is why if rankings are used, it's important to count
them in the best way.

> ---
> Blake
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