[EM] James: Approval & voter median

[MIKE OSSIPOFF]

Again I neglected to write down the subject line so that I could post with 
the same subject line.

James--

I'd said:

>Approval quickly homes in on the voter median, and then stays there.
>Condorcet goes directly to the voter median in its 1st election.
Approval
>& CR do so in thei r 2nd election. That's the price of simplicity and
easy
>proposability.

You replied:

	This is a very interesting assertion, and if it is true, it is an
excellent pro-approval argument, but I will still need more convincing
before I accept it as true.

I reply:

Well, I'd hoped that my demonstration with Favorite, Sleazy & Worst would be 
convincing. But check out the article by Myerson & Weber about their new 
voting equilibrium. They demonstrate it too.

You continued:


	It is often much easier for me to work with simplified examples in
order
to evaluate the properties of a method--creating imaginary voters with
well-defined preferences, and then imagining their likely behavior
given
different methods and different scenarios. I request that you
participate
in this process with me.
	Your statements about approval seem to be universal in nature, that
is,
you seem to assert that approval will always or nearly always lead to
the
election of a median candidate within two election cycles.

I reply:

Yes, I did say that Approval takes 2 elections to get to the voter median, 
but later, in my demonstration, I said that it, depending on how many 
false-compromise lesser-evils there are, it could take longer, but Approval 
would still get there before long. Then I said that _in our particular 
political system,_ with Approval, I'd expect the voter median candidate or 
party to be elected in the 2nd election.

So, in general, Approval can't be necessarily be expected to go to the voter 
median in its 2nd election, but it will go that way and get there soon, and 
then stay there.

First let me comment that the following example seems unnecessarily 
elaborate, compared to my Favorite, Sleazy, & Worst example, which shows why 
I made my claim.

You continued:

So, I
thought
we might continue our discussion by concocting imaginary electorates,
and
seeing whether your statement is likely to apply to them, and if so,
how.
	Here is the first situation I have concocted. It is a relatively
straightforward one, not specifically designed to lead to any specific
result. There are three candidates: Left, Center, and Right (L, C, and
R
for short.) L and R are the candidates from well-established major
parties. Approval voting has recently been adopted in place of
plurality,
and a new party is running a candidate offering sensible compromise
solutions to longstanding problems. C is the last choice of some voters
because of unfamiliarity (and a sense that C's party is less
well-equipped
to govern than the major parties), but most people prefer C to their
least
favorite major party candidate, and C also develops a substantial core
following of his own. Below are the preference relationships for
different
percentages of the electorate. For the sake of simplicity, let's assume
that utility gaps are evenly spaced.

28: L>C>R
5: L>R>C
16: C>L>R
10: C>R>L
10: R>L>C
31: R>C>L

	C is a Condorcet winner, winning pairwise comparisons by 57-43 and
54-46
(substantial margins, if not landslide margins). Therefore, I assume
that
you will agree that C occupies the voter median.
	Mike, my question to you is this: How do you think this approval
voting
scenario will play out?

I reply:

Impossible to say how it will start out, without information about the 
voters' beliefs about eachother's preferences and abouit the canddiates' Pi, 
their likelihood to be in a tie or near-tie.

You continued:

What strategies will the voters use?

I reply:

I'd hope that in the 1st election, the voters would use Approval's 0-info 
strategy, because I claim that our elections are 0-info. So let's say that 
your election is a 0-info election initially, ok?

I'm looking at your message for the 1st time, and so I haven't had the 
opportunity to determine the result of 0-info above-mean strategy in your 
example. I hope that I can do so before I have to send this message and 
quit, but I only have a little time to be on the computer, and so I don't 
know if I'll be able to do that this time. But that won't be any trouble for 
you and others.

The real question is what will happen later, as people find out about 
winnability from previous Approval vote totals. I expect that Approval willl 
go to the voter median, and I'll check out your example to find out if it 
does so in your example.

You continued:

Will C win
in
the first election?

I'll check that out, hopefully before it's time to finish and send this 
reply.

You continued:

The second election, given similar candidates and
voters?

I reply:

Probably, but I'll have to check that out before I answer. Probably tomorrow 
will be my earlies possibility of a next opportunitly to get on the 
computer.

I have a few minutes left, and so let's take a look at the 1st election, the 
0-info elecion in which we assume that people use the above-mean strategy. 
I've copied your example below.

Just maybe, I might have the opportunity to deal with the 1st election in 
this reply, but surely my opportunity to discuss the 2nd election will be 
when I next get an opportunity to get on the computer.

[beginning of your example]

	Here is the first situation I have concocted. It is a relatively
straightforward one, not specifically designed to lead to any specific
result. There are three candidates: Left, Center, and Right (L, C, and
R
for short.) L and R are the candidates from well-established major
parties. Approval voting has recently been adopted in place of
plurality,
and a new party is running a candidate offering sensible compromise
solutions to longstanding problems. C is the last choice of some voters
because of unfamiliarity (and a sense that C's party is less
well-equipped
to govern than the major parties), but most people prefer C to their
least
favorite major party candidate, and C also develops a substantial core
following of his own. Below are the preference relationships for
different
percentages of the electorate. For the sake of simplicity, let's assume
that utility gaps are evenly spaced.

28: L>C>R
5: L>R>C
16: C>L>R
10: C>R>L
10: R>L>C
31: R>C>L

	C is a Condorcet winner, winning pairwise comparisons by 57-43 and
54-46

[end of your example]

I reply:

Everyone votes for their above-mean candidates. Do they vote for their 
middle candidate? It's necessary to suppose that they rate their middle one 
slightly above or below mean. Say half of each group rate their middle 
candidate above mean and half rate him below.

L wins the 1st election, the 0-info one in which people use above-mean 
strategy.

Now, for the subsequent elections that aren't 0-info, because of information 
from previous elections, I'll comment on those elections in subsequent 
postings, but probably won't get an opportunity do do so today.

Mike Ossipoff

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