[EM] approval scenarios, part 1

[James Green-Armytage]

Dear Mike Ossipoff,

you wrote:
>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.

I reply:
	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.
	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. 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? What strategies will the voters use? Will C win in
the first election? The second election, given similar candidates and
voters? If so, how and why? Of course, one cannot authoritatively say who
would win, since it's only a fantasyland scenario, but what I'm interested
in is your understanding of the way in which approval tends toward the
voter median, as expressed through analysis of a particular example.
	Of course, anyone else is very much welcome to answer this question
according to their own opinion. I'm asking Mike in particular because it
was his assertion that got me thinking in this particular direction. But I
think differing viewpoints might be quite helpful.

my best,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm