[EM] approval scenarios, part 1

[Forest Simmons]

> From: "James Green-Armytage" <jarmyta at antioch-college.edu>

<snip>

> 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.
>

If first preference polls were accurate, R would be billed as most likely 
to win, and L as second most likely.  On the basis of this information 
rational strategy voters would place their approval cutoffs next to R on 
the side of L:

28 LC|R
5  L|RC
16 CL|R
10 CR|L
10 R|LC
31 R|CL

The respective approval totals for L, C, and R would be 49, 54, and 51, 
which means that C would likely win the first time around.

If preferences remain the same, then the second time around C would be 
most likely to win, with R second most likely, so the cutoffs would be 
next to C on the side of R:

28 LC|R
5  LR|C
16 C|LR
10 C|RL
10 RL|C
31 R|CL

The respective approval totals for L, C, and R would be 43, 54, and 46, 
which means that C's place as approval winner is stable, until the voter 
preferences change.

Forest