[EM] approval scenarios, part 1

[Bart Ingles]

James Green-Armytage wrote:

> 	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

Since there was an open invitation, here's my take.  Assuming the 
utilities are equally spaced for all voters (an unlikely scenario, but I 
didn't choose the example), so that voters have no incentive other than 
pure strategy, I would expect to see:

28 LC
5 LR
26 C
10 RL
31 RC

With approval tallies of:

43 L
85 C
46 R

If the election were run a second time, the R voters might think they 
have a shot at winning, and bullet vote:

28 LC
5 LR
26 C
41 R

For totals of:

33 L
54 C
46 R

It's well known that there can be scenarios where approval would 
theoretically cycle between two or more winning candidates, but this 
doesn't appear to be one of them.

Bart