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
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