Your right. This is a situation where strategic voting is effective.
I think your example breaks any sane voting system.
I wonder if this can be semi-rescued in the limit of a large number of voters each having an infinitesimal influence?
Edit: No it can’t. Imagine a multitude of voters. As the situation slides from 1⁄3 on each to 2⁄3 on BCA, there must be some point at which the utility for an ABC voter increases along this transition.
Yeah, “3 parties with cyclic preferences” is like the aqua regia of voting systems. Unfortunately I think it means you have to replace the easy question of “is it strategy-proof” with a hard question like “on some reasonable distribution of preferences, how much strategy does it encourage?”
Yep. And I’m seeing how many of the traditional election assumptions I need to break in order to make it work.
I got independence of irrelevant alternatives by ditching determinism and using utility scales not orderings. (If a candidate has no chance of winning, their presence doesn’t effect the election)
What if those preferences were expressed on a monetary scale and the election could also move money between voters in complicated ways?
Your right. This is a situation where strategic voting is effective.
I think your example breaks any sane voting system.
I wonder if this can be semi-rescued in the limit of a large number of voters each having an infinitesimal influence?
Edit: No it can’t. Imagine a multitude of voters. As the situation slides from 1⁄3 on each to 2⁄3 on BCA, there must be some point at which the utility for an ABC voter increases along this transition.
Yeah, “3 parties with cyclic preferences” is like the aqua regia of voting systems. Unfortunately I think it means you have to replace the easy question of “is it strategy-proof” with a hard question like “on some reasonable distribution of preferences, how much strategy does it encourage?”
Yep. And I’m seeing how many of the traditional election assumptions I need to break in order to make it work.
I got independence of irrelevant alternatives by ditching determinism and using utility scales not orderings. (If a candidate has no chance of winning, their presence doesn’t effect the election)
What if those preferences were expressed on a monetary scale and the election could also move money between voters in complicated ways?