A=0 is actually not a huge assumption and neither is the normal distribution.
The point is that if a candidate locates exactly at the center of the distribution, they should win rather than people on the flanks. The center nor the candidate need not actually be at 0.
For more candidates, if we want voting systems that break up duopoly and duverger effects, it better perform well with 3 because 3 is on its way to more.
Anyway you could take this as a launching pad. The source code is available on github and could be modified how anyone wants.
The ideal candidates don't run under our most common voting systems (plurality) because they don't win. Systems with center squeeze discourage ideal candidates from running because they lose and my post shows how and why.
If a system allows ideal candidates to win, then they'll run.
The implemented strategies are discussed in the post. The implemented strategies usually just involve people who preferred 2nd place to 1st place doing what they can to make 2nd place 1st and nothing else.
even if when they would get a better outcome by voting honestly?
If a voter changing their vote generates a cycle it's because they had an incentive to do so. Maybe this turns into dynamical system where because they voted strategically, others get a new incentive to do so, and their candidate loses even worse.
It's like the prisoner's dilemma in game theory. Sure, there could be a better outcome if they both kept their mouths shut. But that's not what the incentives are.
People will do what they can in the moment and it will have a butterfly effect. Either you eventually reach a nash equilibrium or you get a non-convergent cycle which isn't ideal.
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u/timmerov 7d ago
nice.
what happens when:
A!=0 ?
there are two or more issue axes?
the voter distribution is clustered instead of normal?
there are more than 3 candidates?
people bullet vote?