Kevin Venzke wrote:
Hello,

The last thing I did with my simulation is check whether on average a
candidate would prefer to have withdrawn (considering the results of
thousands of trials of one position) than stand, with the assumption that
they care what happens when they lose. (I'm not sure that's actually a
good assumption: It would be better to assume the voters are the ones who
care, and don't support a candidate who spoils the election.)

I got odd results. It could very well be a bug. But for example I found
that (sincere) FPP had very few scenarios where a candidate would prefer
to exit the race. Maybe it's because I had filtered out uncompetitive
elections. But, even if FPP can handle some three-way races doesn't mean
that we can score FPP based on them, with the assumption that they will
occur.

That seems like a big problem with my simulation, that there are always
three candidates, and no check for incentives for more or fewer to be
nominated.

I think that a nomination simulation would have to be more complex, to take feedback into account. Candidates would position themselves somewhere in opinion space, then move closer to the winners depending on the outcome of the simulation (and possibly decide to drop out if this would elect a candidate closer to their position).

Even so, the simulation would fail to catch certain aspects of the election cycle itself. Consider a two party state under FPTP. In a pure opinion-space analysis, the two parties would converge on a common point (the "center") in an effort to eat into each others' voters, yet in reality that doesn't seem to happen - the Republican and Democratic parties appeal to different voters.

Changes in voter sentiment might be able to handle some of that problem; by having voters change their opinions between elections, candidates know not to get too specialized (because it takes time to move about in opinion space). That would also limit stagnation in even advanced systems: if you have a Condorcet method and a party places itself at the (static) median voter, the game is over and all the other parties can just as well go home.

There are other effects as well: Parties and candidates might also slide into corruption unless checked by competition. One could model that by a candidate wanting to both be elected and to be placed at a certain point in opinion space (individual corruption), or by candidates being attracted towards a certain area in opinion space (coordinated corruption, e.g. by lobbying). Candidates may be of use (as opposition), even if not elected - not sure how to model that; and the candidates, particularly organized ones, may choose to employ strategy if doing so is feasible (as the New York parties did under STV) - I'm not sure how to model that, either.
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