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Approval voting eliminates the reduction of politics to the boardwalk ice cream vendor problem.

What's more, I'm tired of driving 7.5 hours to the boardwalk every time I want ice cream, and then not being able to find any parking spaces around the exact center of it, where the vendors tend to cluster.

Since FPTP mathematically converges on two parties, the two parties also mathematically converge on the perceived political center, and then advertise in opposite directions from the same spot. When the voting is structured to prioritize how far customers are willing to walk for the flavors they like, rather than going the shortest distance to the only flavor available (vanilla), we all get more choices.

> the two parties also mathematically converge on the perceived political center

There is a mathematical theory about this, but it assumes a number of things that aren't true about real political behavior (basically, it ignores that political engagement that matters isn't limited to voting, and that voting behavior isn't simply “every eligible voter will vote, and will vote for the candidate nearest to them by some political distance function”; it may also ignore that distribution of political views is neither uniform nor unimodal with a central peak, but instead has peaks away from the center [0]), and empirically doesn't seem to predict the actual behavior of parties very well at all.

[0] it's not clear if it ignores this or just doesn't consider distribution because distribution wouldn't matter if the things it does ignore were true; certainly some of it's defenders seem to think that political views are unimodal and centrally-peaked and that that mitigates any problems from the other oversights, which it might, if it were true.)

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