Wait… your county has a GDP of over half a million dollars per capita? That is insanely high!
Also, note that your probability of swinging the election is only 1/√n if the population is split exactly 50⁄50; it drops off superexponentially as the distribution shifts to one side or the other by√n voters or more. On the other hand, if you’re actively pushing an election, not just voting yourself, then that plausibly has a much bigger impact than just your one vote.
Also, note that your probability of swinging the election is only 1/√n if the population is split exactly 50⁄50; it drops off superexponentially as the distribution shifts to one side or the other by √n voters or more.
Yesss, this seems related to shadonra’s answer. If my “500k coin flips” model were accurate, then most elections would be very tight (with the winner winning by a margin of 1⁄800, i.e. 0.125%), which empirically isn’t what happens. So, in reality, if you don’t know how an election is going to turn out, it’s not that there are 500k fair coins, it’s that there are either 500k 51% coins or 500k 49% coins, and the uncertainty in the election outcome comes from not knowing which of those worlds you’re in. But, in either case, your chance of swinging the election is vanishingly small, because both of those worlds put extremely little probability-mass on the outcome being a one-vote margin.
if you’re actively pushing an election, not just voting yourself, then that plausibly has a much bigger impact than just your one vote
That… is… a very interesting corollary. Although… you only get the “superexponential” benefit in the case where you’re far out on the tail of the PDF—in the “500k 49% coins” world, throwing 100 votes for Heads instead of 1 would increase your chances of swinging the election by a factor of much, much more than 100x, but your probability of swinging the election is still negligible, since the 50% mark is, uh, 14 standard deviations out from the mean. Right?
Umm, that’s a very misleading statistic—King County, WA has a very uneven distribution of contribution to GDP, as it includes a number of international powerhouses that local politics don’t affect very much (nonzero, but nowhere near the few percent you’re estimating). per-capita averages are just about useless for any planning or valuation of action.
Wait… your county has a GDP of over half a million dollars per capita? That is insanely high!
Also, note that your probability of swinging the election is only 1/√n if the population is split exactly 50⁄50; it drops off superexponentially as the distribution shifts to one side or the other by √n voters or more. On the other hand, if you’re actively pushing an election, not just voting yourself, then that plausibly has a much bigger impact than just your one vote.
Yesss, this seems related to shadonra’s answer. If my “500k coin flips” model were accurate, then most elections would be very tight (with the winner winning by a margin of 1⁄800, i.e. 0.125%), which empirically isn’t what happens. So, in reality, if you don’t know how an election is going to turn out, it’s not that there are 500k fair coins, it’s that there are either 500k 51% coins or 500k 49% coins, and the uncertainty in the election outcome comes from not knowing which of those worlds you’re in. But, in either case, your chance of swinging the election is vanishingly small, because both of those worlds put extremely little probability-mass on the outcome being a one-vote margin.
That… is… a very interesting corollary. Although… you only get the “superexponential” benefit in the case where you’re far out on the tail of the PDF—in the “500k 49% coins” world, throwing 100 votes for Heads instead of 1 would increase your chances of swinging the election by a factor of much, much more than 100x, but your probability of swinging the election is still negligible, since the 50% mark is, uh, 14 standard deviations out from the mean. Right?
I agree! (Well, actually more like $1-200k/capita, because there are more people than voters, but still.) Sources: population, GDP, turnout.
Umm, that’s a very misleading statistic—King County, WA has a very uneven distribution of contribution to GDP, as it includes a number of international powerhouses that local politics don’t affect very much (nonzero, but nowhere near the few percent you’re estimating). per-capita averages are just about useless for any planning or valuation of action.
Yeah, a fair point!