Now I ask you to consider whether benefit (1) would in fact be the case for important elections (elections say where the elected will govern over 10 000 000 people). If 100 Worlds had an election decided based on one vote, which percentage of those would be surreptitiously biased by someone who could tamper with the voting? How many would request a recount? How many would ask it’s citizens to vote again? Would deem the election illegitimate? Etc… Maybe some of these worlds would indeed accept the original counting, or do a fair recounting that would reach the exact same number, I find it unlikely this would be more than 80 of these 100 worlds, and would not be surprised if it was 30 or less.
It does indeed look hard to predict what will happen here exactly. Luckily it pretty much factors out of the analysis.
I’ll demonstrate with a toy example. Say the election goes to whoever gets more votes, EXCEPT if the counts only differ by 1 vote. In that case there’s a 100% chance that the election is deemed illegitimate and the military step in. Say you’re voting for Party B rather than Party A. You know Party A has 1,000 votes, and you think Party B has about 1,000 votes.
If you move Party B from 1,000 to 1,001 votes you make no difference—you get the election declared illegitimate either way. Instead your impact comes from the cases where Party B was getting 998 votes already (you move from Party A win to military takeover) or Party B was getting 1,001 votes already (you move from military takeover to Party B win).
If you’re uncertain enough about the outcome that all of those possibilities for vote numbers look about equally likely to you, then the net expected effect of your vote is a small chance (the chance that the votes stand at any one particular number) to move from a Party A win to a Party B win—just the same as if you disregarded all the possible complications.
I don’t understand what you’re pointing us to in that link. The main part of the text tells us that ties are usually broken in swing states by drawing lots (so if you did a full accounting of probabilities and expectation values, you’d include some factors of 1⁄2, which I think all wash out anyway), and that the probability of a tie in a swing state is around 1 in 10^5.
The second half of the post is Randall doing his usual entertaining thing of describing a ridiculously extreme event. (No-one who argues that a marginal vote is valuable for expectation-value reasons thinks that most of the benefit comes from the possibility of ties in nine states.)
Perhaps some of those details are interesting, but it doesn’t look to me like it changes anything of what’s been debated in this thread.
It does indeed look hard to predict what will happen here exactly. Luckily it pretty much factors out of the analysis.
I’ll demonstrate with a toy example. Say the election goes to whoever gets more votes, EXCEPT if the counts only differ by 1 vote. In that case there’s a 100% chance that the election is deemed illegitimate and the military step in. Say you’re voting for Party B rather than Party A. You know Party A has 1,000 votes, and you think Party B has about 1,000 votes.
If you move Party B from 1,000 to 1,001 votes you make no difference—you get the election declared illegitimate either way. Instead your impact comes from the cases where Party B was getting 998 votes already (you move from Party A win to military takeover) or Party B was getting 1,001 votes already (you move from military takeover to Party B win).
If you’re uncertain enough about the outcome that all of those possibilities for vote numbers look about equally likely to you, then the net expected effect of your vote is a small chance (the chance that the votes stand at any one particular number) to move from a Party A win to a Party B win—just the same as if you disregarded all the possible complications.
Now I ask you (and everyone reading) to consider this: http://what-if.xkcd.com/19/
I don’t understand what you’re pointing us to in that link. The main part of the text tells us that ties are usually broken in swing states by drawing lots (so if you did a full accounting of probabilities and expectation values, you’d include some factors of 1⁄2, which I think all wash out anyway), and that the probability of a tie in a swing state is around 1 in 10^5.
The second half of the post is Randall doing his usual entertaining thing of describing a ridiculously extreme event. (No-one who argues that a marginal vote is valuable for expectation-value reasons thinks that most of the benefit comes from the possibility of ties in nine states.)
Perhaps some of those details are interesting, but it doesn’t look to me like it changes anything of what’s been debated in this thread.