Hi Toby, thanks for posting this here. The value of a vote is something I’ve wondered about for a long time; I was aware of the models in Banzhaf 1965 and Brennan 2011 and found them inadequate for the reasons you mention. I really like your lower bound argument for the chance of a decisive vote. But I still have a question about something you mention in the introduction,
the chance of your vote being decisive can’t be much lower than 1 in the number of voters. So voting will be worth it around the point where the value your preferred candidate would bring to the average citizen exceeds the cost of you voting.
Why is it the point where the cost of you voting is less than the value your preferred candidate would bring? Shouldn’t you be comparing the cost of voting to the difference in the expectations of the distribution of the value your preferred candidate would bring and the distribution of value the other candidate would bring?
Ah, that’s what I meant by the value your candidate would bring. There isn’t any kind of neutral outcome to compare them against, so I thought it clear that it meant in comparison to the other candidate. Evidently not so clear!
Hi Toby, thanks for posting this here. The value of a vote is something I’ve wondered about for a long time; I was aware of the models in Banzhaf 1965 and Brennan 2011 and found them inadequate for the reasons you mention. I really like your lower bound argument for the chance of a decisive vote. But I still have a question about something you mention in the introduction,
Why is it the point where the cost of you voting is less than the value your preferred candidate would bring? Shouldn’t you be comparing the cost of voting to the difference in the expectations of the distribution of the value your preferred candidate would bring and the distribution of value the other candidate would bring?
Ah, that’s what I meant by the value your candidate would bring. There isn’t any kind of neutral outcome to compare them against, so I thought it clear that it meant in comparison to the other candidate. Evidently not so clear!