i just realized this this morning
traditional wisdom : voting is a bad idea because small chance of changing outcome
but -- this is wrong because you ignore the effects of voting.
say your chances of changing the election outcome (in the US) are 1E-8
but a president can have a large effect on a country. suppose we just look at economic policies, and say that one president will increase the income of the lower/middle class by just one percent, whereas the other will not change anything. this is a very conservative estimate.
this one percent translates to ~1E3 dollars over the 4 year term of the president -- for 3E8 people.
therefore, voting is functionally equivalent to giving (1E3)(3E8)(1E-8) = 3000 dollars to an average citizen.
suppose voting takes 2 hours, and you can make $100 in those two hours instead of voting. now it's debatable whether it's better to given $3000 to some american citizen or $100 to buy 20 malaria nets for africans. nevertheless, it's no longer clearly irrational to vote, and, in a swing state, it is probably a very good idea to vote