[EM] Power of votes with approval

[Adam Tarr]

Stephane Rouillon wrote:

>You maximize the power of your vote by voting for half of the candidates.
>This would be the optimal strategy if you had no knowledge from 
>pre-election polls.

No; if you have no knowledge of the polls, you should vote for every 
candidate above your MEAN candidate, not your MEDIAN candidate.  So if you 
love one candidate and hate all the others, you should vote only for the 
loved candidate in the zero-information case, since only that candidate is 
above average.

>However, the optimal strategy with information obtained from polls, is to 
>vote for your
>favourite and any other candidate you like that the poll says it would 
>beat your
>favourite.

No again.  If your favorite candidate is in last place in the polls, this 
strategy suggests you should vote for every candidate, which is obviously a 
waste.  What you probably meant to say is, "vote for **the candidate you 
would vote for in a plurality election** and any other candidate you like 
that the poll says it would beat **that candidate**.  This assumes that you 
would vote "lesser-of-two-evils" in a plurality race.

This strategy is pretty good, but it's not quite the best - there are 
situations where this approach could make you regret your vote, even if the 
polls are fairly accurate.  A better strategy is, "vote for anyone you like 
more than the front runner, and the front runner as well if you like 
him/her more than the second place candidate."  The only difference here is 
that if you like the second place candidate more than the first place 
candidate, you will vote for candidates you like more than one but less 
than the other.

-Adam


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