[EM] Power of votes with approval

[Adam Tarr]

Stephane Rouillon wrote:

>1) I would cut all candidates into two equal groups the ones I like, the
>ones I do not.
>
>Without poll information, I believe it is the vote that would optimize
>my voting power...

I agree, provided "the ones I like" means the ones I consider better than 
average.

>2) If I can get some poll information I judge reliable enough:
>out of my desired candidates, I would vote for the one I prefer the most
>
>and would approve too all my desired candidates that obtain a better
>position
>according to the poll.
>Example: sincere preferences A>B>C>D | E>F>G>H
>No poll: vote ABCD.
>The poll: D>H>B>A>C>G>F>E. I would vote ABD.
>
>Is it the same you say?

No, here I disagree with you.  In the good-information case, you don't need 
to worry about whether a candidate is better or worse than average ("liked" 
or "not liked"); only ordinal rankings are needed.

In the example you cite, I would not vote ABD, but rather ABCD.  It makes 
no sense to vote for D and not for C.  If there are many voters who think 
like you, then your support for C may allow C to beat D.  There isn't 
really a reason in approval to vote for one candidate and not approve a 
candidate you like more.

Moreover, your strategy could easily end up making you not vote for either 
leading candidate.  Take the case of A>>B>C sincere preferences, and C>B>A 
in the polls.  Your strategy suggests voting for A and not for B, which is 
clearly not optimal since the race appears to be between B and C.

Once again, I suggest that you should vote for every candidate you like 
more than the front-runner, and also vote the front-runner if you like 
him/her more than the second place candidate.  Say your preferences are 
A>B>C>D>E>F, and the polls show C>E>D>B>F>A.  You should vote for A and B 
because you prefer them to the front-runner C, and you should vote for C 
because you prefer C to E (the second place candidate).  So your vote is ABC.

-Adam


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