Casting ballots for multiple people

In an election where you can vote for up to X-number of candidates, does it always make sense to vote for the maximum amount?

For instance, if you are supporting a candidate running for a council, and you’re allowed to vote for up to 7 candidates, are you better off just voting for the one guy you like and no one else?

Does voting for more candidates just dillute your chances? Or is a vote a vote, and it doesn’t really matter how many others you cast a ballot for? Does always voting for the maximum number of candidates weaken your vote? Does my vote carry more weight when I just vote for one person?
The answer to this may be extremely obvious, I’m just painfully bad at figuring these sorts of things out. (And this is on my mind, as there’s a city council primary in my city today.)

If there is just one person that you want to maximize the chances for, then just vote for that one person. Any other votes will decrease the chances of your favorite because you will be adding votes to competing candidates.

This seems pretty obvious, yet little-realized. I once counted the ballots in such an election and discovered that I was the only voter who had voted for less than the maximum allowed.

This would depend on how the votes are counted. If they simply tally all the votes cast and award seats to the 7 candidates with the most total votes, then it could pay not to vote all 7 if you had a strong preference.

Suppose without your vote the totals were:

AAA 1000
BBB 900
CCC 800
DDD 700
EEE 600
FFF 500
HHH 399
III 12

If you vote for just your candidate (or any other way that does not include a vote for HHH) your candidate will be seated. If you vote for both your candidate and HHH, then the last seat will have to be decided in a runoff or some other fashion, and your candidate might not be seated.

If you’re interested, this is a great book on different voting systems. Very readable.

Gaming the Vote: Why Elections Aren’t Fair (and What We Can Do About It)

In my experience, if you’re allowed to vote for 7 candidates, it is because there are 7 seats open, and there will be 7 winners. In such a case, I can’t see how the extra votes would dilute your vote for the main guy. It’s only in the case where you can give 7 votes for fewer than 7 winners that there’d be a problem.

See my reply two above yours for a specific example of how it can hurt.

A lot of people may just see it the way I do: we’ll take a win for any of the candidates that meet our definition of acceptable. Voting once for my favorite candidate may slightly increase his odds of being elected, but I’d rather see my second favorite candidate win out over my least favorite.