Let's say you're in a group of 20 people, and each person has 3 votes for different people. They're all voting for a 5 member committee, and the 5 people who get the most votes win. Ties are resolved with a revote. You want to be elected, everyone running can vote, and you can vote for yourself.
The question: Is it more beneficial for you to vote for the people you think will win, or people you don't think will win?
My thinking: If you vote for people you think will win, then you're eliminating the chance of potential rivals (who you're not sure will win) winning that are close to you in terms of votes. If you vote for people who you think won't win, you're lowering the chance of the people you think will win by not voting for them.
You have no control over the number of votes you receive nor the number of votes everyone else receives. Whether or not you vote for the rival, you must still have to have more votes than your competitor. The only action you can take that minimizes the number of votes from your competitor is to not vote for them. Therefore you should vote for yourself and "throw away" your other two votes (vote for anybody who is not likely to win).
If you vote for a rival, all you do is help that rival; who, if they can beat your competitor, may also be able to help you. Any rival of a competitor is a competitor to you and you shouldn't help any competitors.