For longer more detailed answer, you could try mathematics. Voting theory is a branch of mathematics. @Brilliand answered this correctly.
(I looked for a good website on voting theory in the pure math sense, haven't found one, everyone has taken to explaining it politically).
The multiple voting system is a good system, people sometimes don't like it cause people can say "he got 3 votes and I got just 1", but everyone has the option to use 3 votes, so it's not unbalanced, it's just different. On average, multiple votes hurts polarizing candidates and helps candidates that the other party doesn't "hate", so it tends towards a more moderate outcome. That's the problem with any voting "fix" if applies is at the end of the day, one candidate is helped another is hurt and the one hurt is bound to cry foul.
Take the MVP system, writers vote for baseball players in a 10 to 1 scale, the best player getting 10 points, the 10th best, 1 point. And the points are added up and the player with the most points (but not necessarily the most first place votes) wins the MVP award. This system can be questioned when the player who finishes 2nd with 16 first place votes, behind the player who finishes first with 10, cries foul, but it's still a pretty good system. But if the 16 voters of the guy they voted #1 want him to win, they could vote for the guy who gets 10 first place votes much later, and game the totals, but it would be fairly obvious when a guy who's up for #1 gets a bunch of 9 and 10 votes that some foul play was afoot.
One person one vote is tough to fix, but candidates (not voters) can do it by running and effectively stealing votes from another candidate (Anderson taking votes from Carter, Ross Perot, (perhaps) taking votes from Bush the dad, and the infamous Ralph Nader taking votes from Al Gore). That's not voter theory, but it demonstrates the point that it's very hard to run a fair election. I'm getting off subject though - sorry.
To expand on Brilland's answer - you vote for the candidate you like best among those who have a chance, that's just common sense.
And if you have two votes left, and you want to support, the green party or the economy first party or the religion of your choice party, that probably won't win, but you want to show support - vote away.
In short, it makes sense to vote for the candidate that you like among those with a shot at wining, and it makes sense to also vote for the candidate (or two) you like the best, but there's also something to be said for just recognizing something you agree with (an environmentalist voting green party for example).
Likewise, if there's someone you sort of like and he's favored to win, and you like person #2 better, you can not vote for the person you sort of like in the hopes that your #2 will win the election, but if enough people do that, maybe some other person's #2 - a guy you hate will win, so there's an argument to weighing chance of wining against how much you like someone and not overthinking.
The difficulty with showing this (and maybe someone on the math board can give a true mathematical argument), but the difficulty is that the way to vote changes based on how much you like each person, and how good a chance each person has on wining. If you like A better than B, but B has a 30% chance of wining and A has a 20% chance of wining, the math gets very murky and there's no clear answer. You need to weigh whether you're wiling to vote for B (cause he's much better than C), or not vote for B cause A is much better than B. - for an individual vote, a probability chart could be drawn up where you weigh chances against desired outcome. . . . but that hinges on the poles and the projected outcomes being accurate (and Dewey didn't beat Truman).
For an individual with a specific election, a probability chart could still be drawn out and a proper strategy could be devised, but in general terms, there's no way to assign a precise strategy, though I think Brilland's answer is as close as anyone is going to get to a general answer to this. (though I don't like the use of the term random - as it's not random, but math only works with precise input. The question the way it's asked is in terms of general input, so there's no precise answer.
I know that people will ask for citations, but mathematical stations for answers to general questions are hard to comeby. I was a math major in college, I really did used to study this stuff.