CZ:Approval Voting
A voter can approve of as many candidates as he or she likes, and the candidate approved of by the greatest number of voters is elected. A voter approves of a candidate by listing the candidate on the ballot, and the order of the candidates on the ballot makes no difference.
This means that the voting is simply approval or disapproval. If you like the candidate, you vote. If you don;t like him, then you omit his name. There is no first or second choice etc. although you can make a first choice by voting for only one candidate.
The theory underlying this is that the system maximises people's approval positions: in other words, if you are equally happy with all three candidates then it will not matter to you which is elected. Others may approve of only one, or two. The result of adding up the votes for each candidate in this way is that the candidate with the most approval overall is the winner.
In a traditional Westminster style first-past-the-post system where a winner is elected by simple majority, the favoured candidate is the one who is the most popular in a direct competitive sense. This electoral approach is more crude, and disregards alternative positions. In practical terms, if someone likes candidate A a lot, quite likes B and hates C, in the old westminster system, if A is not elected and C is returned, then this voter has had no role in electing candidate C and is not happy. In the approval system, the voter would have omitted candidate C from the ballot and there would be some possibility that this act would have reduced the chance of C being elected.
So, if you are indifferent between all three candidates then vote for all three. If you approve of only one for this post, vote only for him. If you would be happy with two but do not like a third, vote for those two.
See also this site for more details and examples. For a real experiment, in France 2002, see this paper [1]