Some people I’ve been talking with have been wondering how an extremely mediocre person such as Ulmert got to be the prime minister of Israel. Well, it is nigh time I start writing on subjects I fully comprehend. So, I present to you another lesson in election theory – when can more power mean less power?
We’ll take an example from voting theory, because it is a nice example with interesting lessons, and it demonstrates several aspects of game theory. Suppose we have three people on a committee: Alex, Bob, and Chris. They need to choose between options a, b, and c. A very reliable method of voting is the simple majority vote. In this method, each committee member gives his vote to one option. The option with the largest munger of votes wins.
The trouble is, what happens on a tie? Say Alex votes a, Bob votes b, and Chris votes c. Then each option got 1 vote, and it’s a tie. How do you break a tie?
There are two obvious (and common) tiebreaker rules. The first is to define some option as the default. In case of a tie, that specific option wins. Slightly more common is to define one of the committee members as chairman – giving him the right to decide in case of a tie.