1. Decisions How do we make choices?

2. Types of Decisions Individual—our opinion is our decision. Group—Individual opinions are expressed by voting(at least in a democratic society)and some procedure is used to combine these individual preferences for a group decision.

3. Two Basic Questions What type of election decision procedure should we use to combine individual decisions (preferences) into a group decision? How can we be sure that what is decided is really what the group wants?

4. Two Alternative Case What procedure should we use to decide between two alternatives? What are some advantages of this procedure?

5. Desirable Properties of Majority Rule (Two Alternative Case) All voters are treated equally. (Swapping marked ballots gives no change) Both alternatives are treated equally. (If all votes are reversed, so is the winner.) If a new election were held and a single voter changed from a vote for the previous loser to the previous winner, then the outcome would be the same as before.

6. May’s Theorem If the number of voters is odd, and if we are interested only in voting procedures that never result in a tie, then majority rule is the only voting system for two alternatives that satisfies the conditions listed on the previous slide.

7. Kenneth O. May (1915-1977) Mathematician, Political Activist PhD, Univ. of California, 1946 Mathematics plays a crucial role in social science!