7 - Example: Election I

Summary

Prerequisites: Chapters 1, 2, and 6.

The president of the USA is elected by electors from all 50 states. All the electoral votes from a state go to the most popular candidate in that state. If one week before the election a candidate knows that she is behind in a few states, and leading in others, what would be a good strategy for the remaining time? Concentrating on those states where she is behind, or accepting that they are lost and concentrating on others? The decision will depend on several factors, including whether the state can still be turned, and on the size of the state. California is more important than Montana in the presidential election. In this chapter we look at a simplified model with only three districts and analyze a few cases formally. Looking at simpler cases may allow us to extract rules for larger situations.

First Example

We start with a special game, part of a family of games that will be introduced later.

ELECTION 1 or ELECTION(7, 8, 13| −1, −1, 1|3, 3) In Kalumba there are three electoral districts, C, D, and E. As in the election of the President of the USA, the President of Kalumba is elected by electoral votes. There are 7 electoral votes from district C, 8 from district D, and 13 from district E. Districts do not split electoral votes. There are two presidential candidates, Ann and Beth, and in the last phases of their campaigns they simultaneously decide how to allocate the three remaining resources each has. Each must be allocated entirely to one district. A district may receive more than one resource. Each district will vote for the candidate who put more resources into the district (not just during the last phase), and will abstain in case of a tie. In districts C and D, Ann is 1 resource unit behind, and in district E, Ann has an advantage of 1 resource unit. How should Ann and Beth distribute their resources?