# Introduction

We apply the main idea from last time, iterative deletion of dominated strategies, to analyze an election where candidates can choose their policy positions. We then consider how good is this classic model as a description of the real political process, and how we might build on it to improve it. Toward the end of the class, we introduce a new idea to get us beyond iterative deletion. We think about our beliefs about what the other player is going to do, and then ask what is the best strategy for us to choose given those beliefs?

# Median-Voter Theorem

The median voter theorem is a proposition relating to ranked preference voting put forward by Duncan Black in 1948.[1] It states that

if voters and policies are distributed along a one-dimensional spectrum, with voters ranking alternatives in order of proximity, then any voting method which satisfies the Condorcet criterion will elect the candidate closest to the median voter. In particular, a majority vote between two options will do so.

There many examples in American History of elections(Kennedy vs Nixon,Clinton)

The application of this model is to do with product placement.

As we can see, the same type of firms tend to crowd together, competing for voters who happen to be close. Competing may bring them extra losses while such behaviors can help them avoid being out competed by each other in terms of position.