**Please show scratch work!!! You are running for city council in a town contain
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**Please show scratch work!!!
You are running for city council in a town containing 100 voters (assume everyone will vote). Because you know the town so well, you have a good idea of the ideological positions of every individual voter, which range on a 7-point scale from Very Liberal to Very Conservative. Thus you know that the town's preferences, or the total number of people holding each ideological position, break down as follows: 20 1486 36 12 VLL SL MSC CVC This means, for example, that you know that there are 4 voters who are Slightly Conserva tive. Assume that the ideology categories are evenly spaced so, for example, the distance between Very Liberal and Slightly Liberal is equal to the distance between Moderate and Conservative. Also assume that any voter will vote for the candidate whose stated ideolog ical position is closest to their own, and that if both candidates are equally distant from a category, each individual voter in that category has a 0.5 probability of voting for either candidate. 2.8 If you know that your opponent will take a Liberal position, where should you position yourself if you simply want to maximize the number of votes you receive? How many votes will you receive if you take this position? 2.9 Suppose that all you care about is winning, and you want to choose the ideol ogy that will maximize your chances. You are moving first, but you believe your opponent will rationally choose to take the ideological position that maximizes his or her vote share in response to you. What position should you take? What position does your opponent take in response? With what probability will you win the election?Explanation / Answer
Solution 2.8 I will position myself at Slightly Liberal so that I will get all the votes from SL to VC. And my votes will count 66.
Solution 2.9 If I am moving first I will position my self at Slightly Conservative. My opponent in my respone will position herself/himself at Moderate or Conservative. I will win the election with probability 1 as my votes will count 52.
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