1. Suppose Marie has the following ranking over the policy characteristics of a presidential candidate: (a) Prefers lower taxes > Prefers larger military >- Shares her religious beliefs. Suppose you work for a think tank, doing research that involves predicting voter preferences over candidates. Suppose there are three candidates: 0 John Jackson, who favors lowering taxes and increasing military spending. 0 Jack Jameson, who favors lowerng taxes and shares Marie's religious beliefs. 0 James Johnson, who favors increasing military spending and shares l-'Iarie:s religious beliefs. Use these to derive preference relations between each pair of candidates, based on these platforms. Are these preferences transitive? 1What is Marieis preference ordering over all candidates? Now suppose she receives utility based on the policies enacted by these candidates if elected, as follows: 0 Utility of 8 if taxes are lowered after the election {and 0 if they are not). 0 Utility of 6 if military spending increases after the election (and 0 otherwise). 0 Utility of 4 if the president shares her religious beliefs (and 0 otherwise). lWhat is lit-{arias utility from each candidate, assuming their respective platforms would be enacted with probability 1 upon election? Does the ranking of numerical utilities match the preference ordering you derived in part {a}? 1What is the benet of assuming numeric preferences over simply preference relations? Now suppose due to uncertainty as to which party will win the Senate, there is only a 25% chance that taxes could be lowered after the election and a two thirds probability that military spending could be increased. 1lu"v.-"hat is Marie's expected utility from each candidate? Does this uncertainty change who she will vote for in the election