6. One person, One vote means:

a. One person is to be voted by all.

b. One person has one vote and each vote has one value.

c. A person can vote only once in his life.

d. Both a and c

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Explaining the Democratic System of Government

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Raushan RajLv8

2 Nov 2020

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a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is, and determine the Nash equilibrium.

b) Now Suppose d = r > 1, find the set of Nash equilibria. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

c) Now Suppose d < r, find the set of Nash equilibria.

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D democrats and r Republicans are voting in the US Presidential election. Each person decides whether to vote or not vote. The voters get a payoff of 2,1,0 if their preferred candidate wins, ties, or loses (respectively). Voters that vote incur a cost of 0 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is, and determine the Nash equilibrium.

b) Now Suppose d = r > 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

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2. Suppose three neighbors must vote on the installation of a traffic light that costs $210. All three will share the cost of the light - that is, each person will contribute $70 to the installation. Leona values the light at $50; Lionel values the light at $50; and Theo, who drives the most, values the light at $200.

a) Explain why the traffic light is a public good.

b) Is it efficient for the traffic light to be installed? Why or why not?

c) Suppose a majority rule vote is held to determine whether the light should be installed. Will the light be installed? Explain any differences between this result and your answer in part (b).