Question 2. (80 points).

It is often argued that one advantage of deferring decisions to committees is that committees are less prone to "capture", the undue influence of lobbyists. The logic is simply that in a committee several individuals will need to be influenced, and that will require more time and money than influencing a single individual. But is this logic correct? (This question is based on "Bribing Voters" by Ernesto Dal Bo',American Journal of Political Science, 2007).

Consider the following scenario. A lobbyist wants to obtain the approval of a proposalX. The lobbyist is not budget constrained and can afford a large expense to ensure approval, but would prefer to do so at as little cost as possible. In all that follows, think of this as a one-shot game with no future repetitions and no reputation effects. However, the lobbyist always respects his promises.

1. (5 points). Imagine first that approval of the policy depends on a single policy-maker. The policy-maker is opposed to the proposal and derives a disutility that, expressed in dollar terms, equals, if the proposal is approved.is publicly known. On the other hand, the policy-maker values the transfer received from the lobbyist. If we call itb, the policy-maker's utility isb if the proposal is approved, and 0 otherwise. What is the minimum cost to the lobbyist of ensuring approval?

Suppose now that the proposal is decided by a committee of 5 voters. The decision is taken by simple majority, and all voters will vote simultaneously. All 5 voters oppose the proposal and each of them derives disutilityfrom its 3

passing (again this fact and the value ofare publicly known). All 5 voters would value positively transfers received from the lobbyist, and their utility if the proposal passes or does not pass is identical to the utility of the single policy-maker described above.

As in real-life legislatures, all votes are observable-i.e. the lobbyist will be able to observe not only the final number of votes on each side but also who cast which vote. He offers each of the 5 voters the following contract: "I will pay you+if you vote in favor of the proposalandyour vote is pivotal" whereis a small positive amount.

2. When deciding how to vote, a voter does not know whether or not he is pivotal. He needs then to consider the different possible scenarios. (i) (10 points). Identify in which scenarios the voter is indifferent between voting Yes or No, and in which scenarios the voter has a strict preference over voting Yes or No, given the contract offered by the lobbyist. (ii) (10 points) For the rest of this question, you can assume that when indifferent the voter votesas ifhe were pivotal. How will the voter vote then? (iii) (5 points). Given your answer to (ii) above, how many votes will then be cast in favor of the proposal, and how many against?

(iv) (10 points). How much does the lobbyist need to pay? How does this amount compare to the cost of lobbying a single policy-maker? 3. (10 points). After having received the lobbyist's offer but before voting, the committee members can meet and discuss how to vote. Would communica tion alone allow them to coordinate on a different outcome? 4. (10 points). Suppose now that the committee members' preferences arenotpublicly known. What is publicly known however is that the maximal disutility any committee member can suffer from the proposal is some known value. Can the lobbyist offer a new contract that will allow him to obtain a favorable vote now? How much will it cost him?

5. Afraid of the possibility of capture, the committee decides to raise the threshold for passing the proposal to 4 positive votes. Let's go back for simplicity to the scenario of point 3-a commonly known disutilitythat each voter would suffer from the proposal passing.

(i) (10 points). Will this change the outcome?

(ii) (10 points). Would requiring unanimity change the outcome?

ansions Help Last edit was it] minutes ago Openverslonhlstory _ _ _ trial - =... . A n' c:: Iv 5v IE $: v E - i: - E E '1' n.- a. u- 1 2 a 4 v s a Question 2. {El-l3 points}. It is often argued that one advantage of deferring decisions to committees is that committees are less prone to "capture", the undue inuence of lobbyists. The logic is simply that in a committee several individuals will need to be inuenced, and that will require more time and money than inuencing a single individual. But is this logic correct? {This question is based on "Bribing Voters" by Emesto Dal 30', American Journal of Political Science, EDEN}. Consider the following scenario. A lobbyist wants to obtain the approval of a proposal X. The lobbyist is not budget constrained and can afford a large expense to ensure approval. but would prefer to do so at as little cost as possible. In all that follows. think of this as a oneshot game with no future repetitions and no reputation effects. However. the lobbyist always respects his promises. 1. {5 points}. Imagine first that approval of the policy depends on a single policy-maker. The policy-maker is opposed to the proposal and derives a disutility that. expressed in dollar terms. equals 6. if the proposal is approved. IE! is publicly known. On the other hand. the policy-maker values the transfer received from the lobbyist. If we call it b, the policymaker's utility is b G if the proposal is approved, and 0 otherwise. IIll'u'hat is the minimum cost to the lobbyist of ensuring approval? E'l'tSll'lS HEIFI atrial - 9.9 + B I U A 1' c:: Qv 5. IE 3: - EE - i: - T - 1 2 s 4 1... s 5 Suppose now that the proposal is decided by a committee of 5 voters. The decision is taken bysirgplhe majority. and all voters will vote simultaneously. All 5 voters oppose the proposal and each of them derives disutility Efrom its 3| passing (again this fact and the value of E are publicly known}. All 5 voters would value positively transfers received from the lobbyist. and their utility if the proposal passes or does not pass is identical to the utility of the single policymaker described above. As in real-life legislatures, all votes are observableLe. the lobbyist will be able to observe not only the final number of votes on each side but also who cast which vote. He offers each of the 5 voters the following contract: "I will pay you 9 + c if you vote in favor of the proposal and your vote is pivotal" where E is a small positive amount. 2. When deciding how to vote. a voter does not know whether or not he is pivotal. He needs then to consider the different possible scenarios. {i} [ll] points}. Identifyr in which scenarios the voter is indifferent between voting Yes or No. and in which scenarios the voter has a strict preference over voting 'fes or No. given the contract offered by the lobbyist. {ii} {1 points} For the rest of this question. you can assume that when indifferent the voter votes as if he were pivotal. How will the voter vote then? [iii] {5 points}. Given your answer to {ii} above. how many votes will then be cast in favor of the proposal. and how many against? {iv} {1ft points}. How much does the lobbyist need to pay? How does this amount compare to the cost of lobbying a single policy-maker? 3. {10 points}. After having received the lobbyist's offer but before voting. the committee members can meet and discuss how to vote. Would cpmm'ggjgagtjgg alone allow them to coordinate on a different outcome? 4. {1D points}. Suppose now that the committee members\" preferences are not publicly known. What is publicly known however is that the maximal disutility any committee member can suffer from the proposal is some known value 9. Can the lobbyist offer a new contract that will allow him to obtain a favorable vote now? How much will it cost him? 5. Afraid of the possibility of capture. the committee decides to raise the threshold for passing the proposal to 4 positive votes. Let's go back for simplicity to the scenario of point 3a commonly known disutility E that each