Midterm examination Designing Political Institutions

# Midterm examination Designing Political Institutions -...

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Midterm examination Designing Political Institutions ; Prof Steven J Brams March 21, 2011 Nathaniel Elghanayan Question 1) MD)Yes it is possible. Refer to table 1 Here candidate B wins by MD but only voter 1 would have voted for candidate B in AV voting. Refer to table 1 The number chosen for each Candidates MD is determined in a way described in mathematical analysis of MD part 1 Question 2) MN) Yes it is possible for only 1 person to approve of the winning candidate by AV voting standards. In the example of table 2 that would be voter 5. Refer to table 2. This is because 1 voter can attach a weight of 6 to his preferred candidate and 1 to his least preferred candidate. This means his candidate gets a boost ((6-1)/number of voter) boosts which here comes out to a full 1 point here where n = 5. Whereas the other the other 4 voters could all give a weight have 2 to their preferred candidate and 1 to their least preferred candidate. Leading to a net boost of (2-1/n) that is repeated 4 times totaling to a boost of 4/5 in the mean. Which means that the influence of 1voter can be worth that of 5 others and exceeds that of 4. Here extreme opinions lead to undemocratic outcomes. Question 3) In these examples of two candidates there are only 3 ways to be insincere in the voting process successfully are: a) not voting b) lowering the ranking of your preferred candidate c) raising the ranking of your non preferred candidate Part 1) MN with 2 or more candidates is monotonic because voting for your preferred candidate more positively will never hurt your candidate and the more positively you vote for your candidate the better off he will be (refer to question Math) refer Mathematical analysis

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of MN part 1 you have an incentive to always vote 6 for your candidate and 1 for your opponent. This optimizes the final mean of your candidate but it never hurts your preferred candidate since the candidate will get. Part 2) MD is not monotonic; sometimes voting for your candidate can harm your candidate because what matters is the relative size of the median number. Table Question 4 MD It can also can be manipulated by, by no show (refer to question 4). In Table 3 the voter can hurt his candidate by voting if his vote is below the median vote he can hurt his candidate. Although if one votes at the maximum number of allowable points for ones candidate one can never hurt them (MD Mathematical part 2 = NFLUENCING) 4) Are MD and MN vulnerable to the no shows paradox? MD Yes, MD is vulnerable to the no show paradox. Here by not showing up voter 1 and 2 are able to get their preferred candidate B elected even if they are voting sincerely. Tables question 4-part MD View mathematical analysis MD MN MN is not vulnerable to the no show paradox. Here by not showing up, even when there are more than 2 candidates you can never hurt your preferred candidate because your vote for your preferred candidate always adds more to the mean than a vote for your non-preferred candidate. Tables question 4 part MN 5) MN’s
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