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Unformatted text preview: 1) If an election consists of twelve candidates {A, B, C, D, E, F, G, H, I, J, K, L} a) How many different preference lists are possible? 12!=479,001,600 b) How many subsets of candidates can be formed from the given set? 2 12= 4096 c) How many subsets consist of five candidates? 12 nCr 5=792 d) If Sequential PairWise Voting is used in the election, how many different agendas are possible? 12!=479,001,600 e) If the Condorcets Method is used in the election, how many headtohead (2) match ups are there? 12 nCr 2=66 2) A group of individuals consists of 8 Republicans, 10 Democrats, 5 Independents, and 2 Reformists a) How many 4person committees can be formed from this group? 25 nCr 4= 12,650 b) How many 4person committees consist of exactly one representative from each political party? (8 nCr 1)(10 nCr 1)(5 nCr 1)(2 nCr 1)= 800 c) How many committees consisting of 4 Democrats, 3 Republicans, 2 Independents, and 1 Reformist can be formed from this group? (10 nCr 4)(8 nCr 3)(5 nCr 2)(2 nCr 1) =235,200 d) In how many ways can we form a 3person committee if one must be the chairman, a different person must be the vicechairman, and the third person must be a minuterecorder? 25 nPr 3=13,800 3) In how many ways can a 25member team of the Marine Corps choose a First Sergeant, a Master Sergeant, a Gunnery Sergeant, a Staff Sergeant, a Sergeant, and a Corporal? 25 nPr 6= 127,512,000 4) Explain the difference between a dictator and a voter with veto power . A dictator has all the power, can pass, and can block a motion alone. A voter with veto power does not have all the power, can block a motion alone, but cannot pass a motion alone. 5) Explain the difference between a pivotal voter and a critical voter . Pivotal voter is the first voter who, in a permutation of voters, has a cumulative weight equal to or greater than the quota. Critical voter is a voter whose votes are absolutely necessary for a coalition t o pass a motion or to block a motion (without the votes of a critical voter, a coalition cannot get its way and becomes a losing coalition). 6) Explain the difference between a sequential coalition and a winning coalition . Sequential coalition is a permutation of all voters in a weighted voting system. Winning coalition is a subset of voters who all favor a motion and have enough weighttotal to pass the motion....
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This note was uploaded on 03/08/2011 for the course SLS 2000 taught by Professor Mitchell during the Spring '06 term at FIU.
 Spring '06
 Mitchell

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