A Survey of Mathematics with Applications (10th Edition)

Chapter 14

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Majority ; In an election, the candidates are ... more

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Preference ; When the number of outcomes for each ... more

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; The formula that is used to determine the ... more

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6 ; Substitute 4 for into the formula to find ... more

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plurality ; Voting methods play a very helpful ... more

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Count ; In the Borda count method, each candidate ... more

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Pairwise comparison ; Voting methods are used to ... more

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Plurality ; There are several methods of choosing ... more

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Number of Votes2321FirstDCBCSecondBDDBThirdCBCD ; ... more

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; Add the number of votes mentioned in the ... more

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Add the number of votes mentioned in the ... more

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; Find the number of votes for the choices , , ... more

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; Find the number of votes that received.9 ... more

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; Count the number of times each choice was voted... more

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L ; Substitute 3 for into the formula to find ... more

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W ; Find the number of votes that choice W ... more

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W ; Find the number of votes for the choices W, O... more

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Three way tie, no winner ; Since there are 3 ... more

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V ; Count the instances when each choice was voted... more

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L ; Find the number of votes for cities S, L, H, ... more

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S ; Find the number of votes that City S received... more

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No winner, a tie between Person L and Person H ; ... more

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City S ; Substitute 4 for into the formula to ... more

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Candidate B ; In Borda counting method, when there... more

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Person M ; Apply the plurality method to find the ... more

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Candidate M ; Substitute 3 for into the formula ... more

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Person M ; Count the number of the first-place ... more

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Person B ; Count the number of the last-place ... more

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Choice L ; Apply the plurality method to find the ... more

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Road E ; In Borda counting method, when there are ... more

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Choice O ; Count the number of first-place votes ... more

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Road E ; Substitute 3 for into the formula to ... more

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Choice E ; Count the number of last-place votes ... more

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The Borda count method provides more information ... more

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Breaking a tie can be done with the help of an ... more

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Candidate A and candidate D ; Find the total ... more

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Number of Votes552FirstABCSecondBCBThirdCAA ; Draw... more

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Majority ;  If a single candidate is the first ... more

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Monotonicity ;  The monotonicity criterion is only... more

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Head-to-Head ;  The head-to-head criterion is when... more

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Irrelevant Alternatives  ;  If one or more of the ... more

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Borda Count ;  It is known that the plurality ... more

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Pairwise Comparison ;  It is known that the ... more

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Plurality with Elmination ; It is known that the ... more

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Plurality ; It is known that the plurality method ... more

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Entire Proof Answer: Find the number of votes P ... more

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No, the majority criterion is not satisfied as ... more

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No, because P wins its head-to-head comparisons ... more

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No, because C wins its head-to-head comparisons ... more

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No; C wins by plurality with elimination but A ... more

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No; B wins in head-to-head comparisons and C wins ... more

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No; A wins using plurality method. If B drops out... more

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No; B wins using the plurality method. If C drops ... more

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Yes; B wins by the Borda count method. If C drops ... more

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No; A wins by the Borda count method. If B drops ... more

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No; C wins by plurality with elimination method. ... more

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No; B wins by plurality with elimination method. ... more

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No; D wins by pairwise comparison. If voters ... more

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No; A wins by the Borda count method. If the ... more

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No; B wins by pairwise comparison. If A, C, and E ... more

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No; C wins by pairwise comparison. If A, B, and E ... more

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No; A wins with majority of votes, but B wins by ... more

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No; A wins with majority of votes, but B wins by ... more

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A candidate who holds a plurality will only gain ... more

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Number of votes8562FirstBCACSecondAACAThirdCBBB ; ... more

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Assume that the prime minister of Country C has to... more

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Paper-based method: In this method, the ... more

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Divisor ; The standard divisor is obtained by ... more

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Quota ; The standard quota is obtained by dividing... more

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Upper ; The standard quota is sometimes rounded to... more

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Lower ; The standard quota is sometimes rounded to... more

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Quota ; The quota rule is said to be satisfied if ... more

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Modified ; Modified quota is obtained by dividing ... more

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Hamilton’s       ; In Hamilton’s method of ... more

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Quota ; The quota rule is said to be satisfied if ... more

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; Divide total population 8,000,000 by the total ... more

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; The standard divisor is calculated by dividing ... more

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11; 8; 6 ; The standard divisor is calculated by ... more

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11; 8; 6 ; The standard divisor is calculated by ... more

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8; 9; 12; 21 ; Let the modified divisor be .The ... more

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8; 10; 12; 20 ; Let the modified divisor be .The ... more

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8; 10; 12; 20 ; Let the modified divisor be .The ... more

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34; 136; 41; 18; 21 ; Let the modified divisor be... more

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33; 137; 41; 18; 21 ; Let the modified divisor be... more

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34; 136; 41; 18; 21 ; Let the modified divisor be ... more

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43;32;27;18 ; Assume the modified divisor to be .... more

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43;32;26;19 ; Assume the modified divisor to be .... more

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42;32;27;19 ; Assume the modified divisor to be .... more

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12; 21; 17; 7; 34; 9 ; Assume the modified divisor... more

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; Assume the modified divisor to be 765.The ... more

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; Assume the modified divisor to be 753.The ... more

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63;81;42;14 ; Assume the modified divisor to be .... more

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63; 82;42;13 ; Assume the modified divisor to be .... more

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62; 82;42;14 ; Assume the modified divisor to be .... more

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A: 3,226,000; B: 1,679,500; C: 2,255,000; D: 2,839... more

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A: 517; B: 425; C: 489; D: 517; E: 531; F: 461 ; ... more

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The first house of representative included 120 ... more

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There was a need of new method of apportionment. ... more

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Population ; The population paradox arises when ... more

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New states ; The new state paradox occurs in a ... more

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Alabama ; The Alabama paradox occurs in the case ... more

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Large ; According to the Balinski and Young’s ... more

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Small ; According to the Balinski and Young’s ... more

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Hamilton’s ; From the comparison table of ... more

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No; The clinic does not suffer a loss after the ... more

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Webster method is the best method used for ... more

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Number of ... more

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,2221FirstCABCSecondACABThirdBBCA ;   The order of... more

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; Count and add the number of votes from the ... more

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Choice C ; Count the total number offirst-place ... more

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Restaurant D ; Find the number of votes that ... more

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Restaurant C. ; Find the total number of votes. ; ... more

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There is a tie between restaurants C, D, and B; no... more

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Restaurant C ; Find the total number of votes. ; ... more

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; Count and add the total number of votes from ... more

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Game V ; Count the total number of first-place ... more

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Game S ; Find the number of votes game that S ... more

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V ; Find the total number of votes. ; Count the ... more

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There is a tie between S, B, and V, there is no ... more

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S ; Find the total number of votes. ; First count ... more

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No ; Find the number of votes that A received, ... more

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Count and analyze the votes using head-to-head ... more

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Borda count method ; A candidate is said to be ... more

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The plurality with elimination method ; Consider ... more

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Pairwise comparison method and Borda count method... more

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4, 3, 3 ; The standard divisor is calculated by ... more

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5; 2; 3 ; Let the modified divisor be 500.The ... more

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4; 3; 3 ; Let the modified divisor be 700.The ... more

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5; 2; 3 ; Let the modified divisor be 575.The ... more

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Yes ; Find the standard divisor by dividing 6000 ... more

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11, 7, 5 ; The standard divisor is calculated by ... more

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11, 7, 5 ; Let the modified divisor be 28.The ... more

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10, 7, 6 ; Let the modified divisor be .The ... more

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11, 7, 5 ;  Let the modified divisor be .  The ... more

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No ; The standard divisor is calculated by ... more

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4,46 ; The standard divisor is calculated by ... more

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4, 46 ; Let the modified divisor be 990.The ... more

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5, 45 ; Let the modified divisor be 1020.The ... more

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4, 46 ; Let the modified divisor be 1000.The ... more

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Yes ; The standard divisor is calculated by ... more

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; Count and add the total number of votes from ... more

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None of the choices have a majority of votes. ; ... more

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P ; Count the total number of the first-place of ... more

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P ; Find the number of votes that Choice D ... more

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D ; Find the total number of votes. ; Count the ... more

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D ; To determine the winner, compare between ... more

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142 ; Count and add the total number of votes from... more

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Animal S ; Count the total number of the first-... more

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Animal I ; Find the number of votes that Animal S ... more

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Animal H ; Find the total number of votes. ; Count... more

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Animal L ; To determine the winner, compare ... more

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Plurality method, Borda count method, and ... more

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No; Logo E wins with a majority of votes, but ... more

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6; 9; 15 ; From the table, the total population is... more

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6; 9; 15 ; Let the modified divisor be 1040.The ... more

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6; 9; 15 ; Let the modified divisor be 1160.The ... more

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6; 9; 15 ; Let the modified divisor be 1100.The ... more

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No, Alabama paradox does not occur. ; Divide 33,... more

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No, Alabama paradox does not occur. ; Find the ... more

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No, new states paradox does not occur. ; Find the ... more

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