Preface for the Reader |
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xi | |
Preface for the Instructor |
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xv | |
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1 | (124) |
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3 | (2) |
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5 | (20) |
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5 | (1) |
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1.1 Two-Candidate Methods |
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6 | (3) |
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1.2 Supermajority and Status Quo |
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9 | (1) |
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1.3 Weighted Voting and Other Methods |
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10 | (3) |
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13 | (5) |
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18 | (3) |
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1.6 Exercises and Problems |
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21 | (4) |
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2 Social Choice Functions |
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25 | (20) |
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25 | (1) |
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25 | (3) |
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2.2 Social Choice Functions |
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28 | (2) |
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2.3 Alternatives to Plurality |
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30 | (7) |
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2.4 Some Methods on the Edge |
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37 | (2) |
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2.5 Exercises and Problems |
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39 | (6) |
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3 Criteria for Social Choice |
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45 | (16) |
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45 | (1) |
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3.1 Weakness and Strength |
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46 | (2) |
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3.2 Some Familiar Criteria |
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48 | (2) |
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50 | (7) |
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3.4 Exercises and Problems |
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57 | (4) |
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4 Which Methods Are Good? |
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61 | (18) |
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61 | (1) |
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62 | (1) |
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4.2 Proofs and Counterexamples |
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63 | (11) |
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4.3 Summarizing the Results |
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74 | (1) |
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4.4 Exercises and Problems |
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75 | (4) |
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79 | (14) |
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79 | (1) |
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5.1 The Condorcet Paradox |
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79 | (3) |
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5.2 Statement of the Result |
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82 | (2) |
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84 | (2) |
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86 | (4) |
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5.5 Exercises and Problems |
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90 | (3) |
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6 Variations on the Theme |
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93 | (32) |
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93 | (1) |
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94 | (1) |
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95 | (3) |
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98 | (6) |
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6.4 Mixed Approval/Preference Ballots |
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104 | (2) |
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106 | (2) |
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108 | (5) |
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6.7 Social Ranking Functions |
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113 | (3) |
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6.8 Preference Ballots with Ties |
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116 | (1) |
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6.9 Exercises and Problems |
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117 | (4) |
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121 | (4) |
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125 | (108) |
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127 | (2) |
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129 | (16) |
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129 | (1) |
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7.1 The Apportionment Problem |
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130 | (2) |
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132 | (3) |
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135 | (2) |
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137 | (5) |
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7.5 Exercises and Problems |
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142 | (3) |
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145 | (22) |
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145 | (1) |
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146 | (3) |
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149 | (3) |
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8.3 Assessing Jefferson's Method |
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152 | (3) |
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8.4 Other Divisor Methods |
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155 | (2) |
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157 | (6) |
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8.6 Exercises and Problems |
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163 | (4) |
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9 Criteria and Impossibility |
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167 | (18) |
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167 | (1) |
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167 | (3) |
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9.2 Quota Rules and the Alabama Paradox |
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170 | (2) |
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9.3 Population Monotonicity |
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172 | (2) |
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9.4 Relative Population Monotonicity |
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174 | (2) |
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9.5 The New States Paradox |
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176 | (1) |
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177 | (3) |
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9.7 Exercises and Problems |
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180 | (5) |
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10 The Method of Balinski and Young |
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185 | (14) |
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185 | (1) |
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10.1 Tracking Critical Divisors |
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186 | (5) |
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10.2 Satisfying the Quota Rule |
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191 | (2) |
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10.3 Computing the Balinski-Young Apportionment |
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193 | (4) |
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10.4 Exercises and Problems |
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197 | (2) |
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11 Deciding among Divisor Methods |
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199 | (14) |
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199 | (1) |
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199 | (4) |
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203 | (3) |
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206 | (4) |
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11.4 Exercises and Problems |
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210 | (3) |
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12 History of Apportionment in the United States |
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213 | (20) |
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213 | (1) |
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12.1 The Fight for Representation |
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214 | (10) |
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224 | (1) |
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12.3 Exercises and Problems |
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225 | (2) |
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227 | (6) |
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233 | (122) |
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235 | (2) |
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13 Strategies and Outcomes |
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237 | (18) |
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237 | (1) |
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238 | (2) |
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13.2 The Naive and Prudent Strategies |
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240 | (4) |
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13.3 Best Response and Saddle Points |
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244 | (4) |
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248 | (4) |
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13.5 Exercises and Problems |
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252 | (3) |
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14 Chance and Expectation |
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255 | (18) |
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255 | (1) |
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255 | (2) |
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14.2 All Outcomes Are Not Created Equal |
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257 | (3) |
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14.3 Random Variables and Expected Value |
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260 | (3) |
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14.4 Mixed Strategies and Their Payoffs |
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263 | (3) |
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14.5 Independent Processes |
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266 | (1) |
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14.6 Expected Payoffs for Mixed Strategies |
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267 | (2) |
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14.7 Exercises and Problems |
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269 | (4) |
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15 Solving Zero-Sum Games |
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273 | (18) |
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273 | (1) |
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273 | (4) |
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15.2 Prudent Mixed Strategies |
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277 | (2) |
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15.3 An Application to Counterterrorism |
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279 | (3) |
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282 | (4) |
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15.5 Exercises and Problems |
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286 | (5) |
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16 Conflict and Cooperation |
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291 | (22) |
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291 | (1) |
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292 | (1) |
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16.2 Guarantees, Saddle Points, and All That Jazz |
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293 | (2) |
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295 | (4) |
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299 | (9) |
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16.5 Exercises and Problems |
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308 | (5) |
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313 | (18) |
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313 | (1) |
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314 | (2) |
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316 | (7) |
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17.3 The Proof of Nash's Theorem |
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323 | (5) |
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17.4 Exercises and Problems |
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328 | (3) |
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18 The Prisoner's Dilemma |
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331 | (24) |
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331 | (1) |
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18.1 Criteria and Impossibility |
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332 | (7) |
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18.2 Omnipresence of the Prisoner's Dilemma |
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339 | (4) |
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343 | (2) |
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345 | (2) |
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18.5 Exercises and Problems |
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347 | (4) |
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351 | (4) |
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355 | (42) |
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357 | (2) |
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359 | (20) |
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359 | (1) |
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19.1 Weighted Voting Methods |
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360 | (3) |
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19.2 Non-Weighted Voting Methods |
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363 | (4) |
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367 | (4) |
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371 | (4) |
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19.5 Exercises and Problems |
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375 | (4) |
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379 | (18) |
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379 | (1) |
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20.1 Violations of Criteria |
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379 | (2) |
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381 | (5) |
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386 | (3) |
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20.4 Exercises and Problems |
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389 | (4) |
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393 | (4) |
Solutions to Odd-Numbered Exercises and Problems |
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397 | (52) |
Bibliography |
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449 | (4) |
Index |
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453 | |