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© in This Web Service Cambridge University Cambridge University Press 978-1-107-06043-2 - Handbook of Computational Social Choice Edited by Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang and Ariel D. Procaccia Index More information Index adjacency matrix, 60 bloc voting, 207 Adjusted Winner, 305 blocking coalition, 360 affine equivalence, 28 blocking pair, 337 agenda, 79, 454 Borda in judgment aggregation, 402 score, asymmetric, 28 agenda control, 456, 457, 460 score, symmetric, 28 for balanced binary trees, 459, 460 voting rule (Borda count), 28, 97, 147, 154, 163, #Agenda Control Problem, 462 164 agenda-implementability, 80 Borda, Jean-Charles de, 3 alternative vote, 37 bracket, 454, 465, 472, 473 amendment procedure, 78 Brams-Taylor algorithm, 321 anonymity, 31 Bribery, 161, 163 in judgment aggregation, 404 $Bribery, 161, 163, 164 anonymous game, 374 bribery, 159, 473 antiplurality voting rule, 37, 147 approximability of, 158, 166 apportionment, 15 in combinatorial domains, 166 appreciation of friends game, 373 in judgment aggregation, 167, 425 approval voting rule, 53, 147, 152, 154, 163 in path-disruption games, 167 sincere-strategy preference-based, 147, 154 bribery problem, 161 approximate manipulation, 140 priced, 159 approximation algorithm, 118, 387 with discrete price functions, 161 Archimedean property, 40, 152 with $discrete price functions, 161 argumentation, 423 with swap-bribery price functions, 161 Arrovian social choice, 261 shift, 164 Arrow’s Theorem, 6 BTT conditions, 132 in judgment aggregation, 419 Bucklin voting, 148, 154, 163 automated reasoning, 14, 425 simplified, 148 AV, see approval voting rule budgeted social choice, 209 aversion to enemies game, 373 bye, 459 axiomatic method, 30, 427 C1 social choice function, 38, 57, 60 Baldwin voting rule, 37 C2 social choice function, 38, 85 Banks set, 68 C3 social choice function, 39 Banzhaf index, 382 cake division problem, 265 computational properties, 386 campaign management, 159, 168 belief merging, 206, 421 with truncated ballots, 168 binary aggregation, 422 Campbell-Kelly Theorem, 35 binomial arborescence, 463 candidate cloning, 158, 168 bipartisan set, 66 candidate decloning, 168 of a weighted tournament, 101 Carroll, Lewis, see Dodgson, Charles Lutwidge Black’s rule, 97 CCAC, 150, 154 Black’s Theorem, 51 CCAUC, 150, 154 529 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-06043-2 - Handbook of Computational Social Choice Edited by Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang and Ariel D. Procaccia Index More information 530 index CCAV, 151, 154 majority, 175 CCDC, 150, 154 strong unanimity, 174 CCDV, 151, 154 transitivity, 175 CCPC-TE, 155, 154 unanimity, 174 CCPC-TP, 155, 154 conservative extension, 81 CCPV-TE, 155, 154 consistency, 40, 276 CCPV-TP, 155, 154 of a judgment set, 402 CCRPC-TE, 155, 154 of an aggregator, 405 CCRPC-TP, 155, 154 constructive manipulation, 473 Chamberlin and Courant, 208 Constructive-Control-by-Adding-an- choice set, 60, 367 Unlimited-Number-of-Candidates, 150 claims problem, 265 Constructive-Control-by-Adding- classical fair division problem, 264 Candidates, 150 closure under complementation, 402 Constructive-Control-by-Adding-Voters, 151 closure under propositional variables, 412 Constructive-Control-by-Deleting- coalition, 402 Candidates, 150 coalition structure, 357 Constructive-Control-by-Deleting-Voters, 151 coalitional manipulation, 473 Constructive-Control-by-Partition-of- coarsening of a tournament solution, 61 Candidates, 155 Coleman index, 382 Constructive-Control-by-Partition-of- collaborative filtering, 452 Voters, 155 collective combinatorial optimization, 16 Constructive-Control-by-Runoff-Partition- combinatorial domain, 198, 200 of-Candidates, 155 connection with judgment aggregation, 423 Contagion Lemma, 6 committee elections, 197, 198, 207 contractual Nash stability (CNS), 360 communication complexity, 235 contractually individual stability (CIS), 361 compact preference representation language, 210 control, 149 compilation complexity, 143, 247 approximability of, 158 complement constructive, 149 of a coalition (C), 402 by adding an unlimited number of candidates, of a propositional formula (∼ϕ), 402 150, 152, 153 complement-freeness by adding candidates, 149, 150, 152, 153 of a judgment set, 402 by adding voters, 149, 152, 153 of an aggregator, 405 by deleting candidates, 149, 150, 152, 153 complete vs. incomplete information, 138 by deleting voters, 149, 152, 153 completeness by partition of candidates, 154, 155 of a judgment set, 402 by partition of voters, 154, 155 of an aggregator, 405 by runoff partition of candidates, 154, 155 completion (extension) principle, 204 destructive, 154 complex competition format, 474 by deleting candidates, 156 complexity theory, 17 experimental study of, 158 component of a tournament, 60 in combinatorial domains, 158 composition property, 277 in judgment aggregation, 159, 425 composition-consistency, 62 in sequential elections, 159 computational complexity of manipulation, 131 online computer-assisted theorem proving, 14 in sequential elections, 159 conditional preference table, 212 control problem, 149 conditional preferential independence, 211 counting variant of a, 167 conditionally lexicographic preference, 213 converse consistency, 276 Condorcet cooperative game, 13, 358, 378 consistency, 35, 61, 148, 453, 455 cooperative vs. noncooperative game theory, 144 domain (DCondorcet), 35 Copeland voting rule, 28, 63, 148, 153, 154, 163, 464 extension, 35, 453, 454 cooperative game, with non-transferable utility, 358 generative model, 471 core, 360 in judgment aggregation, 403 computational properties, 383 jury theorem, 184 definition, 380 loser, 35, 63 core stability, 360 Marie Jean Antoine Nicolas de Caritat, Marquis de, covering relation, 67 4, 24 deep, 82 non-losers, 63 McKelvey, 82 paradox, 4, 34, 57 CP-net, 211 principle, 25 crowdsourcing, 17, 424 voting rule, 152, 154 cumulative voting, 207 winner, 34, 58, 103, 148, 454, 464 winning set, 210 DCAC, 154 consensus class, 174 DCAUC, 154 Condorcet, 175 DCAV, 154 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-06043-2 - Handbook of Computational Social Choice Edited by Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang and Ariel D. Procaccia Index More information index 531 DCDC, 154 electoral control, see control DCDC, 156 electorate DCDV, 154 single-crossing, 158 DCPC-TE, 154 nearly, 158 DCPC-TE, 158 Elevator Lemma, 276 DCPC-TP, 154 envy DCPC-TP, 158 cycle, 301 DCPV-TE, 154 maximal, 300 DCPV-TP, 154 possible / necessary, 303 DCRPC-TE, 154 ratio, 302 DCRPC-TE, 158 envy-freeness, 295, 313 DCRPC-TP, 154 equal treatment of equals, 269, 278 DCRPC-TP, 158 equal-division lower bound, 271 Debord’s Theorem, 86 equal-division Walrasian rule, 270 decomposition of a tournament, 60 equitability, 313 Deegan-Packel index, 382 essential set (ES), 82, 101 descending demand procedure, 308 even-number-negatable agenda, 417 destructive manipulation, 473 Even-Paz algorithm, 314 dichotomous preferences, 55 expected quality of the winner, 472 dichotomy result Extension-Bribery, 168 on control, 158 on manipulation, 158 f -equivalence, 248 on possible winners, 158, 164 fair allocation, 261 dictatorship, 31 fair division with single-peaked preferences, 264 in judgment aggregation, 415 fallback voting, 148, 154, 163 discursive dilemma, 400 false-name-proofness, 144 distance, Hamming, 205 Field Expansion Lemma, 6 distance, 175 Fishburn’s classification, 38 discrete, 176 Fisher market, 327 edge reversal, 177 fixed electorate, 29 footrule, 176 fooling set, 236 Kendall tau, 176 fractional hypergraph matching, 375 Sertel, 177 frequency of manipulability, 141 swap, 176 full P -agenda control, 457, 458 vote insertion, 177 full agenda control, 457 votewise, 180 fully proportional representation, 208 distance rationalizability, 104 distance-based aggregation Gale–Shapley algorithm, 334, 338, 339 in judgment aggregation, 410, 425 game-theoretic models of manipulation, 142 distortion, 250 Gamson’s hedonic game, 374 distributed fair division, 308 general agenda control, 457 districting, 15 geometric reward mechanism, 443 doctrinal paradox, 400 GETCHA, 71, 82 Dodgson approximation, 118 Gibbard-Satterthwaite Theorem, 46, 76, 128 Dodgson score, 104 quantitative versions, 141 Dodgson voting rule, 45, 103, 125 GOCHA, 83 Dodgson winner problem, 109, 110 group activity selection game, 374 Dodgson, Charles Lutwidge, 4, 103 group classification, 16 DodgsonScore problem, 111 Group Contraction Lemma, 6 domain, 264 group recommendation, 16 domain restrictions, 29 Groupthink, 439 in judgment aggregation, 407 dominance relation, 59 Hamming distance, 205 double-elimination tournament, 474 between two judgment sets, 403 duality, 282 Hare voting rule, 37 Dubins-Spanier algorithm, 314 hedonic coalition formation game, additively Duggan-Schwartz Theorem, 50 separable, 364 dummy player, 381 hedonic coalition formation game, fractional, 357, dynamic programming, 116 374 dynamic social choice, 17 hedonic coalition formation game, with dynamics, 143 B-preferences, 365 hedonic coalition formation game, with ε-monotonic probability matrix, 460 W-preferences, 366 edit distance, 104 hedonic coalition net, 362 effort, 472 heuristic algorithm egalitarian-equivalence, 272 frequently self-knowingly correct, 113 election fraud detection, 159 highish outdegree, 467, 468 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-06043-2 - Handbook of
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