Index

w3s , 49RWC N (α), 91

Academy of Motion Pictures, 42Adam Smith, xv, 31, 69, 70aggregate excess demand, 70Alabama Paradox, 153Alexander, L., 43Alice in Wonderland, 73American Mathematical Society,

45anonymity, 89approval voting, 74

Banzhaf value, 79, 82BASIC, 73Basic subspace, 106Belokurova, G., 38best response, 3Black, D., 100Boa Viagem, 6Borda basis, 108Borda, J.C.

Borda Count, 48Brouwer fixed point theorem, 4Buchanan, P., 43bullet vote, 77

Cabral, H., 6Carroll, Louis, 73carrying capacity, 30Chicago; Olympic bid, 45climate change, 127Clinton, H., 81coalition-proof, 120Coffee, Jr., J., 152Condorcet, 142

loser, 60, 63

winner, 60, 63, 65connecting information, 144Copeland, 72cumulative voting, 74

dark matter, xvi, 139, 158Dartmouth College, 73Dodgson Dictionary, 73Dodgson–Ratliff committee, 73Dole, R., 43Don Squad, xviidynamical systems, 1

Einstein, A., xivEqual Proportions, 155evolutionary game theory, 1expected value, 4

Fisher, M., xviiForbes, S., 43

gameG B

3 , 125G B

4 , 125G B

5 , 126G B

8 , 126GN

1 , 114GN

3 , 115GN

7 , 116GN

8 , 126G1, 4, 113, 117G2, 5G3, 112, 113, 122, 138G4, 112, 113, 129, 138G5, 112, 126, 138G6, 112, 117G7, 113, 133G9, 127, 130G10, 129, 132

169

170 Index

G12, 136game theory, 1, 2general relativity, xivGerver, J., xvigrim trigger, 130Grofman, B., xvii

Hamilton methodmodified, 157

Hamilton, A., 153Hare method, 45harmonic apportionment, 155Hazelrigg, G., 139Heili, 148house monotone, 154hyperbolic point, 19

IIA, 142IIIA, 146impossibility theorem, 139, 142independence

probability, 150index

global, 18local, 18

Institute for MathematicalBehavioral Sciences, xvii, 1

invisible hand, 31

Jacobian, 19Jefferson method

modified, 157Jefferson, T., 155Jeffords, J., 81Jessie, D., xvi, xvii, 112

Kakutani fixed point theorem, 4Kemeny Dictionary, 73Kemeny, J., 73Kendall, R., xviiKISS, xvKlein four group, 109Kurtz, T., 73

Le Verrier, U., xiiilimit cycle, 30Lincoln, A., 51Lotka–Voltera equation, 28Luce, D., xvii

McIntee, T., xvii

me vs. we, 125Mercury, xiiiMerlin, V., 63mixed strategy, 4multiple voting rules, 72, 74

Nakamura number, 95, 98nanotechnology, 139Narens, L., xvi, xviiNash equilibrium, 3Nash, J., 4networks, 38neutrality, 90NewsHour, 151Newton’s laws, xiiiNobel Prize, Economics, 2

Occam’s razor, xv, 9optimization, 1Orrison, M., xviOscars, 41

Pacific Institute of MathematicalSciences, 1

Pareto condition, 143Pareto point, 5Pareto superior, 120Pippen, S., 79plurality dictionary, 57plurality word, 57Poincaré, H., 158Poincaré–Hopf theorem, 20, 38policy, 9politically correct, 47positional voting rule, 47

antiplurality, 47Borda Count, 48normalized, 49plurality, 47procedure hull, 50, 52, 82procedure line, 50

power index, 79hull, 82

PPAD, 4predator-prey equations, 28predictions, 32Prisoner’s Dilemma, 5, 112, 133procedure line, 102profile action vector, 94, 105pure strategies, 3

Index 171

QRE, 134quantal response equilibrium, 134

ranking square, 108ranking wheel configuration, 91ransomware, 152Rapaport, A., 129Recife, Brazil, 6reductionist approach, xvi, 140replicator dynamics, 8reversal subspace, 105Rio de Janeiro, 45Rosier, R., xviRousseau, 127

Schwarzian derivative, 160secret ballot, 89Shapley value, 82Simpson’s paradox, 83, 151Simpson-paradox dictionary, 84Skyrms, B., xviiSmallest Divisor, 155Smith, W., 44

social norms, 6Sonnenschein, H., 70stag hunt, 127strategic voting, 77strong Nash equilibrium, 121structural stability, 16supermajority voting, 72

Tatjana, 148tit-for-tat, 129Titanic, 88Trump, D., 43, 81Tyler, 141

ultimatum game, 5, 8, 13, 20US Supreme Court, xvi

validation, 33

Walras’ laws, 70Webster’s method, 155whole vs. parts, 142winding number, 18