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Copyright Copyright © 2018 by Scott E Page Cover design by Chin-Yee Lai Cover © 2018 Hachette Book Group, Inc Hachette Book Group supports the right to free expression and the value of copyright The purpose of copyright is to encourage writers and artists to produce the creative works that enrich our culture The scanning, uploading, and distribution of this book without permission is a theft of the author’s intellectual property If you would like permission to use material from the book (other than for review purposes), please contact permissions@hbgusa.com Thank you for your support of the author’s rights Basic Books Hachette Book Group 290 Avenue of the Americas, New York, NY 10104 www.basicbooks.com First Edition: November 2018 Published by Basic Books, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc The Basic Books name and logo is a trademark of the Hachette Book Group The Hachette Speakers Bureau provides a wide range of authors for speaking events To find out more, go to www.hachettespeakersbureau.com or call (866) 376-6591 The publisher is not responsible for websites (or their content) that are not owned by the publisher Library of Congress Control Number: 2018942802 ISBNs: 978-0-465-09462-2 (hardcover); 978-0-465-09463-9 (ebook) E3-20181019-JV-PC CONTENTS Cover Title Page Copyright Dedication Epigraph Prologue The Many-Model Thinker Why Model? The Science of Many Models Modeling Human Actors Normal Distributions: The Bell Curve Power-Law Distributions: Long Tails Linear Models Concavity and Convexity Models of Value and Power 10 Network Models 11 Broadcast, Diffusion, and Contagion 12 Entropy: Modeling Uncertainty 13 Random Walks 14 Path Dependence 15 Local Interaction Models 16 Lyapunov Functions and Equilibria 17 Markov Models 18 Systems Dynamics Models 19 Threshold Models with Feedbacks 20 Spatial and Hedonic Choice 21 Game Theory Models Times Three 22 Models of Cooperation 23 Collective Action Problems 24 Mechanism Design 25 Signaling Models 26 Learning Models 27 Multi-Armed Bandit Problems 28 Rugged-Landscape Models 29 Opioids, Inequality, and Humility About the Author Notes Bibliography Index To Michael D Cohen (1945–2013) It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience —ALBERT EINSTEIN Prologue To me success means effectiveness in the world, that I am able to carry my ideas and values into the world—that I am able to change it in positive ways —Maxine Hong Kingston This book began as the result of a chance meeting with Michael Cohen in 2005 near the flower garden in the mall adjacent to the University of Michigan’s West Hall Michael, a scholar known for his generosity, made a comment that altered my teaching career With a twinkle in his eyes, Michael said, “Scottie, I once taught a course called Introduction to Modeling for Social Scientists, based on a book written by Charles Lave and James March You should resurrect the course It needs you.” It needed me? I returned to my office a little confused, so I chased down an old course syllabus I discovered that Michael had misled me The course did not need me I needed it I had been wanting to develop a course that would introduce students to the core ideas of complex systems—networks, diversity, learning, large events, path dependence, tipping points—that would be relevant to their daily lives and future careers By teaching modeling, I could make students better thinkers while introducing them to complexity I could teach them tools that would improve their abilities to reason, explain, predict, design, communicate, act, and explore The course’s motivating idea would be that we must confront the complexity of the modern world with multiple models At semester’s end, rather than see the world from a particular angle, students would see the world through many lenses They would be standing in houses with many windows, able to look in multiple directions My students would be better prepared for the complex challenges before them—improving education, reducing poverty, creating sustainable growth, finding meaningful work in an age of artificial intelligence, managing resources, and designing robust financial, economic, and political systems The next fall, I resurrected the course I contemplated rebranding it as Thirty-Two Models That Will Turn You into a Genius, but the culture at Michigan frowns on hyperbole, so I stuck with Michael’s title: An Introduction to Modeling Lave and March’s book proved to be a brilliant introduction However, modeling had made huge advances in the intervening decades I needed an updated version that included models of long-tailed distributions, networks, rugged landscapes, and random walks I needed a book that discussed complexity So I began to write For two years, the ground proved rocky My plow moved at a slow place One spring day, I again ran into Michael, this time in the arch-way underneath West Hall I had been questioning the course, which was now drawing twenty students Were models too abstract for undergraduates? Should I teach a different course on a specific issue or policy domain? Michael offered up a smile, noting that any endeavor worth pursuing merited questioning As we parted, Michael commented on the importance and value of helping people think clearly He told me not to give up, that he took joy in my challenges In the fall of 2012, the ground under the course shifted Vice Provost Martha Pollack asked me to teach an online version—what is now called a MOOC With a tablet computer, a $29 camera, and a $90 microphone, Model Thinking was born With assistance from too many people at Michigan, Coursera, and Stanford University to thank properly (a quick shout-out to Tom Hickey, who did yeoman’s work), I reorganized my lectures into a form suitable for an online course, dividing each subject into modules and removing all copyrighted material With my dog Bounder as an audience, I taped and retaped lectures The first offering of Model Thinking drew 60,000 students That number now approaches a million The popularity of the online course led me to abandon the book I thought the project unnecessary, but, over the next two years, my email inbox began to fill with requests for a book to complement the online lectures Then Michael Cohen lost his battle with cancer, and I felt that I needed to finish the book I reopened the manuscript folder Writing a book requires large blocks of time and spaces that allow for clear thought The poet Wallace Stevens wrote, “Perhaps the truth depends on a walk around the lake.” I relied on a close analog: mind-clearing swims across Winans Lake, where my family spends our summers Throughout the writing process, the continuous life I share with the love of my life, Jenna Bednar, our sons, Orrie and Cooper, and our enormous dogs, Bounder, Oda, and Hildy, has brought laughter, comfort, and opportunities—among them Orrie having one week to correct the penultimate draft’s mathematical errors and Jenna having two weeks to identify instances of unclear writing, logical flaws, and muddled thinking As has been true of most of my written work, this manuscript might be best described as an original draft by Scott Page with substantial revision by Jenna Bednar During the seven-year period of writing this book, my children have transitioned from pre-teens to young adults Orrie is now off to college Cooper follows next year In the interval between sketching the initial outline and submitting the final version, my family has consumed copious amounts of bibimbap, pasta carbonara, and oatmeal chocolate chip cookies, taken the saws and loppers to scores of fallen branches and limbs, repaired dozens of breaks in the backyard fence, embarked on numerous failed initiatives to reduce the entropy in the basement and garage, and wished and hoped for the ice on the lake to be suitable for skating We have also had to accept loss Midway through the project, my mother, Marilyn Tamboer Page, died from a sudden heart attack while enjoying the bliss of her routine daily walk with her dog Not a day goes by when I not reflect on the love she showered on her family and the support she gave to others The book before you is as complete as it can be at this moment in time Doubtless, new models will be created, and old models will find new uses creating gaps in this current offering As I humbly send the manuscript out into the world, I feel that my efforts will have been repaid if you, the reader, find the models and ideas within to be useful and generative, and that you are able to carry them out into the world and change it in positive ways If one day, when sitting in some professor’s or graduate student’s office, preferably at a college or university in my beloved Midwest, I scan the bookshelves and find this book leaning, as it has during its writing, on a well-worn copy of Lave and March, then my efforts will have been all the sweeter The Many-Model Thinker To become wise you’ve got to have models in your head And you’ve got to array your experience —both vicarious and direct—on this latticework of models —Charlie Munger This is a book about models It describes dozens of models in straightforward language and explains how to apply them Models are formal structures represented in mathematics and diagrams that help us to understand the world Mastery of models improves your ability to reason, explain, design, communicate, act, predict, and explore This book promotes a many-model thinking approach: the application of ensembles of models to make sense of complex phenomena The core idea is that many-model thinking produces wisdom through a diverse ensemble of logical frames The various models accentuate different causal forces Their insights and implications overlap and interweave By engaging many models as frames, we develop nuanced, deep understandings The book includes formal arguments to make the case for multiple models along with myriad real-world examples The book has a pragmatic focus Many-model thinking has tremendous practical value Practice it, and you will better understand complex phenomena You will reason better You exhibit fewer gaps in your reasoning and make more robust decisions in your career, community activities, and personal life You may even become wise Twenty-five years ago, a book of models would have been intended for professors and graduate students studying business, policy, and the social sciences along with financial analysts, actuaries, and members of the intelligence community These were the people who applied models and, not coincidentally, they were also the people most engaged with large data sets Today, a book of models has a much larger audience: the vast universe of knowledge workers, who, owing to the rise of big data, now find working with models a part of their daily lives Organizing and interpreting data with models has become a core competency for business strategists, urban planners, economists, medical professionals, engineers, actuaries, and environmental scientists among others Anyone who analyzes data, formulates business strategies, allocates resources, designs products and protocols, or makes hiring decisions encounters models It follows that mastering the material in this book—particularly the models covering innovation, forecasting, data binning, learning, and market entry timing—will be of practical value to many Thinking with models will more than improve your performance at work It will make you a better citizen and a more thoughtful contributor to civic life It will make you more adept at evaluating economic and political events You will be able to identify flaws in your logic and in that of others You will learn to identify when you are allowing ideology to supplant reason and have richer, more layered insights into the implications of policy initiatives, whether they be proposed greenbelts or mandatory drug tests These benefits will accrue from an engagement with a variety of models—not hundreds, but a few Mallon, Mary, 140 Malthus, Thomas, 97, 209 many-model thinking, 40 bagging and, 41–42 blind spots and, 2–3 classes in, cognitive closure and, 56–58 data and, 3–4 defining, independent lies and, 28–30 for inequality, 343–354 need for, 5–7 opioid epidemic and, 339–342 separability and, 11–12 for value, 241–242 maoi, 269–270 market creation, 215–216 Market Entry Game, 243, 246 Markov model, 341 decision, 199 examples, 190–192 one-to-many and, 194–197 Matching Pennies, 244 Matthew effect, 70 Mauboussin, Michael, 88 maximal entropy, 148–150 maximization, entropy and, 146 Maybach Landaulet, 297 Mayer, Marissa, 227 McCarthy, Tom, 98 McDonald’s, McKinsey, mean in normal distribution, 60 regression to, 87 measurement error, 85 mechanism design, 283 median voter theorem, 232 medical school, 80 Merton, Robert, 69–70, 73 message space, 284 metabolic rates, 38–39 micro-macro loop, 55 Micromotives and Macrobehavior (Schelling), 184 Microsoft, 167 Milgram, Stanley, 124 Miller, John, 209–210 Minimize Risk Game, 245 Mirzakhani, Maryam, 181 Mississippi River Basin Model Waterways Experimentation Station, 23 model error decomposition theorem, defining, 35 model granularity, 222–223 modeling and models characteristics of, of people, 46–47 power laws and, 73–75 practice of, types of, 13–15 uses of, 15 models, of social phenomena, 44 monotonic ordering, 16 Monte Carlo method, for random networks, 121 Moore, Marianne, 131 Mount Fuji landscape, 328, 328 (fig.), 334 Mount-Reiter diagram, 284–286 multi-armed bandit problems, 319, 326, 340 Bayesian, 321–324 multiple congestible goods, 277 multiple-variable regression, 88–89 multivariable linear models, 87–90 Munger, Charlie, music lab experiments, 76 Myerson value, 130 myopic best response, 174 Nash equilibrium, 244, 262, 275–277 National Institutes of Health, National Milk Day, 229 nations failure of, 104–105 success of, 104–105 negative externality, 186–187 negative feedbacks, 201 systems dynamics models and, 211 threshold models with, 220–222 negatives, 92 neorealism, 313 net payoff, 288 network formation functions and, 123–126 logic and, 122–123 model, 123 quality and degree, 123 network robustness, 127–128 network size, random walk models and, 158–159, 158 (fig.) network structure betweenness and, 118 clustering coefficient and, 118 common, 121–122 defining, 118 degree in, 118 geographic, 119 (fig.), 120, 122 (fig.) hub-and-spoke, 119 (fig.), 120, 139 path length in, 118 power-law, 121, 122 (fig.) random, 121, 122 (fig.) rectangular grid, 139 small-world, 121, 122 (fig.) new-reality thinking, 89–90 Newton’s first law, Niarchos, Stavros, 37 NK model, 331–334 defining, 332 Nobel Prize, 161 node failure, 127 (fig.) noise environmental, 85 traders, 224 non-excludability, 272 nonlinear classifications, 92–93 nonlinear models, 105–106 non-rivalry, 272 Nooruddin, Irfan, 192 normal distribution, 59, 150 mean in, 60 Six Sigma methods, 65–66 with standard deviation, 61 (fig.) structure in, 60–61 symmetry of, 61 variance in, 60–61 normal random walk, 156 normal-form zero-sum games, 244–245 objects, 332 Ocala, 241–242 Ockham, William, 15 Ockham’s Razor, 15 O’Keeffe, Georgia, 27 Olympics, 88 omitted variables, 84–85 Omnibus Budget Reconciliation Act, 20 one-to-many approach, 141–142 defining, 36 Markov model and, 194–197 one-to-many property, 27 online bubbles, 120 opioid epidemic, many-model thinking and, 339–342 opportunity, 80–81 opposite proverbs, 18 ordering, preferences, 49 Oscars, 29 Ostrom, Elinor, 43, 281 outcome function, 284 outcome path dependence, 164 outcomes, 164, 165 (fig.) classes of, 147–148 entropy and, 147–148 out-of-sample error, 41 PageRank, 195, 197 (fig.) paradoxes chain store, 247 of coordination, 174, 175 friendship, 16, 17 (fig.), 124 Grossman and Stiglitz, 160 Parrondo’s, 16 sales-durability, 194 Simpson’s, 16 of skill, 88 Pareto domination, 284 Pareto efficiency, 284 Parrondo’s paradox, 16 partial pooling, 299 patenting, 336–337 path dependence, 167–168 tipping point and, 168 (fig.) path length, in network structure, 118 payoffs in hedonic competition model, 237 to neighbors, 264 (fig.) net, 288 in Prisoners’ Dilemma, 261 in spatial competition model, 230 sucker’s, 256 peer effect models, 250 people, modeling, 46–47 percentage, of variance, 34 Perron-Frobenius theorem, 192–194 defining, 193 ergodicity and, 193 fixed transition rule and, 193 noncyclic, 193 states in, 193 persistent inequality model, 352–353 Phelps, Michael, 88 Piaget, Jean, 13 Piketty, Thomas, 348 ping-pong model, 220 defining, 221 response threshold in, 221 system state in, 221 time series for, 222 (fig.) pivot mechanism, 293, 294 placebos, 65 Plato, on knowledge, players, 108 Plott’s no-winner result, 234 pluralism, 104 Polya process, 163–166, 198 applications, 168–169 defining, 164 extension of, 166 pooling, 299 population, doubling, 209–210 positioning, 30 positive feedbacks, 69–70, 209–210 model, 345–346 potentials, 203 poverty traps, 353 power seats and, 113 (fig.) Shapley-Shubik index of, 112–114 power laws logic and, 73–75 models and, 73–75 power-law distributions, 69 defining, 70 structure of, 70–73 World Wide Web and, 71 (fig.) power-law network, 121, 122 (fig.) predator-prey model, 204–207 systems dynamics models of, 205 prediction, 15 empirical studies of, 32 explanation and, 24 REDCAPE and, 23—24 predictive models, 241–242 preferences, 14 fundamental, 240 instrumental, 240 ordering, 49 preferential attachment model, 73 presidential elections, 326 price competition in crowded markets, 239 (fig.) in sparse markets, 239 (fig.) Princip, Gavrilo, 167 Prisoners’ Dilemma, 2, 255–262, 255 (fig.) payoffs in, 261 probabilities contact, 135 diffusion, 135 sharing, 135 transition, 190, 191 product competition, hybrid model of, 238–240 production function, 101 program trading, 225 property rights, 104 proposer effects, 236 (fig.) prospect theory, defining, 52 psychological biases, in rational-actor model, 51–53 public goods, 272–275 public projects decision problems, 292 mechanisms for, 292–294 pure coordination games, 174 pure exchange economies, 186–187 p-value, 85–86 quality and degree network formation, 123 quantity, 30 quantum computing, 80 Race to the Bottom, 2, 181, 182 radial symmetry, 233 random, 147 random friends, 125, 126 random mixing, 135 random networks, 122 (fig.) Monte Carlo method for, 121 random walk models, 155–158 efficient markets and, 159–161 network size and, 158–159, 158 (fig.) normal, 156 simple, 155, 156 (fig.) rational actors, 43, 45, 56 rational choice arguments for, 50 benchmarks and, 50 consistency and, 50 learning and, 50 stakes and, 50 uniqueness and, 50 rational-actor model, 10, 11 beliefs in, 48 benchmarks in, 51 completeness in, 49 consistency in, 51 of consumption, 48 continuity in, 49 defining, 47–48 independence in, 49 psychological biases in, 51–53 transitivity in, 49 rationality, 45 individual, 293 realism, 14 messiness and, 50 reason, in REDCAPE, 15–18 rectangular grid network, 139 REDCAPE, 13, 355 communication in, 20–21 defining, 15 design in, 20 explanation and, 19 exploration and, 24–25 prediction and, 23—24 reason in, 15–18 regression line, 85 (fig.) regression to the mean, 87 reinforcement, individual learning and, 306–308 relocations, 218 heterogenous thresholds and, 218 (fig.) in Schelling’s segregation model, 220 (fig.) renewable resource extraction, 277–280 rent-from-capital model, 348 repeated game model, 256 repetition, cooperation and, 256–259 replicator dynamics, 308–310, 312 replicator equation, 309 reputation, cooperation and, 256–259 resource extraction, renewable, 277–280 response threshold, in ping-pong model, 221 revenue equivalence theorem, 289–292 revolving-door model, 218 rewards, 307 distributions, 322 effect, 309 Richter scale, 71 riots, 213–214 algorithmic, 224 double, 215–216 model, 214–220 threshold, 214 risk aversion, concavity and, 99 risk dominance, 313 risk-loving, convexity and, 99 Rockefeller, John D., 329 Rometty, Ginni, 107 routine, 185 Rowling, J K., 69 R-pentomino, 177 r-shaped adoption curve, broadcast model and, 133 (fig.) rugged landscapes, 330–331, 334–335 peaks, 331 (fig.) rule of 72, 96, 105, 349 rule of law, 104 rule-based actors, 43 rule-based behavior, 45 rule-playing behaviors, 259–262 salaries in search model, 80–81 sales-durability paradox, 194 sample-then-greedy, 320, 321 Samuelson, Paul, 36, 160 sand pile model, defining, 74 savings rate, 101 Saxonhouse, Arlene, 195 scatterplot, 85 (fig.) Schelling, Thomas, 184, 216 Schelling’s party model, 216 defining, 217 Schelling’s segregation model, 353 relocations in, 220 (fig.) tolerance threshold in, 219 seats, power and, 113 (fig.) second-price auction, 288 segregation models of, 216–220 production of, 217 (fig.) See also Schelling’s segregation model selection bias, 89 self-organization, 75, 184–186 self-organized criticality model, 74 self-organizing activities model, 185 separability, many-model thinking and, 11–12 separation, 298, 299 with continuous signals, 301 sequential games, 246–247 sets testing, 87 training, 87 Shapley, Lloyd, 110 Shapley value, 107, 108 alternative uses test and, 111–112, 112 (fig.) axiomatic basis for, 110–111 defining, 109 Shapley-Shubik index, 112–114 sharing probability, 135 Shelley, Percy Bysshe, 189 shocks lognormal distribution and, 66–67 multiplication of, 66–67 sign, defining, 85 signals uses of, 301–302 value of, 301–302 significance, defining, 85 simple growth model, 101 simple random walk, 155 plot of, 156 (fig.) Simpson’s paradox, 16 sinks, 202 SIR model, 2, 131, 137–142 Six Degrees of Separation, 124 defining, 126 Six Sigma methods, normal distribution, 65–66 skill, paradoxes of, 88 skill-luck equation, 87–88 Slaughter, Anne-Marie, 117 slow thinking, 51 small-world network, 121, 122 (fig.) social choice correspondence, 284 social learning, 308–310 social mobility, 351 social phenomena, models of, 44 socially optimal, 277 Solow* growth model, 102–104 defining, 103 sorting models, 250 Soviet Union, 11, 104–105, 268 S&P 500, 154 spaghetti graph, 42 sparse markets, 239 price competition in, 239 (fig.) spatial attributes, 227 in spatial competition model, 230 spatial competition model, 228–229, 326 alternatives in, 230 attributes in, 230–231 defining, 230 Downsian, 231–240 ideal point in, 230 individuals in, 230 payoffs in, 230 spatial attributes in, 230 with Voronoi neighborhoods, 231 (fig.) square root rules, 63 stable lines, in local majority model, 176 (fig.) stakes, rational choice and, 50 standard deviation defining, 61 normal distribution with, 61 (fig.) stark probabilistic model, 32 State Farm insurance, states, 190 statistical equilibrium, 189 status quo effects, 234–236 Stevens, Wallace, 339 stick, value as a shovel, 329 Stigler, George, 241 strong types, 299, 301 structure, in normal distribution, 60–61 structure-logic-function organization, 60 stuffed-cheetah problem, 8–9 subgame perfect equilibrium, 246–247 suboptimal equilibrium, 173 substance, 30 success equation, 87, 129 sucker’s payoff, 256 superspreaders, 139–140 supertankers, 36–37, 37 (fig.) surprise principle, 307 symmetry, 111 entropy and, 146 of normal distribution, 61 radial, 233 system state, in ping-pong model, 221 systems dynamics models components of, 202 (fig.) of financial systems, 209 (fig.) guides to action and, 207–208 negative feedbacks and, 211 parts of, 202–204 of predator-prey model, 205 Taleb, Nassim, 153 TARP See Troubled Asset Relief Program taxes, 211 Taylor, Frederick, 329 Taylorism, 329 temptations, 256 testing sets, 87 thinking fast, 51 slow, 51 Thoreau, Henry David, 171 Thorndike, Edward, 306–307 threshold models, with negative feedbacks, 220–222 time series, for ping-pong model, 222 (fig.) tipping point, 138, 167–168 path dependence and, 168 (fig.) tolerance threshold, 217 in Schelling’s segregation model, 219 total disagreement, 183, 184 (fig.) total value, 108 Tractatus Logico-Philosophicus (Wittgenstein), training sets, 87 transition probabilities, 190, 191, 351 transition rule, 182 transition-to-addiction model, 341 transitivity, in rational-actor model, 49 TROLL, 260 Troubled Asset Relief Program (TARP), 21–22 truth-telling, 285 TurboTax, 76 Tversky, Amos, 51–52 two-dimensional median, 233 typhoid, 140 uncertainty, 144 unconditional generosity, 303 uniform distribution, 149, 150 uniqueness, rational choice and, 50 United States Air Force, 10–11 utility functions, 48–49 vaccination threshold, 138 valence attributes, in hedonic competition model, 237 valuation error, defining, 35 value, 332 last-on-the-bus, 108, 115 many-model thinking for, 241–242 of signals, 301–302 value at risk (VaR), 170 value function, 108 VaR See value at risk variables dependent, 84 independent, 84 multiple-variable regression, 88–89 multivariable linear models, 87–90 omitted, 84–85 variance in normal distribution, 60–61 percentage of, 34 veto players, 234–236 Vinlanders, 270 volatility long-tailed distributions and, 77–78 VaR and, 170 voluntary participation, 285 von Neumann, John, 95 Voronoi neighborhoods, 231 spatial competition model with, 231 (fig.) Wainer, Howard, 63 Walmart, 78 Waltz, Kenneth, 313 Warbler males, 260 wasteful subsistence behavior, 303 weak ties, 125 weak types, 299, 301 weights, 307 in hedonic competition model, 237 West, Geoffrey, 69 Wilhelm, Kaiser, 167 William III (King), 211 Williams, Serena, 319 wisdom hierarchy, 8–12 data in, information in, wisdom of crowds, 30 Wittgenstein, Ludwig, Wolfram’s classes, 147, 148 (fig.) The Woman Warrior (Kingston), women CEOs, 39 workers, 348 World War I, 167 World War II, 37 World Wide Web, 195, 196 (fig.) power-law distributions and, 71 (fig.) WORLD3 model, 208–210 proponents of, 210 zero intelligence agents, 56 zero property, 111 of entropy, 146 zero-sum games, normal-form, 244–245 Zimbabwe, 96 Zipf’s law, defining, 72 Zuckerberg, Mark, 198 Zurcher, Harold, 50 ... many -model thinkers Becoming a many -model thinker requires learning multiple models of which we gain a working knowledge; we need to understand the formal descriptions of the models and know how to. .. the other licenses that company won The license for Southern California would be worth more to a company that also owned the license for Northern California, for example Economists refer to these... the two models An insight from the organizational model changes the payoffs in the rational-choice model Allison adds a governmental process model The other two models reduce countries to their
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