Körner T.W. Naive Decision Making: Mathematics Applied to the Social World

Cambridge University Press, 2008, 400 pages, ISBN: 0521516161How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making everyday decisions, which my often be based on very little or uncertain data. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with relatable observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Suitable for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.A day at the racesMoney for nothing
The ideal bookmaker
Negative money
Probability and expectation
Back to the races
Betting last at the tote
Betting first
Real race-tracksThe long runThe laws of probability
Cards, dice and coin tossing
Random variables
Independence
A law of large numbers
A long day at the races
The two-horse raceThe vice of gambling and the virtue of insuranceBernard Shaw
Annuities
Smallpox
Should we inoculate?
Utility and Jensen’s inequalityPassing the timeThe three towers
Euclid’s algorithm
Arithmetic modulo n
Arithmetic modulo p
Arithmetic modulo pq
Mr Jonas entertainsA pack of cardsFind the largest
Records
How to choose a restaurant
Back to sorting
Shortest pathsOther peopleMarrying
Voting
PreferringSimple gamesScissors, Paper, Stone
Scissors, Paper
Can we generalise?
Morra
Can we generalise further?
A noisy duelPoints of agreementAn evening out
Technical points
What about reality?
Fixed points
Nash equilibrium
Hawks, doves and othersLong duelsA, B and C
The three-sided duel
One-person duels
HHH
Tit for tat
Foundational mattersA night at the casinoHow to gamble if you must
Boldness be my friend
Difference and differential equations
The casino’s view
A flutter on the lottery
Life is a lotteryProphecyCoin tossing
A needle in a haystack
Tchebychev improved
A better needle?
Final reflections
First the music, then the words
Mathematics and decision makingAppendix A The logarithm
Appendix B Cardano
Appendix C Huygens’s problems
Appendix D Hints on pronunciation