Naive Decision Making. Mathematics Applied to the Social World
This book deals with situations when mathematics can be useful for making decisions when the outcomes are uncertain or when one must respect the interests of others. The author presents various aspects of mathematical decisions using not only realistic examples but also jokes, games, quotations, etc. Chapter 1 shows that some sorts of betting are more sensible than others. Chapter 2 deals with a simple theory of probability (e.g. the weak law of large numbers). In chapter 3, insurance, pensions and a matter of life and death are discussed by means of mathematics of the race-track. Chapter 4 introduces the notion of algorithms (e.g. Euclid’s algorithm). Chapter 5 uses the model of a shuffled pack of cards to illustrate various topics (e.g. finding the shortest route from A to B). In chapter 6, the subjects of marrying, voting and preferring are analyzed using e.g. Arrow’s theorem. Chapter 7 is devoted to simple games, such as ‘Scissors, Paper, Stone’. Chapter 8 uses Nash’s arguments for various points of agreement. Chapter 9 is devoted to various forms of duels. Chapter 10 looks at casinos both from the point of view of the customers and from the point of view of the owners. Chapter 11 is called ‘Prophecy’ and shows that appropriate odds can be found by means of statistics. The ‘Final reflections’ in the last chapter admits the existence of limits of naive decision making that is discussed in the book. The book can serve as a supplementary text for undergraduate courses in probability, game theory and decision making. Moreover, many exercises are included with solutions available online.