Book contents
- Frontmatter
- Contents
- Introduction
- 1 A day at the races
- 2 The long run
- 3 The vice of gambling and the virtue of insurance
- 4 Passing the time
- 5 A pack of cards
- 6 Other people
- 7 Simple games
- 8 Points of agreement
- 9 Long duels
- 10 A night at the casino
- 11 Prophecy
- 12 Final reflections
- Appendix A The logarithm
- Appendix B Cardano
- Appendix C Huygens's problems
- Appendix D Hints on pronunciation
- Bibliography
- Index
5 - A pack of cards
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Introduction
- 1 A day at the races
- 2 The long run
- 3 The vice of gambling and the virtue of insurance
- 4 Passing the time
- 5 A pack of cards
- 6 Other people
- 7 Simple games
- 8 Points of agreement
- 9 Long duels
- 10 A night at the casino
- 11 Prophecy
- 12 Final reflections
- Appendix A The logarithm
- Appendix B Cardano
- Appendix C Huygens's problems
- Appendix D Hints on pronunciation
- Bibliography
- Index
Summary
Find the largest
Suppose that we are helping some very cultured friends move house. They have already installed several walls of bookcases but left us to unpack the many crates of books which go on the bookcases. We decide to place the books in alphabetical order. This is not as easy as it seems, but we will be helped by various pieces of knowledge and guesswork. However badly jumbled the books have been in packing, there will probably be runs in near perfect alphabetical order. We expect that about a third of the authors will have initial letters A to G, about one third G to N and about one third N to Z. We know that most authors with initial letter W will have second letter A, E, H, I, O, R or Y and so on.
If we seek to mechanise the sorting process involved, then we can either attempt to identify and incorporate all these random and not very precise pieces of information or we must produce methods which make no use of them at all.
To make sure that we do not use extraneous information, let us consider the following model for sorting n cards bearing the numbers 1 to n. The cards are placed face down in front of you. You have an assistant who will look at any two cards that you indicate and tell you which of the two cards bears the largest number.
- Type
- Chapter
- Information
- Naive Decision MakingMathematics Applied to the Social World, pp. 148 - 175Publisher: Cambridge University PressPrint publication year: 2008