Week 3: Rational Choice
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The document provides an overview of rationality and rational choice theory. It discusses rationality in: 1) Argument, focusing on basic logical rules like modus ponens and modus tollens. 2) Ultimate ends, noting debates around whether rationality determines ends or if preferences are independent. 3) Beliefs, introducing Bayes' theorem and how beliefs are updated with new evidence. It uses examples like spending on lotteries to illustrate rationality in action and choice. Game theory, like the Prisoner's Dilemma, is presented as a way to understand rational interactions. The document concludes with a brief discussion of failures of rational rationality like biases and heuristics.
Week 3: Rational Choice
- 1. Rational Choice Chris Hanretty 1 / 33
- 2. Rationality in argument Rationality in ultimate ends Rationality in beliefs Rationality in action Rationality in games Failures of rationality 2 / 33
- 3. Warnings 1. Little of this lecture covered by the readings This lecture prepares you for the readings 2. We have to start with rationality before discussing rational choice A lot of this stuff seems basic. 3 / 33
- 4. #1: Rationality in argument 4 / 33
- 5. Long history of prizing rationality Aristotle, Metaphysics: ``man is a rational animal'' Rationality bound up with philosophy, philosophical argument In particular, basic moves in logic 5 / 33
- 6. Basic moves in logic 1. Law of Contradiction: for any proposition p, it is not the case that both p and not-p. 2. Law of the excluded middle: for any proposition p, it is either the case that p or not-p. 3. Modus ponens (if/then): if p, and if (if p then q), then q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 6 / 33
- 7. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: for any proposition p, it is either the case that p or not-p. 3. Modus ponens (if/then): if p, and if (if p then q), then q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 7 / 33
- 8. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: for any proposition p, it is either the case that p or not-p. 3. Modus ponens (if/then): if p, and if (if p then q), then q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 8 / 33
- 9. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: p ∨ ¬p 3. Modus ponens (if/then): if p, and if (if p then q), then q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 9 / 33
- 10. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: p ∨ ¬p 3. Modus ponens (if/then): if p, and if (if p then q), then q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 10 / 33
- 11. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: p ∨ ¬p 3. Modus ponens (if/then): p; p → q; ∴ q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 11 / 33
- 12. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: p ∨ ¬p 3. Modus ponens (if/then): p; p → q; ∴ q 4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 12 / 33
- 13. Basic moves in logic 1. Law of Contradiction: ¬(p ∧ ¬p) 2. Law of the excluded middle: p ∨ ¬p 3. Modus ponens (if/then): p; p → q; ∴ q 4. Modus tollens (more if/then): ¬q; p → q; ∴ ¬p 13 / 33
- 14. Concrete example of modus ponens 1. The lecturer is talking 2. If the lecturer is talking, the lecture has started 3. ∴ the lecture has started If you accept the premises, you must (rationally) accept the conclusion. 14 / 33
- 15. Rationality To be rational just is to argue in this fashion, using only legitimate moves in your argumentation and accepting them when others use them against you 15 / 33
- 16. On the internet, no-one knows you're irrational The internet is (famously) home to much irrational argument And many people arguing that their opponents are irrational Environmental politics example (à la Monbiot pre Fukushima) 1. if something is a low-carbon means of generating electricity, it is good 2. nuclear power is a low-carbon means of generating electricity 3. ∴ nuclear power is good 16 / 33
- 17. #2: Rationality in ultimate ends 17 / 33
- 18. Spock, John Redwood The popular view of beings driven by rationality Idea: certain actions are compelled by rationality 18 / 33
- 19. The Kantian view The categorical imperative (in one of its formulations) ``act only in accordance with that maxim through which you can at the same time will that it become a universal law'' Immoral acts are ultimately self-contradictory (p ∨ ¬p) Kant not much use in the social sciences 19 / 33
- 20. The Humean view Hume's Treatise on Human Nature ``Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them'' Preferences or passions or desires or inclinations not subject to rationality 20 / 33
- 21. Social science Rationally-given ends big stuff in moral philosophy Less relevant in social sciences Consider aesthetic or political choices Rationality alone cannot explain choices We know to know what people were aiming at 21 / 33
- 22. #3: Rationality in beliefs 22 / 33
- 23. Extraordinary claims require extraordinary evidence -- Carl Sagan 23 / 33
- 24. Bayes' principle We update our beliefs in the light of new evidence But we also have prior beliefs Probability of something being true given new evidence equal to baseline probability of that thing being true, times probability you'd get that evidence if the thing was true, divided by the probability of the evidence 24 / 33
- 25. Bayes: example Suppose you are living with a partner and come home from a business trip to discover a strange pair of underwear in your dresser drawer. You will probably ask yourself: what is the probability that your partner is cheating on you? The Signal and the Noise 25 / 33
- 26. What do you need to know? Baseline probability of partner cheating: 4% Probability of underwear appearing given infidelity: 50% Probability of underwear just appearing: 5% 26 / 33
- 27. What do you need to know? Baseline probability of partner cheating: 4% Probability of underwear appearing given infidelity: 50% Probability of underwear just appearing: 5% 0.04 ∗ 0.5 = 40% 0.05 27 / 33
- 28. #4: Rationality in action 28 / 33
- 29. The set-up A given individual faces a finite number of choices Each choice has associated utility for that person People prefer choices with higher utility to choices with lower utility. People can be indifferent between choices with equal utility. People have complete and transitive preference orderings across choices If choice a delivers greater utility than b, but a person still chooses b, that person has acted irrationally 29 / 33
- 30. Concrete example Joe derives utility from consuming vodka, equivalent to £20. This utility is the same across all brands. He incurs disutility from spending money. 30 / 33
- 31. Concrete example Joe derives utility from consuming vodka, equivalent to £20. This utility is the same across all brands. He incurs disutility from spending money. £12 £18 £40 31 / 33
- 32. Concrete example Joe derives utility from consuming vodka, equivalent to £20. This utility is the same across all brands. He incurs disutility from spending money. £12 £18 £40 Given what we have said about Joe and his preferences/utility, it would be irrational for him to buy Absolut (or Grey Goose). 32 / 33
- 33. Slightly more interesting example Take spending on lotteries Choose is between keeping your pound or buying a ticket Utility of keeping your pound = £1 Utility of winning the lottery = £8 million, say Probability of winning = 1 in 14 million, say Expected utility of ticket = utility of winning × probability of winning 33 / 33
- 34. Slightly more interesting example Take spending on lotteries Choose is between keeping your pound or buying a ticket Utility of keeping your pound = £1 Utility of winning the lottery = £8 million, say Probability of winning = 1 in 14 million, say Expected utility of ticket = 8 × 1 14 34 / 33
- 35. Slightly more interesting example Take spending on lotteries Choose is between keeping your pound or buying a ticket Utility of keeping your pound = £1 Utility of winning the lottery = £8 million, say Probability of winning = 1 in 14 million, say Expected utility of ticket = 54p 35 / 33
- 36. Escape routes Individuals don't have perfect information (But then why do individuals persist with imperfect info?) Ideas of rational ignorance Hiring at Goldman Sachs Switching electricity providers People buy lottery tickets for the thrill . . . or newspapers for the influence . . . or footballs for the passion 36 / 33
- 37. Summary Powerful, simple statement of the view that people do what is in their rational self-interest Requires us to characterise the utility function of the choosers We're sometimes wrong about that Sometimes rational choice theorists shift the goalposts 37 / 33
- 38. #5: Rationality in games 38 / 33
- 39. Game theory Rational choice theory as applied to interactions Two types of interactions 1. competitive (zero-sum) game theory 2. non-competitive (positive-sum) game theory Competitive game theory much larger 39 / 33
- 40. Prisoners' dilemma Most famous example of competitive game-theory Two prisoners arrested to a crime committed jointly Police cannot prove the greater crime unless one prisoner confesses Police can prove a lesser crime without confession 40 / 33
- 41. What the police say to the prisoners We know you committed tax fraud, and we can send you to prison for one month, just for that alone. But we are prepared to offer you a deal. If you confess to us that you and your partner were involved in the bank robbery, then we will let you go free. Your accomplice will go to prison for six months. 41 / 33
- 42. What the police say to the prisoners (2) #2 Cooperate Silent Cooperate -3,-3 0,-6 #1 Silent -6,0 -1,-1 42 / 33
- 43. Why is this a dilemma? Because both players could secure an objectively better outcome, but don't Assumed to apply to lots of real-world scenarios Best known application: nuclear proliferation 43 / 33
- 44. #6: Failures of rationality 44 / 33
- 45. Lots of failures of rationality Nobel prize winners: Kahneman and Tversky Incomplete list of rationality failures: anchoring, conjunction fallacy, base-rate neglect, over-confidence 45 / 33