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# Week 3: Rational Choice

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### Week 3: Rational Choice

1. 1. Rational Choice Chris Hanretty 1 / 33
2. 2. Rationality in argumentRationality in ultimate endsRationality in beliefsRationality in actionRationality in gamesFailures of rationality 2 / 33
3. 3. Warnings1. Little of this lecture covered by the readings This lecture prepares you for the readings2. We have to start with rationality before discussing rational choice A lot of this stuﬀ seems basic. 3 / 33
4. 4. #1:Rationality inargument 4 / 33
5. 5. Long history of prizing rationalityAristotle, Metaphysics: ``man is arational animalRationality bound up with philosophy,philosophical argumentIn particular, basic moves in logic 5 / 33
6. 6. Basic moves in logic1. 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 q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 6 / 33
7. 7. Basic moves in logic1. 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 q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 7 / 33
8. 8. Basic moves in logic1. 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 q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 8 / 33
9. 9. Basic moves in logic1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): if p, and if (if p then q), then q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 9 / 33
10. 10. Basic moves in logic1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): if p, and if (if p then q), then q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 10 / 33
11. 11. Basic moves in logic1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): p; p → q; ∴ q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 11 / 33
12. 12. Basic moves in logic1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): p; p → q; ∴ q4. Modus tollens (more if/then): if (if p then q), and if not-q, then not-p 12 / 33
13. 13. Basic moves in logic1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): p; p → q; ∴ q4. Modus tollens (more if/then): ¬q; p → q; ∴ ¬p 13 / 33
14. 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 startedIf you accept the premises, you must(rationally) accept the conclusion. 14 / 33
15. 15. RationalityTo be rational just is to argue in thisfashion, using only legitimate moves inyour argumentation and acceptingthem when others use them againstyou 15 / 33
16. 16. On the internet, no-oneknows youre irrationalThe internet is (famously) home to much irrationalargumentAnd many people arguing that their opponents areirrationalEnvironmental politics example (à la Monbiot preFukushima) 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. 17. #2:Rationality inultimate ends 17 / 33
18. 18. Spock, JohnRedwoodThe popular viewof beings drivenby rationalityIdea: certainactions arecompelled byrationality 18 / 33
19. 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. 20. The Humean viewHumes Treatise on HumanNature``Reason is, and ought onlyto be the slave of thepassions, and can neverpretend to any other oﬃcethan to serve and obeythemPreferences or passions ordesires or inclinations notsubject to rationality 20 / 33
21. 21. Social scienceRationally-given ends big stuﬀ inmoral philosophyLess relevant in social sciencesConsider aesthetic or political choicesRationality alone cannot explainchoicesWe know to know what people wereaiming at 21 / 33
22. 22. #3:Rationality inbeliefs 22 / 33
23. 23. Extraordinary claims requireextraordinary evidence -- CarlSagan 23 / 33
24. 24. Bayes principleWe update our beliefs in the light ofnew evidenceBut we also have prior beliefsProbability of something being truegiven new evidence equal to baseline probability of that thing being true, times probability youd get that evidence if the thing was true, divided by the probability of the evidence 24 / 33
25. 25. Bayes: exampleSuppose you are living with apartner and come home from abusiness trip to discover a strangepair of underwear in your dresserdrawer. You will probably askyourself: what is the probabilitythat your partner is cheating onyou? The Signal and the Noise 25 / 33
26. 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. 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. 28. #4:Rationality inaction 28 / 33
29. 29. The set-upA given individual faces a ﬁnite number of choicesEach choice has associated utility for that personPeople prefer choices with higher utility to choices with lowerutility.People can be indiﬀerent between choices with equal utility.People have complete and transitive preference orderings acrosschoicesIf choice a delivers greater utility than b, but a person still choosesb, that person has acted irrationally 29 / 33
30. 30. Concrete exampleJoe 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. 31. Concrete exampleJoe 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. 32. Concrete exampleJoe derives utility from consuming vodka, equivalent to £20.This utility is the same across all brands.He incurs disutility from spending money.£12 £18 £40Given what we have said about Joe and hispreferences/utility, it would be irrational for him to buyAbsolut (or Grey Goose). 32 / 33
33. 33. Slightly more interesting exampleTake spending on lotteriesChoose is between keeping your pound orbuying a ticketUtility of keeping your pound = £1Utility of winning the lottery = £8 million, sayProbability of winning = 1 in 14 million, sayExpected utility of ticket = utility of winning ×probability of winning 33 / 33
34. 34. Slightly more interesting exampleTake spending on lotteriesChoose is between keeping your pound orbuying a ticketUtility of keeping your pound = £1Utility of winning the lottery = £8 million, sayProbability of winning = 1 in 14 million, sayExpected utility of ticket = 8 × 1 14 34 / 33
35. 35. Slightly more interesting exampleTake spending on lotteriesChoose is between keeping your pound orbuying a ticketUtility of keeping your pound = £1Utility of winning the lottery = £8 million, sayProbability of winning = 1 in 14 million, sayExpected utility of ticket = 54p 35 / 33
36. 36. Escape routesIndividuals dont have perfectinformation(But then why do individuals persistwith imperfect info?)Ideas of rational ignorance Hiring at Goldman Sachs Switching electricity providersPeople buy lottery tickets for the thrill. . . or newspapers for the inﬂuence. . . or footballs for the passion 36 / 33
37. 37. SummaryPowerful, simple statement of theview that people do what is in theirrational self-interestRequires us to characterise the utilityfunction of the choosersWere sometimes wrong about thatSometimes rational choice theoristsshift the goalposts 37 / 33
38. 38. #5:Rationality ingames 38 / 33
39. 39. Game theoryRational choice theory as applied tointeractionsTwo types of interactions 1. competitive (zero-sum) game theory 2. non-competitive (positive-sum) game theoryCompetitive game theory much larger 39 / 33
40. 40. Prisoners dilemmaMost famous example of competitivegame-theoryTwo prisoners arrested to a crimecommitted jointlyPolice cannot prove the greater crimeunless one prisoner confessesPolice can prove a lesser crimewithout confession 40 / 33
41. 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. 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. 43. Why is this a dilemma?Because both players could secure anobjectively better outcome, but dontAssumed to apply to lots of real-worldscenariosBest known application: nuclearproliferation 43 / 33
44. 44. #6:Failures ofrationality 44 / 33
45. 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