Week 3: Rational Choice

Rational ChoiceChris Hanretty

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Rationality in argument

Rationality in ultimate ends

Rationality in beliefs

Rationality in action

Rationality in games

Failures of rationality

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Warnings

1. Little of this lecture covered by thereadingsThis lecture prepares you for thereadings

2. We have to start with rationality beforediscussing rational choiceA lot of this stuff seems basic.

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#1:

Rationality inargument

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Long history of prizingrationality

Aristotle, Metaphysics: ``man is arational animal''Rationality bound up with philosophy,philosophical argumentIn particular, basic moves in logic

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Basic moves in logic1. Law of Contradiction: for any

proposition p, it is not the case thatboth p and not-p.

2. Law of the excluded middle: for anyproposition p, it is either the case thatp or not-p.

3. Modus ponens (if/then): if p, and if (ifp then q), then q

4. Modus tollens (more if/then): if (if pthen q), and if not-q, then not-p 6 / 33

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 thatp or not-p.


4. Modus tollens (more if/then): if (if pthen q), and if not-q, then not-p

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1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: for any

proposition p, it is either the case thatp or not-p.



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1. 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 q


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1. 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 q


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1. Law of Contradiction: ¬(p ∧ ¬p)2. Law of the excluded middle: p ∨ ¬p3. Modus ponens (if/then): p; p → q; ∴ q


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4. Modus tollens (more if/then): ¬q;p → q; ∴ ¬p

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Concrete example of modusponens

1. The lecturer is talking2. If the lecturer is talking, the lecture has

started3. ∴ the lecture has started

If you accept the premises, you must(rationally) accept the conclusion.

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Rationality

To be rational just is to argue in thisfashion, using only legitimate moves inyour argumentation and acceptingthem when others use them againstyou

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On the internet, no-oneknows you're irrational

The internet is (famously) home to much irrationalargument

And many people arguing that their opponents areirrational

Environmental politics example (à la Monbiot preFukushima)

1. if something is a low-carbon means of generatingelectricity, it is good

2. nuclear power is a low-carbon means ofgenerating electricity

3. ∴ nuclear power is good16 / 33

#2:

Rationality inultimate ends

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Spock, JohnRedwoodThe popular viewof beings drivenby rationalityIdea: certainactions arecompelled byrationality

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The Kantian view

The categorical imperative (inone of its formulations)

``act only in accordance withthat maxim through whichyou can at the same time willthat it become a universallaw''

Immoral acts are ultimatelyself-contradictory (p ∨ ¬p)Kant not much use in thesocial sciences

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The Humean view

Hume's Treatise on HumanNature

``Reason is, and ought onlyto be the slave of thepassions, and can neverpretend to any other officethan to serve and obeythem''

Preferences or passions ordesires or inclinations notsubject to rationality

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Social science

Rationally-given ends big stuff inmoral philosophyLess relevant in social sciencesConsider aesthetic or political choicesRationality alone cannot explainchoicesWe know to know what people wereaiming at

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#3:

Rationality inbeliefs

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Extraordinary claims requireextraordinary evidence -- CarlSagan

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Bayes' principle

We update our beliefs in the light ofnew evidenceBut we also have prior beliefsProbability of something being truegiven new evidence equal to

I baseline probability of that thing beingtrue,

I times probability you'd get that evidenceif the thing was true,

I divided by the probability of the evidence

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Bayes: example

Suppose 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

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What do you need to know?

Baseline probability of partnercheating: 4%Probability of underwear appearinggiven infidelity: 50%Probability of underwear justappearing: 5%

0.04 ∗ 0.50.05

= 40%

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What do you need to know?

Baseline probability of partnercheating: 4%Probability of underwear appearinggiven infidelity: 50%Probability of underwear justappearing: 5%

0.04 ∗ 0.50.05

= 40%

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#4:

Rationality inaction

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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 lowerutility.

People can be indifferent between choices with equal utility.

People have complete and transitive preference orderings acrosschoices

If choice a delivers greater utility than b, but a person still choosesb, that person has acted irrationally

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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

Given what we have said about Joe and his

preferences/utility, it would be irrational for him to buy

Absolut (or Grey Goose).

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£12 £18 £40



Absolut (or Grey Goose).

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£12 £18 £40



Absolut (or Grey Goose). 32 / 33

Slightly more interestingexample

Take spending on lotteries

Choose is between keeping your pound orbuying 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

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Expected utility of ticket = 8× 114

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Expected utility of ticket = 54p

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Escape routesIndividuals don't have perfectinformation(But then why do individuals persistwith imperfect info?)Ideas of rational ignorance

I Hiring at Goldman SachsI Switching electricity providers

People buy lottery tickets for the thrill. . . or newspapers for the influence. . . or footballs for the passion

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Summary

Powerful, simple statement of theview that people do what is in theirrational self-interestRequires us to characterise the utilityfunction of the choosersWe're sometimes wrong about thatSometimes rational choice theoristsshift the goalposts

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#5:

Rationality ingames

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Game theory

Rational choice theory as applied tointeractionsTwo types of interactions1. competitive (zero-sum) game theory2. non-competitive (positive-sum) game

theory

Competitive game theory much larger

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Prisoners' dilemma

Most 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

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What the police say to theprisoners

We know you committed tax fraud, andwe can send you to prison for onemonth, just for that alone. But we areprepared to offer you a deal. If youconfess to us that you and your partnerwere involved in the bank robbery, thenwe will let you go free. Your accomplicewill go to prison for six months.

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What the police say to theprisoners (2)

#2Cooperate Silent

#1Cooperate -3,-3 0,-6

Silent -6,0 -1,-1

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Why is this a dilemma?

Because both players could secure anobjectively better outcome, but don'tAssumed to apply to lots of real-worldscenariosBest known application: nuclearproliferation

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#6:

Failures ofrationality

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Lots of failures of rationality

Nobel prize winners: Kahneman andTverskyIncomplete list of rationality failures:

I anchoring,I conjunction fallacy,I base-rate neglect,I over-confidence

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Week 3: Rational Choice

Education

Transcript of Week 3: Rational Choice