2. Rationality in argument
Rationality in ultimate ends
Rationality in beliefs
Rationality in action
Rationality in games
Failures of rationality
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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18. Spock, John
Redwood
The popular view
of beings driven
by rationality
Idea: certain
actions are
compelled by
rationality
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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
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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
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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
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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
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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
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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%
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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.
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42. What the police say to the
prisoners (2)
#2
Cooperate Silent
Cooperate -3,-3 0,-6
#1
Silent -6,0 -1,-1
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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
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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
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