Rational Choice Theory Flashcards
Irrational Thinking
Impulsive
Emotional
No control over themselves
Basic Principles
All behaviour- apart from reflexes/ involuntary physio responses- all interesting actions- based on decisons
Rationality (Decision Theorists)
means: making a choice that is best for decision maker given circumstances/ preferences
if thirsty, buy £1.50 drink etc
making choice that aligns with yourself
choosing right option to achieve preferred result
Decisions
Deliberate Actions
Choosing between atleast two alternatives
If only one decision, doing nothing- alternative
Normative Theory
Descriptions of how someone SHOULD behave or choose if rational
Positive/Descriptive Theory
How people ACTUALLY choose in practice
Risk/ Uncertainty
Decision making under risk- knowing possible outcomes- some ability to estimate probabilities
Under uncertainty- lack of information- cannot assign probability to outcome. Decision process - more complex/ less predictable
History
Early thinking- Jeremy Bentham 1738- 1832
Utilitarianism- later, John Stuart Mill
Theory of development- economists
Expected utility theory- Neumann and Morgenstern 1947
Psychological theory
Decision Scientists
Maths- Probability of Conjunction
Probablity- ranges 0 (nothing) to 1 (certain)
Making a decision, the probability of all outcomes must = 1 (add up to)
Probab. of Conjunction- prob of two independent events- if one happens wont effect likelihood of the other = pq (p x q)
- e.g head coin toss, p= 0.5. to get a six = 1/6= q = 0.167.
- Conjunction of getting both heads and a three- pq= 0.5 x 0.167= 0.083
MULTIPLY
INDEPENDENT EVENTS
Maths- Probability of Disjunction
Prob. of two mutually exclusive events happening
- one or the other. cant happen at the same time
ADD probabilities up
p + q or p + q + r so on
for event of either 5 or 6 on the dice, p = 0.167 + 0.167= 0.333
Expected Value Theory
Gamble- draw a named card from deck- get 120£ if correct- e.g pick 4 of spades
Theory- what is expected value with mutually exclusive outcomes
Expected- means AVERAGE if we play over and over, whats expected value likely to be
Must include calculating all possibilities
Two outcomes- get gamble or not
EV (G amble) = prob of getting 4spades (1/52 x £120) + (51/52 x £0) = £2.31
expected value of playing that gamble- expected payoff- what you would earn on average if played multiple times over/over
Rational People/ EV
Rational people gamble and buy insurance
- altho they shld know- EV of buying must be less than cost
-if it wasn’t- companies wldnt make profit - they’re gambling on you buying and not needing
EV- shld be negative- yet we still buy it- reduce uncertainty
St Petersburg Paradox
Daniel Bernoulli 1738- exploded idea- not always rational to maximise EV
Coin toss- if win, get £1- game over
If lose, get another toss- payoff doubles- if win, take increased double- keep getting tails- keep double
Payoff doubles, each toss- if House has unlim £ - what is ev of game?
EV= 1/2 + 1/2 + 1/2 … = £INFINITY - if house has unlimited funds
To maximise EV- you should always play game- no matter the entry cost- because infinity always higher than entry cost
most ppl put £10 to play game- 50% chance u lose it all for £1 on first toss- heads
Balanced by small prob of winning fortune if theres. long string of tails
-irrational- led to development of expected utility theory
Expected Utility Maximisation
Bernoulli- not always maximising value- but maximising,
Utility- value to us of things as well as literal value- money
presents idea: Utility function— graph- as monetary value goes up, the utility of it goes up- but not at same rate- at a decreasing rate
£10 might give u ten in Utility but £20 wont give you twenty in utility- not doubled- slow decreasing slope- MARGINAL UTILITY
We dont try to maximise value- maximise utility to ourselves- not always the same thing
Subjective Expected Utility Theory
Von Neuman & Morgenstern
realised, formalised as mathematical approach
subjective means we calculate the likelihoods and possiblilites
dont know them but we have a way of gauging them
EU theory says we maximise
formalisation of what utility is- interval scale- have nothing- arbitary nature- more is more than less
maximise utility over value
EU = p1u1 + p2u2+ …
must include all possibilites that something can happen
Applications of Subjective to decisions
How to apply subjective expected utility to everyday decisions
Leonard Jimmy Savage 1954/72
-provides examples of how we do that on everyday decisions using subjective prob. from formalised theory
Imagine fav jumper worth 30£- if rained on- ruined- cant ever wear- value a lot
Decision- to take umbrella around- cost of -5 UTILITY SCALE
but comes with disutility cost- reduces utility- pain in the ass- lost a lot on trains
-protects jumper but cost
plug in subjective prob- imagine .2 prob of rain
We know prob- so make decision using payoff matrix
Payoff Matrix
2x2 payoff matrix:
Decision. | Rain Fine. Utility all cases- negative- expect no rain
Carry. | -5 -5. If carry inconvenience is same in both scenarios
Don’t Carry | -30 0 If you dont carry you lose 30 utility- rain
Prob. Rain. Fine
.20 .80
(SEU)- sub expected util- Carry= (.2 x -5) + (.8 x -5) = —1 + —4 =. —5
(SEU)- Don’t Carry=. (.2. x. -30) +. (.80. x 0 ) = -6 = 0 = —6
-Most rational decision- according to decision theory- you should choose TO carry the umbrella
-rational according to subjective utility theory
Expected Utility Theory- Problems
- Allais Paradox
- Newcomb’s Problem
- Intertemporal Choice
- Monty Hall Problem
Allais Paradox
Maurice Allais- nobel prize
Gamble
A- wld u prefer £1m flat , or
B- .89 prob of £1m
.10 prob of £5m
.01 prob of £0
C- .11 prob of £1m
.89 prob of £0
D- .10 prob of 5m
.90 prob of 0£
Most ppl prefer A to B - bc of certainty effect- no risk
but most ppl D to C - chances r very similar but the prize is larger in D
A and B - are identical
Independence Assumption
Irrelevant alternatives shouldnt affect decision making
bc irrelevnt
Allais paradox challenges that bc it shows when certainty is played into this it does affect peoples choices
- ppl really robust- cant ignore irrelevant informatio
- utility cant explain reversal of preferences
Transitivity Assumption
If somebody prefers one thing to another
Chocolate over vanilla, vanilla to strawberry
Should prefer chocolate over strawberry too
Preferences should always be complete- shld know what they prefer even if they cant express preference
Newcomb’s Problem (a)
Philosophical problem- Robert Nozick
2 boxes on table
one you can see- has a Grand in
One you cant see inside
Can choose to either take both boxes- or just box u cant see inside
AI system- good at predicting behaviour- already predicted what u will take
If predicted that u only choose opaque box- will put 1mil in
If predict u choose both- puts nothing in it
Wld u take both or only opaque box?
Newcomb’s Problem (b)
Why does this matter?
two solutions both rational
ExpecValueTheory- says to take opaque box- predictor 95% correct
EV (A- BOTH) = .95 X £1000 + .05 X £1,001,000 = £51,000
1HR 6 MIN
