Bounded rationality - Thinking 3+4

Question 1

What are descriptive model?

Answer 1

Models of how decision processes operate, irrespective of whether the outcome of the decision is good or bad.

Question 2

What are normative models?

Answer 2

Normative models evaluate a decision in terms of the goals of the decision maker. Here, decisions can be good or bad and a decision is good if it reaches these goals.

Question 3

What type of thinking is rational?

Answer 3

normative

Question 4

What is a good descision?

Answer 4

A decision is good to the extent that it enables the decision maker to reach their goals.

Question 5

What are the features of a good descision?

Answer 5

Assumes the agent has full access to all alternatives

Knows the probability of their outcomes

Knows the value of their outcomes

Can integrate all this information and chooses the option with highest utility

Question 6

What are the key assumptions of rational choice theory?

Answer 6

Assumes the agent has full access to all alternatives

Knows the probability of their outcomes

Knows the value of their outcomes

Can integrate all this information and chooses the option / behaviour with highest utility

Question 7

What are the key assumptions of bounded rationality?

Answer 7

Limited cognitive capacity, limited information on outcomes

Human behaviour can be impulsive
habitual / conditioned
imitating others
random

Question 8

What do we do if the rational choice or outcomes are uncertain?

Answer 8

If the outcomes are uncertain we multiply the utility by the probability of receiving that outcome to give the expected value EV.

EV = p(outcome) * value

Question 9

What are some examples of EV = p(outcome) * value

Answer 9

I)

Option A – £100 with 50% probability, EV = £50

Option B – £1000 with 2% probability, EV = £20

II)
Option A - £1000,000 with 1% probability, EV = £10,000

Option B - £10,000 with 99% probability, EV = £9,900

Question 10

With these two outcomes ,

Option A - £1000,000 with 1% probability, EV = £10,000
Option B - £10,000 with 99% probability, EV = £9,900

which would a classical economist/rational choice theory choose?

Answer 10

in both cases: I and II, option A is always better….

but is this really rational?

Question 11

What is the St Petersburg Paradox?

Answer 11

Peter tosses a coin and continues to do so until it should land “heads” when it comes to the ground. He agrees to give Paul one ducat if he gets heads on the very first throw, two ducats if he gets it on the second, four if on the third , eight if on the fourth, and so on, so that with each additional throw the number of ducats he must pay is doubled.

(Bernoulli, 1738)

Question 12

What is the expected value of the St Petersberg paradox?

Answer 12

infinite, EV= ½ x 1 + ¼ x 2 + 1/8 x 4 … = ∞

		       ½          ½           ½

Question 13

What is the St Petersberg paradox?

Answer 13

Hence RCT would suggest that a player should be willing to pay virtually any sum of money, since EV is infinite

However, although the expected value of the gamble is infinite, the subjective utility is low, since the chance to win a high value is quite low
This became known as the St. Petersburg Paradox.

 It is a case where Rational choice theory fails to make sensible predictions about “rational choice”

Question 14

How did Bernouli explain the marginal declining utility?

Answer 14

To explain this, Bernoulli suggested that EV ≠ EU, instead the utility of wealth is proportional to its logarithm.

Question 15

What is the consequence of the marginal declining utility?

Answer 15

The consequence of this is that each additional unit of wealth is worth less than the previous one.

So the utility of additional currency units decreases as the number of currency units increase.

Question 16

What is an example of marginal declining utility?

Answer 16

If I have £1000,000 I care less about an additional £500, than if I only have £1000.

The extra utility of the high winnings in the St. Petersburg Paradox is no longer high enough to compensate for the very low probabilities.

Question 17

How does the St Petersburg Paradoxon show an inherent limitation of expected value?

Answer 17

Despite its seemingly plausible or trivial nature, it is not general enough for many situations – even under the assumption that the decision maker behaved entirely rational (in terms of maximising their gains)

Question 18

What type of theory is the expected utility theory?

Answer 18

normative, it clearly defines what rational choices are

Question 19

What is expected utility theory?

Answer 19

Expected utility may, however, deviate from expected value in that

it allows the expected utility of a particular choice outcome to be situationally dependent, e.g. dependent on the accumulated wealth

Question 20

What is weak ordering?

Answer 20

For any set of choices we must always be able to say we prefer one over the other or neither (i.e. x > y, x < Y, or x = y).

Question 21

what is transitivity?

Answer 21

choices must be transitive (i.e. x > y, y > z, therefore x > z).

Question 22

What is an example of the risk seeking vs risk adverse behaviour?

Answer 22

Would you prefer

An 80% chance of gaining £4000, otherwise nothing

A certain gain of £3000

Question 23

How can the normative theory be violated through risk seeking and risk adverse behaviour?

Answer 23

Most people prefer a sure gain of £3000 over 80% chance to gain £4000. Although the expected value of the risky option is higher (£3200).
Preferences are reversed when the outcomes are losses. Most people now prefer the risky option over the certain option.

Question 24

How was ppts behaviour different to rational choice theory according to the risk seeking vs risk adverse behaviour study?

Answer 24

Participants’ behaviour here reflects (fairly consistently) the exact opposite of what rational choice theory has predicted, in both cases

Moreover, and significantly, participants do not appear to generally favour the certain option – they only favour the certain option when it comes to making a gain!

Question 25

Summary

Answer 25

Rational choice theory has been a very influential and important model in economics and the field of (economic) decision making

It is relatively straightforward in that it assumes that people (at least statistically) choose the mathematically best option in terms of expected value

It is, however, very limited to the extent in how it can explain human behaviour! Given its numerous violations, other approaches are needed….

Question 26

What is prospect theory?

Answer 26

Kahneman and Tversky developed prospect theory as a descriptive model of decision making.

Intended to account for deviations from rational choice theory

Prospect theory has two main components: Utility and Probability.

Question 27

What is the value function?

Answer 27

Tversky & Kahneman (1981) proposed a new value function that differs for gains and losses.

Question 28

What does the X axis of the value function mean?

Answer 28

The x-axis reflects gains to the right and losses to the left instead of total wealth as Bernoulli described. The midpoint is a person’s current reference point.

Question 29

What is the y axis in the value function?

Answer 29

utility

Question 30

Why do we treat losses more seriously than gains?

Answer 30

Function for gains and losses are asymmetric. This explains why we treat losses as more serious than gains.

Question 31

What are utility functions?

Answer 31

Besides the different overall slope of the straight lines for gains and losses, however, the value – utility functions are nonlinear

Question 32

How do the x and y axis change?

Answer 32

For both, gains and losses, increments near small values lead to a considerably bigger increase in gains / losses, whereas for large values, the increase in utility is smaller

Question 33

What is the certainty effect?

Answer 33

for gains people prefer certainty

Question 34

What does prospect theory state?

Answer 34

According to prospect theory we do not treat probabilities as they are stated. For instance, in a lottery, the EV is very low: the probability of winning is negligible

Instead they are distorted by the pi function, thus an objective p becomes a subjective .

Probabilities near 0 are overweighted relative to objective probabilities, probabilities near to 1 (but not 1) are underweighted!

Question 35

What is a consequence of the Pi function?

Answer 35

One consequence of the pi function is that very low probabilities tend to be over-weighte, e.g. people believe that their chances of winning the lottery are larger than they really are.

Question 36

How are weighting functions different for losses and gains?

Answer 36

While for very large probabilities, tend to be underweighted, i.e. the risk (1-p) is exaggerated

These weighting functions are again different for losses vs gains, e.g. the subjective probability of a loss is deviating more from linearity than for a gain

Question 37

Prospect theory summary -

Answer 37

Prospect theory assumes differential sensitivity to gains and losses: explains loss aversion

Prospect theory assumes nonlinear functions of utility as a function of value

Prospect theory takes into account that subjective probabilities are not a linear function of probability, but sigmoid functions which leads to overestimation of small probabilities and underestimation of high probabilities

 Prospect theory is a descriptive model, established on the basis of empirical data (rather than on the basis of purely abstract assumptions like RCT) and takes the subjective factor, for both value and probability into account

Question 38

What is regret theory?

Answer 38

According to Regret theory we compare outcomes, particularly after the decision has been made.
The assumption is, we will regret a decision if an alternative outcome would have led to a higher payoff (even when the prospect was better).

…and we rejoice if our choice led to a better outcome than other alternatives.

Question 39

Why isnt prospect theory a complete theory?

Answer 39

Prospect theory is not a complete theory : although it describes some deviations from normative expectations by means of the pi function and the value function, it does not give any psychological reasons for the shape of these functions.

Question 40

What is intertemporal choice?

Answer 40

The choice is between a (notional) immediate investment and a long term reward, or an immediate gain (notional no spend) and no long term reward (and potential loss).

Would you prefer
£500 now or
£1000 in ten years?

Question 41

What is the outcome of a temporal choice question?

Answer 41

Most people prefer option a. Which has a lower value than b, but has a higher utility because the utility of b is discounted by its delay.

The normative assumption is that the discount function is an exponential constant rate.

Question 42

What are the letters in discounting?

Answer 42

v = subjective discounted value

k = the discount rate

d = the delay

Question 43

The exponential function has 3 properties that fit empirical behaviour -

Answer 43

1 If there is no delay there is no discounting

2 As delay increases the present value decreases

3 As delay approaches infinity the present value approaches zero

Question 44

What is hyperbolic discounting?

Answer 44

The hyperbolic function has the same 3 properties as the exponential function but does accommodate dynamic inconsistencies.

Question 45

Why do people (and other animals) discount the future?

Answer 45

interest rates and uncertainty and Emotion based theories

Question 46

Why do we discount the future due to interest rates?

Answer 46

If I take £500 now I could (take control and) invest it for a higher rate of return than the delayed alternative.

Question 47

Why do we discount the future due to uncertainty?

Answer 47

The future is uncertain. E.g. the bank holding your investment, and indeed the currency itself, might collapse.
In evolutionary terms, you might not survive several months to receive a large amount of food promised to you, you have to make sure that

Question 48

Why do we discount the future due to emotion?

Answer 48

Loewenstein (1996) suggests that the temporal and physical proximity of options that can reduce aversive states (e.g. hunger, withdrawal) leads to a disproportionate increase in the attractiveness of those options.

Question 49

What does lowenstein argue about people with low discount rates in emotion based theories?

Answer 49

Loewenstein argues that people with low discount rates, rather than exhibiting self-control, are in fact differing in the way they anticipate the emotional state of the outcome.

Question 50

How did Ziegler and Tunner test emotion based theories by Lowenstein?

Answer 50

Ziegler & Tunney (2012) tested this prediction by estimating the discount rates for decisions made when we are the recipient compared to when other people who differ in social distance to ourselves are the recipient.

Question 50

What do emotion based theories predict?

Answer 50

This model makes the prediction that discount rates should be different when we make decisions on behalf of other people, depending on how much empathy we have for them.

Question 51

What did Ziegler & Tunney (2012) find?

Answer 51

Found that discount rate varied as a function of the coefficient of relatedness (as a measure of social distance) with decisions made for ourselves being more impulsive than decisions made for other people.

Except for our close relatives and our best friends. Decisions made for strangers are the least impulsive (cold and impartial)?

Question 52

What did Stillwell and Tunney find about discounting as impulsivity?

Answer 52

Stillwell & Tunney 2011 Tested 9454 Facebook users across the world to determine the relationship between discounting and smoking

Question 53

What is the K parameter derived from in discounting as impulsivity?

Answer 53

The k parameter is derived from financial decisions and it appears to reflect a stable individual ‘trait’ in impulsivity.

Question 54

What do the results show from discounting as impulsivity?

Answer 54

The results clearly show that daily smokers discount future reward more than irregular smokers or none smokers.

Question 55

What is the ultimatum game?

Answer 55

Two players decide how to split a sum of money.

The proposer is endowed with £10 but has to share it with a responder.

The proposer suggests a sum to the responder who must either accept or reject the offer.

If the responder rejects the offer both players lose all.

No discussion is allowed and both players are anonymous.

What should each player do?

Question 56

What does ratioal choice theory sugest about the ultimatum games?

Answer 56

RCT suggests that the proposer should offer the minimum amount possible, and that the responder should always accept any offer no matter how small, because this maximizes expected utility for each player.

Question 57

What is found in the resutls of the ultimatum game?

Answer 57

However, empirically, it is found that the median offer tends to be between 40-50% of the endowment.

Offers below 20% are usually rejected.

So people in deciding to share people can be more altruistic than we might expect (but perhaps not much more) and vindictive.

Question 58

Why might it be “rational” to reject an offer below 20%, in the real world? Why might people do that?

Answer 58

Humans live (and have lived) in societies that are both supportive and competitive.
Giving the competitor a massive advantage (if given the choice to deny them this advantage) could very easily outweigh the benefit of receiving a small reward from the ultimatum game

Question 60

How can rationality be seen in an evolutionary context?

Answer 60

More recently, Gigerenzer & colleagues have considered the origin of heuristics and re-defined rationality.

They suggest that heuristics were evolved in the Environment of Evolutionary Ancestry aka the Pleistocene period.

Rationality of behaviour does depend to some extent on the context – e.g. factors like the stability of the environment