Lecture 4 - Risky choice & EUT

What is risk in action?

Decision maker knows the possible outcomes of a choice (action) and their probabilities but does not know which would happen

• unless probability = 1

What is ambiguity in action?

Settings where some possible outcomes or some probabilities are not known

Risk vs ambiguity in the lab

Risk is more manageable to model than ambiguity

Lab is well suited to testing theories on risk

Expected value (EV) of a lottery

the probability weighted sum of all the possible outcomes of a lottery

What is: {EV(L) , 1}

The lottery comprising getting EV(L) for sure

L vs {EV(L) , 1} - risk preferences

Expected utility (EU) and how does it compare to EV

probability weighted sum of utilities of consequences

EU =/ EV

• if decision maker satisfies classic EUT then max EU may not = max EV

EUT and risk attitudes

EUT represents different attitudes to risk by different shapes of utility function

• e.g. risk averse - concave u(.)

To compare risk preferences, we need to compare u(EV(L)) to EU(L)

EUT vs EV graphically

We compare u(EV(L)) to EU(L)

EU being linear in probabilities

EUT only models utility function (no effects of probabilities)

• impact of a given change in prob does not vary with level of prob

• Relative weight of 2 utilities in EU(L) is ratio of probabilities of corresponding outcomes

Common consequence effect (CCE)

where people change their preferences between two risky options when a shared (common) outcome is added to or removed from both options

• Tendency to choose the safer option when CC > 0

• Reducing CC pushes more people towards riskier option

CCE example - Kahneman & Tversky (1979) RESULTS

CCE & EUT (K&T 1979 example)

EUT says that CC should have no effect on comparison between options - preferences unaltered under EUT by CC

CCE suggests impact of extra chance of ‘winning’ > 0 (depending on level of that chance)

How is CCE observed in different subject design

Within subject:

• Each subject faces the choices in a random order and incentivised by 1 round payout

• Individuals displayed CCE pattern of A & D choices

Between subject:

• Each subject assigned to a group that faces either choice 1 or 2 (and incentivised by chosen option being paid out)

• Different proportions of subjects chose A or C - so not consistent in choices even when not same person making choices (unexplainable by EUT)

Common ratio effect (CRE)

When people switch from risk-averse to risk-seeking choices when the probabilities of outcomes in a gamble are scaled down by a common ratio

• Switch from safer to riskier option as chance of winning (>0) is scaled down by a common ratio

• effect violates the EUT's independence axiom, which posits that scaling probabilities should not change preference order.

CRE & EUT

Under EUT, if L1 > L2  THEN  L4 > L3

No utility function explains preferences differing between choices

CCE & CRE caveats

Many experiments found effects when replicated BUT not all did

• CRE more robust

Not all subjects display effects in same experiment

Strength of effect varies with incentives + parameters

CRE & CCE show modelling EU as linear in probabilities not always best option