8.23 - Experience & choice under uncertainty

explanation of CRE simply & effect of experience

subjects don’t evaluate using real probabilities – use decision weights

Experience may reduce the distortion effect (away from true prob -> towards true prob)

Task experience

Experience gained from repeating a task

• provides familiarity with decision problem + allows for reflection

Task less new each time

Repeated choice task WILL involve task experience

Outcome experience

Experience gained from learning about results

• seeing how uncertainty resolved

• What outcome would have happened if chose the other option

Not necessarily gained in repeated choice

Van de Kuilen & Wakker (2006) - OV

Subjects repeatedly make 2 choices per round (15 rds total) between lotteries with Common Ration structure

• s - safe reward r - risky reward (scaled down with CRE) r > s > 0 AND 0.8r > s

  • Risk neutral would always pick risky

  • p of r = 0.8 p of s

2 feedback conditions

• No feedback - Outcome of lotteries not determined until end

  • TE gained but no OE

• Feedback - In each rd and for each task, uncertainty resolved as subject rolls die to determine outcome of chosen option and records it on decision-sheet, where unchosen option still visible

  • TE + OE (both result obtained and alternative if other choice chosen)

Task order randomised to avoid confounding experience with change in payoff parameters

Incentive - 1 lottery chosen and paid out at end of experiment (no wealth effect)

Van de Kuilen & Wakker (2006) - RESULTS

% of EUT violations (CRE or reverse) per round

With no feedback – the trend is mostly flat / slight up

• TE has almost no effect on reducing EUT violations

Feedback - violations trending downwards

• OE does reduce EUT violations and subjects behaves more like ST predicts

• Proportion of subjects choosing consistently with expected value maximisation (max EV) rises

  • Learn to EV maximise

  • selecting risky option in both problems

  • ~ 27% in R1 → ~ 58% in R15.

Matches field evidence - Starmer 2000

Van de Kuilen & Wakker (2006) - Why CRE falls

Experience through:

• Die rolling - see how high prob of 0.8 really is to 0.2

• Comparing outcome with alternative not picked

• Mix

  • In scaled UP with feedback, if subject selected safer - sees could’ve has r 80% of the time

  • Drives subjects to choose risky so risky chosen in both (consistent preferences)

Bone et al. (1999) - OV

Studies different forms of experience

• Task-repetition & Group discussion

3 stage experiment

1. 12 individual choices with Common Ratio triples (3 choice problems with 2 scaled down versions)

2. Same choices with doubled payoffs BUT now in pairs and must agree on joint choice and division of prize AFTER GROUP DISCUSSION

3. Same as stage 1

We compare S1 - S3 to see effects of discussion

Bone et al. (1999) - RESULT

TE + Discussion doesnt eliminate CRE

• CRE increases a bit

Description or experience

In almost all experiments on choice under risk we’ve covered, subjects see (for each option) a complete, verbal and/or numerical description of all possible outcomes and their probabilities

• Matches complete information assumption for choice under risk

In reality we often dont have complete information (true probabilities mainly)

Instead, we gradually learn from experience - learn true probabilities

Maybe results are artefacts of full description - Inverse S probability weighting function just seen in experiments

Example of non-fully descriptive experiment

Experience doesn’t reveal bad outcome but description does

Reasons why non-full descriptions change behaviour

Sampling bias - small samples may not match true probabilities

Different presentation of information - e.g. sequential release of sample

Ambiguity - When information is from a sample, subjects may realise that it might not match true probability

• plus people tend to be adverse to ambiguity

Cubitt et al. (2022) - OV

Studies if there is a Description-Experience (DE) gap

• Study probability weighting functions

80 choices per subject between 2 monetary outcomes with probability in 1/40 units

• Options resolved by drawing virtual cards with different colours

4 treatments

Cubitt et al. (2022) - treatments

Description - subjects sees probability of all colours

Experience-Unambiguous - Subjects see all 40 cards one at a time and are told it is the full deck

Experience-ambiguous - Same as EU but do not know if 40 seen are the whole deck

Experience restricted - Same as EA but sample is only 18 cards

• focus on cases where sample under-represents rare colour

• Sampling bias in play

Cubitt et al. (2022) - treatment rational

Description vs EU - identical information but manipulated fully-revealed vs sequential

EU vs EA - Manipulates if they know for sure all possibilities

• tests for lack of certainty about probability & experience

EA vs ER - Subjects dont know size of deck but manipulated sample size

• test for effect of small sample bias

Cubitt et al. (2022) - RESULTS: D vs all experience

Inverse-S curve seen for Description BUT not for aggregate of all experience treatments

smaller range of over-weighting than usual (inflection ~ 0.2)

Cubitt et al. (2022) - RESULTS: D vs EU

Almost no difference

Both Inverse S with low over-weighting

Cubitt et al. (2022) - RESULTS: EU vs EA

Knowing seen full deck has a small effect

• some evidence of ambiguity aversion

Almost no over-weighting

Cubitt et al. (2022) - RESULTS: EA vs ER

If ER sample underrepresents low-prob event, subjects under-weight it

Main driver of DE gap

• Low prob events overweighted under description + all other experience

Inverse-S not an artefact of description

Cubitt et al. (2022) - takeaways

Choices and probability-weights affected by whether uncertainty described to subjects or inferred from sampling experience

• especially if experienced sample under-represents a rare event.

Main driver of observed DE gap is sampling bias (from ER treatment)

Aggregate prob-weighting function is Inverse-S for both Description & experience (with controlled out sampling bias)

Implication - Inverse-S probability-weighting not artefact of Description

• BUT bias in small samples may counter overweighting of low-prob events by distorting information, when uncertainty leaned about from small samples

Caveat - Results only applicable where information about uncertainty is only available from limited experience