Herewith are further (partial, impressionistic) notes from the second day of the two-day workshop (programme) on Rationality and Emotions organized by Miriam Teschl at Robinson College here in Cambridge.
S-Shaped Probability Weighting and Hyperbolic Preference Reversal - An Intimate Relationship by Herbert Walther
Walther has published these results as a 2003 paper in Journal of Economic Behaviour and Organization.
http://www.robinson.cam.ac.uk/academic/robinson_rationality_walther.pdf
Overview
- Empirical regularities:
- hyperbolic discounting
- sign effect: loss discounted less than gains
- preference reversal:
- magnitude effect: preference for losses before gains
- s-shaped prob weighting (Gonzales and Wu 1999, Fehr-Duda, 2006 et al.)
- prob weighting can explain Allais paradox
- How to resolve?
- Ans: EU maximizer considers anticipated emotions reactions to resoluton of uncertainty
- prob weight derived via intertemporal state dependent EU max
- using this can explain most empirical effects
Model and Results
Part 1: Generating the S-shape prob distbn
- EU of some binary prospect L(p, w1, w2), w1<w2 is additively separable into:
- EU of wealth
- EU of elation (if you win)
- EU of disappointment (if you lose)
- last two both fade away over time
- Implied prob q(p) is as follows:
- q(p)=p1+(1−p)μ1+(1−p)p(γ+μ) where
- γ=δαδ+θ where δ is discount rate, α is weighting of elation and θ is the exponential rate of elation decay
- μ=δ+βδ+ρ where β is weighting of disappointment and ρ is exponential rate of disappointment decay.
- Really recommend looking at Walther’s paper (fig 1) which is on Robinson website
- Generates the S-shaped effect
- furthermore have testable empirical predictions: higher time preference (i.e. more impatient) should be associated with more pronounced S-shape (i.e. more risk-loving). So e.g. people who are gamblers should be saving less.
Part 2: Empirical regularities
Having generated the S-shaped result Walther goes on to show how this can generate most of the empirical regularities we are interested in.
- Look at some payment/contract whose probability of payment fulfilment is falling over time (this way we get probability in which we need)
- Now have some S-shaped setup and probability that goes into this S-shape is dropping over time (contract is less likely to be fulfilled).
- Hyperbolic discounting: can also now generate hyperbolic discounting within this same framework (other explanations e.g. Souzou 1998, Dasgupta and Maskin (2005) only do it on its own).
- Logic underlying hyperbolicity: at start contract is very likely to be fulfilled so if it does not lots of disappointment – so (exp) discount rate is very high. Over time prob falls and S-shape prob distbn kicks in (so elation outweighing disappointment) and discount rate falls.
- prediction: poor will show more hyperbolicity than rich
- The sign effect: gains discounted more than losses
- Logic: again simple. If loss is very likely little disappointement but a very certain gain has lots of potential for disappointment.
- prediction: again the sign effect is more pronounced for poor than the rich.
- magnitude effect for losses: higher losses have higher impact that lower losses (because straightforward wealth utility becomes more important than disappointment/elation effect).
- preference reversal
- poor will prefer losses before rich subject but gains after rich subject
- preferences are same but marginal utility of wealth is different
Summary
- Simple model that is a small extension of basic EU maximization most of the empirical regularities.
- If diminishing marginal utility of wealth poor people will behave ‘less rationally’ than rich people despite having same preferences
- For the future: Why is prob weighting evolutionary sustainable?
- potential answer: in hunter gather society there are externalities in that (large) gains and losses are shared (this would => S-shaped prob distbn).
“It’s a boy! Behavioural and Neural Evidence on Self Delusion” by Danica Mijovic-Prelec
- Deficits (due to lesion) on right side of brain lead to deficits in left hemisphere
- Furthermore these patients are not aware of the deficit and deny its existence (to the extent of confabulating experiences)
- Sackheim-Gur 1979: self-deception in social psychology
- played people mixture of their own phone and others
- averse to your own voice
- people would not hear their own voice and furthermore physiological measure of stress indicated it went up when ‘not hearing their voice (when it was there) – i.e. when people were self-deceiving
- Sackheim-Gur criteria:
- individual holds 2 contradictory beliefs
- beliefs held simultaneously
- individual is not aware of of holding one of the two beliefs
- nonawareness of this belief is motivated
Experiment
- shown korean figures and asked to classify as male/female
- first stage: get figures and must classify (5c for each correct prediction – correct measured against classification by some control group)
- second stage: must also predict gender of next figure (and then classify)
- paid like before for classification but bonus for being in top x% of predictors
Results
- Focus on items that were ‘well-classified’ by control
- First classification: 65% accurate
- Anticipation: 50% accurate (as expected since randomized)
- Second classification: <65%
- anticipation effects classification
- stronger for males: anticipated as male results in classification as male 72% (for females like first time round)
- calculate self-delusion index for each subject
- four options for response pattern (starting with female) of form 1st classif, anticipation, 2nd classif:
- FMF: honest
- FMM: self-deluding
- FFM: inconsistent
- FFF: consistent
- need to subtract inconsistency from self-delusion percentage to get ‘true’ self-delusion
- index = % self-delusion / % inconsistency (could use difference)
- four options for response pattern (starting with female) of form 1st classif, anticipation, 2nd classif:
- fMRI
- expect that self-deluding subjects behave differently from inconsistent (and honest and consistent)
- notably don’t show this activation on consistent trial (when they also confirm their prediction)
- this is what they find (v. significantly)
- in attentional and cog. control regions
- self-deluding and inconsistent is similar
- however big difference in parahippocampal gyrus (associated with memory)
- expect that self-deluding subjects behave differently from inconsistent (and honest and consistent)
- [rp] question: could some of this come from a priming effect combined with better recall. I anticipate X, which primes me. Then suppose I see the figure and have a vague recall from before. Suppose that people experience different priming effects – then those with a strong priming effect feel conflicted and have more stress (i remember Y sort of but do I really or I just doubtful because of having seen X) which means more fMRI anomalies and and means they are more likely to ‘self-delude’ while those with weak priming simply aren’t sure what they think (not really excited/conflicted) and just go randomly with M/F (so ‘self-delusion’ or ‘inconsistency’ are equally likely).
Herding and Social Influence in Economic Decision Making by Michelle Baddeley
- Solomon Asch
- Length of line experiments (everyone says line is B when actually A)
- Task design: stock-picking
- two charts for past prices of a stock
- shown faces along with their associated choice (controlled by experimenter)
- Results:
- strong effect of other decisions on own decision (on average 72% vs. 50% choose the one chosen by herd)
- perhaps not very surprising here given the lack of info about stocks (and their underlying equivalence) – a small piece of information should have a dramatic effect