miscellaneous factZ – The online home of Rufus Pollock

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
• EU of wealth
• EU of elation (if you win)
• EU of disappointment (if you lose)
• last two both fade away over time

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)
• 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)
• [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