8 $-prospect: P-prospect: Prob. 0.31: Prob. 0.97: $16 $4 nil otherwise nil otherwise Money-value question: Determine for each prospect its subjective monetary value for you. Write those two values on a piece of paper.
9 $-prospect: P-prospect: Prob. 0.31: $16 Prob. 0.97: $4 nil otherwise nil otherwise Common finding Choice: majority prefers P-prospect. Monetary evaluation: Majority assigns higher monetary value to … $-prospect! > < transitivity: $-prospect ~ its monetary value monetary value of P-prospect ~ P-prospect $-prospect
10 2. NonEU theories ≠ regret theory
11 1979 prospect theory (OPT), for regular prospects: 𝑞 1 x 1 𝑞 2 → 𝑥 𝑞 1 𝑉(𝑦 1 ) + 𝑥 𝑞 2 𝑉 𝑦 2 = 𝑃𝑄𝑈 x 2 1- 𝑞 1 - 𝑞 2 0
12 Chew’s (1983) weighted utility 𝑞 1 𝑦 1 𝑞 𝑘 𝑉(𝑦 𝑘 ) 𝑔(𝑦 𝑘 ) . . . . → . . 𝑞 𝑘 𝑔(𝑦 𝑦 𝑜 𝑘 ) 𝑞 𝑜
13 Gul’s (1991) disappointment aversion theory: Assume 𝑦 1 ≥ ⋯ ≥ 𝑦 𝑙 ≥ 𝐷𝐹 ≥ 𝑦 k+ 1 ≥ ⋯ ≥ 𝑦 𝑜 𝑞 1 𝑦 1 . . . . 𝑦 𝑙 . 𝐷𝐹 𝑦 k+1 . . . . 𝑦 𝑜 𝑞 𝑜 Disappointment aversion (DA) theory = 𝑙 𝑜 1 + 𝛾 𝑞 𝑘 𝑉(𝑦 𝑘 ) 𝑞 𝑗 𝑉(𝑦 𝑗 ) + 𝑗=1 𝑘=𝑙+1 𝑙 𝑜 𝑞 𝑗 + (1 + 𝛾)𝑞 𝑘 𝑗=1 𝑘=𝑙+1
14 Quiggin’s (1982) rank-dependent utility Assume 𝑦 1 ≥ ⋯ ≥ 𝑦 𝑜 𝑞 1 𝑦 1 . . . . → . . 𝑦 𝑜 𝑞 𝑜 (𝑥 𝑞 𝑘 + ⋯ + 𝑞 1 − 𝑥 𝑞 𝑘 − 1 + ⋯ + 𝑞 1 )𝑉(𝑦 𝑘 )
15 Tversky & Kahneman’s (1992) (cumulative) prospect theory Assume 𝑦 1 ≥ ⋯ ≥ 𝑦 𝑙 ≥ 0 ≥ 𝑦 k+ 1 ≥ ⋯ ≥ 𝑦 𝑜 𝑞 1 𝑦 1 . . . . → . . 𝑦 𝑜 𝑞 𝑜 𝑙 (𝑥 + 𝑞 𝑗 + ⋯ + 𝑞 1 − 𝑥 𝑞 𝑗 − 1 + ⋯ + 𝑞 1 )𝑉(𝑦 𝑗 ) 𝑗=1 + 𝑜 (𝑥 − 𝑞 𝑘 + ⋯ + 𝑞 𝑜 − 𝑥 𝑞 𝑘 + 1 + ⋯ + 𝑞 𝑜 )𝑉(𝑦 𝑘 ) 𝜇 𝑘=𝑙+1
16 3. Regret theory
17 Loomes & Sugden’s (1982) (regret theory) 𝑞 1 𝑞 1 𝑦 1 𝑧 1 . . . . . (probabilities “correlated”) . ≽ . . . . . . 𝑦 𝑜 𝑧 𝑜 𝑞 𝑜 𝑞 𝑜 ⇔ 𝑜 𝑞 𝑘 𝑉(𝑦 𝑘 ) − 𝑉(𝑧 𝑘 ) ≥ 0 𝑅 𝑘=1 Mathematics: Kreweras (1961), Fishburn (1982); Multi-attribute utility: Bell (1982); Economic foundations: Loomes & Sugden (1982).
18 More fundamental breakaway than other theories: Still today, regret theory (and follow-ups including PRAM) is only quantitatively sophisticated tractable theory that can accommodate preference reversals.
19 The end
Royal Economic Society
On Applications of Regret Theory : Consequences of Comparing what is to what might have been Marcel Zeelenberg Tilburg University
Regret Theory • People compare the outcome of their choice with what the outcome would have been, had they chosen differently, and experience regret and rejoicing as a consequence • These emotions are taken into account when making decisions • Thus, resolution of both the chosen and unchosen option is central to regret theory
The Faces of Regret
You want to buy an instant lottery ticket. You are just in time, there are only 2 lottery tickets left. You choose a ticket and open it. You have won a liquor store token for € 15. Someone else buys the lottery ticket that was left, the one you didn’t choose. This person wins a book token of € 50.
Obtained ed prize 9 € 15 Book Token 8 € 15 Liquor Token 7 Regret 6 4,71 4,64 5 3,91 3,64 4 3 2 1 € 50 Book Token € 50 Liquor Token Missed sed prize
The horrible world that might have been: On April 8 1995 Tim O ’ Brien, an inhabitant of Liverpool, UK (aged 51) took his own life after missing out on a £2 million price in the National Lottery. He did so after discovering that that week ’ s winning combination were the numbers he always selected, 14, 17, 22, 24, 42 and 47. On this occasion, however, he had forgotten to renew his five-week ticket on time. It had expired the previous Saturday.
Brief voorkant
Achterkant
Postcode lotttery .31* State lottery Attitude .23* .10 .12 Subjective Norm Behavioral Expt. .10 Anticipated .29* Regret Significantly larger than in the State lotery
What Next? How do decision makers prevent future regret? Regret averse choices Better choices Insurance Bracing for loss How do decision makers manage current regret? Reverse decision Psychological repair work Individual differences in regret aversion
Thank you Marcel@uvt.nl
Royal Economic Society
The Empirical Success of Regret Theory Han Bleichrodt RES meeting Manchester, 30 March 2015
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12 Action 1 40 41 60 61 100 A’ £ a 1 £0 £0 B’ £12 £12 £0
Q Q(a 0 ) Q(12) a 0 12 Utility Difference
Q Q(a 0 ) Q(12) Q(a 0 12) a 0 a 0 12 12 Utility Difference
Q Q(a 0 ) Q(12) Q(a 1 12) Q(a 0 12) a 0 a 0 12 a 1 12 12 Utility Difference
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12 £ a 0 = £17.52
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12 £ a 0 = £17.52 Action 1 40 41 60 61 100 A’ £ a 1 £0 £0 B’ £12 £12 £0
Loomes (1988) Action 1 40 41 100 A £ a 0 £0 B £ 0 £12 £ a 0 = £17.52 Action 1 40 41 60 61 100 A’ £ a 1 £0 £0 B’ £12 £12 £0 £ a 1 = £22.58
Studies supporting regret theory Loomes & Sugden (1987, EJ) Loomes (1988, Economica) Loomes (1989, Annals OR) Loomes, Starmer, & Sugden (1989, EJ) Starmer & Sugden (1989, Annals OR) Loomes, Starmer, & Sugden (1992, Economica) Loomes & Taylor (1992, EJ) Starmer (1992, Review of Economic Studies)
Preference reversals Action 1 30 31 60 61 100 £-bet £18 £0 £0 P-bet £8 £8 £0 CE £4 £4 £4
Action 1 40 41 100 A £0 £20 B £ 0 £12 Action 1 40 41 60 61 100 A’ £20 £0 £0 B’ £12 £12 £0
Action 1 40 41 100 A £0 £20 B £ 0 £12 Action 1 40 41 60 61 100 A’ £20 £0 £0 B’ £12 £12 £0 Action 1 40 41 81 81 100 A £20 £0 £0 B £0 £12 £12
Action 1 40 41 100 A £0 £20 B £ 0 £12 Action 1 40 41 60 61 100 A’ £20 £0 £0 B’ £12 £12 £0 Action 1 40 41 81 81 100 A £20 £0 £0 B £0 £12 £12 Action 1 40 41 81 81 100 A’ £20 £0 £0 B’ £12 £0 £12
Applications of regret Finance • Barberis, Huang & Thaler (2006) • Gollier & Salanié (2006) • Muermann et al. (2006) • Michenaud & Solnik (2008) Insurance • Braun & Muermann (2004) Health • Ritov & Baron (1990,1995) • Smith (1996) • Murray & Beattie (2001) Auction theory • Feliz-Ozbay & Ozbay (2007) • Engelbrecht-Wiggans & Katok Operations Research • Perakis & Roels (2008) Axiomatizations • Köbberling & Wakker (2003) • Zank (2010)
New insights Neuroeconomics • Camille et al. (2004) • Bourgeois-Gironde (2010) • Giorgetta et al. (2013) New models • Sarver (2008) • Hayashi (2008) • Loomes (2010) • Bordalo, Gennaioli, & Shleifer (2012)
Royal Economic Society
Beyond Regret Graham Loomes, University of Warwick
Beyond Regret Graham Loomes, University of Warwick Models Behaviour
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly)
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly) Probabilistic
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly) Probabilistic Parsimonious/restricted
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly) Probabilistic Parsimonious/restricted Multi-faceted
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly) Probabilistic Parsimonious/restricted Multi-faceted Procedurally invariant
Beyond Regret Graham Loomes, University of Warwick Models Behaviour Deterministic (mostly) Probabilistic Parsimonious/restricted Multi-faceted Procedurally invariant Sensitive to context/frame
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to Payoff comparisons between alternatives
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to Payoff comparisons between alternatives Best and worst payoffs overall; spreads
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values ‘Decent’ chances; weights; probability -payoff combinations
Consider a ‘simple’ choice and a ‘typical’ participant Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Many things s/he might attend to Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values ‘Decent’ chances; weights; probability -payoff combinations And other things may be suggested by different choices . . .
Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery C: 0.30 chance of £45; 0.70 chance of £12 Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values
Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery C: 0.30 chance of £45; 0.70 chance of £12 Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values Similarities between payoffs and/or probabilities
Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery C: 0.30 chance of £45; 0.70 chance of £12 Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values Similarities between payoffs and/or probabilities Extra difficulty of some operations / comparisons
Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery C: 0.30 chance of £45; 0.70 chance of £12 Payoff comparisons between alternatives Best and worst payoffs overall; spreads ‘Absolute’ and ‘relative’ subjective values Similarities between payoffs and/or probabilities Extra difficulty of some operations / comparisons ‘Regret’, ‘disappointment’, ‘similarity’, ‘probability weighting’ are just some of the above; and each might be modelled in more than one way
The General Model Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0
The General Model Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Pairs of items / combinations are sampled momentarily
The General Model Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Pairs of items / combinations are sampled momentarily The same comparison may register differently at different moments – variability of stock of experience / neuronal activity
The General Model Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Pairs of items / combinations are sampled momentarily The same comparison may register differently at different moments – variability of stock of experience / neuronal activity The judgmental ‘evidence’ – which option is favoured and how strongly – is accumulated in some way
The General Model Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0 Pairs of items / combinations are sampled momentarily The same comparison may register differently at different moments – variability of stock of experience / neuronal activity The judgmental ‘evidence’ – which option is favoured and how strongly – is accumulated in some way After sampling – deliberation – produces an imbalance that exceeds some threshold (level of confidence / speed-accuracy trade-off) a decision is triggered
Implications:
Implications: Exactly the same scenario may be processed differently when presented on different occasions – decisions are probabilistic
Implications: Exactly the same scenario may be processed differently when presented on different occasions – decisions are probabilistic May take different amounts of time, depending on balance
Implications: Exactly the same scenario may be processed differently when presented on different occasions – decisions are probabilistic May take different amounts of time, depending on balance Variability is not necessarily an error – it is not an error to get on with life if there are other things to be done
Implications: Exactly the same scenario may be processed differently when presented on different occasions – decisions are probabilistic May take different amounts of time, depending on balance Variability is not necessarily an error – it is not an error to get on with life if there are other things to be done Omitting comparisons / operations will distort recovery / tests
Implications: Exactly the same scenario may be processed differently when presented on different occasions – decisions are probabilistic May take different amounts of time, depending on balance Variability is not necessarily an error – it is not an error to get on with life if there are other things to be done Omitting comparisons / operations will distort recovery / tests Different procedures / frames may influence the sampling in ways that lead to systematically different patterns
Lottery A: 0.25 chance of £60; 0.75 chance of £10 Lottery B: 0.80 chance of £30; 0.20 chance of 0
25% 55% 20% A £60 £10 £10 B £30 £30 0
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