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Tradeoff method’s error propagation
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Tradeoff method’s error propagation; simulations based on a Fechner error model suggest that it is not strong (p. 164). They also have a clever test of whether subjects act strategically in view of the adaptive nature: two questions from the beginning, when subjects could not yet know about adaptive stimuli, are repeated near the end, where subjects know if they ever. Then the second questions should receive higher answers. But they don’t (p. 168). So this gives evidence of no seeing through the adaptive setup and no strategic answers. They find no subject doing the linear-constant-distance heuristic for TO. All of this because TO not from matching but from binary choice. %} Bleichrodt, Han, Alessandra Cillo, & Enrico Diecidue (2010) “A Quantitative Measurement of Regret Theory,” Management Science 56, 161–175. {% %} Bleichrodt, Han, David Crainich, & Louis Eeckhoudt (2003) “The Effect of Comorbidities on Treatment Decisions,” Journal of Health Economics 22, 805–820. {% %} Bleichrodt, Han, David Crainich, & Louis Eeckhoudt (2003) “Comorbidities and the Willingness to Pay for Health Improvements,” Journal of Public Economics 87, 2399–2406. {% %} Bleichrodt, Han, David Crainich & Louis Eeckhoudt (2008) “Aversion to Health Inequalities and Priority Setting in Health Care,” Journal of Health Economics 27, 1594–1604. {% %} Bleichrodt, Han, Enrico Diecidue, & John Quiggin (2004) “Equity Weights in the Allocation of Health Care: The Rank-Dependent QALY Model,” Journal of Health Economics 23, 157–171. {% equity-versus-efficiency; Tradeoff method: used that to measure the utility of QALYs. An impressive sample: not only 69 students, but also 208 members from the general public in 22 group sessions of about 15 each, with three interviewers present at each session. In an experiment, subjects had to choose between different hypothetical allocations of QALY scores over n individuals. The authors used the tradeoff method to measure how people transformed QALYs into utilities and, next, used these to measure the rank-dependent weights that people assigned to individuals. They found preference for equality in sense of overweighting of the worst-off, but also: inverse-S: people overweight the richest and poorest, suggesting insensitivity to groupsize. Insensitivity dominated pessimism, so that the typical inverse-S shape resulted. The authors then advance an interesting argument: insensitivity is a cognitive limitation at the level of numerical misperception, so that it is reasonable to correct for it. (cognitive ability related to likelihood insensitivity (= inverse-S)) They present the equity weighting that results after doing so, which is, obviously, convex and pessimistic. %} Bleichrodt, Han, Jason N. Doctor, & Elly Stolk (2005) “A Nonparametric Elicitation of the Equity-Efficiency Tradeoff in Cost-Utility,” Journal of Health Econonomics 24, 655–678. {% %} Bleichrodt, Han, Jason N. Doctor, Martin Filko, & Peter P. Wakker (2011) “Utility Independence of Multiattribute Utility Theory Is Equivalent to Standard Sequence Invariance of Conjoint Measurement,” Journal of Mathematical Psychology 55, 451–456. Link to paper
Bleichrodt, Han, Martin Filko, Amit Kothiyal, & Peter P. Wakker (2017) “Making Case-Based Decision Theory Directly Observable: Dataset,” American Economic Journal: Microeconomics 9, 123–151. Link to paper
Bleichrodt, Han & Louis Eeckhoudt (2005) “Saving under Rank-Dependent Utility,” Economic Theory 25, 505–511. {% Investigate effects of probability weighting in a two-period market with cost-benefit ratios that come out too high. Elasticity of probability weighting is an important index. %} Bleichrodt, Han & Louis Eeckhoudt (2006) “Survival Risks, Intertemporal Consumption, and Insurance: the Case of Distorted Probabilities,” Insurance: Mathematics and Economics 38, 335–346. {% %} Bleichrodt, Han & Louis Eeckhoudt (2006) “Willingness to Pay for Reductions in Health Risk when Probabilities Are Distorted,” Health Economics 15, 211–214. {% %} Bleichrodt, Han & Martin Filko (2008) “New and Robust Testes of QALYs when Health Varies over Time,” Journal of Health Economics 27, 1237–1249. {% %} Bleichrodt, Han & Martin Filko (2010) “A Reply to Gandjour and Gafni,” Journal of Health Economics 29, 329–331. {% %} Bleichrodt, Han, Martin Filko, Amit Kothiyal, & Peter P. Wakker (2017) “Making Case-Based Decision Theory Directly Observable,” American Economic Journal: Microeconomics 9, 123–151. {% Kirsten&I, finitely many time points %} Bleichrodt, Han & Amiram Gafni (1996) “Time Preference, the Discounted Utility Model and Health,” Journal of Health Economics 15, 49–67. {% They use the time-tradeoff sequences of Attema et al. (2010) to measure deviations from constant discounting. Do it for (economic) money and (health) life duration. A minority of 25% to 35% exhibit increasing impatience. The authors use Rohde’s (2010) convenient hyperbolic factor to analyze their data. They only fit discount families that cannot accommodate increasing impatience, being hyperbolic, quasi-hyperbolic, constant, and proportional. Of these, hyperbolic and proportional are relatively best. The authors write, in their conclusion: “To explain increasing impatience other discount functions are needed (Ebert and Prelec 2007; Bleichrodt et al. 2009).” %} Bleichrodt, Han, Yu Gao, & Kirsten I.M. Rohde (2016) “A Measurement of Decreasing Impatience for Health and Money,” Journal of Risk and Uncertainty 52, 213–231. {% Propose, if I understand well, that U(dead) = 0 for all individuals, and U(M) = 1 where M, depending on an individual, is the best conceivable health state for the group that the individual belongs to. %} Bleichrodt, Han, Carmen Herrero, & José Luis Pinto (2002) “A Proposal to Solve the Comparability Problem in Cost-Utility Analysis,” Journal of Health Economics 21, 397–403. {% %} Bleichrodt, Han & Magnus Johannesson (1997) “The validity of QALYs: An Experimental Test of Constant Proportional Trade-Off and Utility Independence,” Medical Decision Making 17, 21–32. {% %} Bleichrodt, Han & Magnus Johannesson (1997) “Standard Gamble, Time-Trade-Off and Rating Scale: Experimental Results on the Ranking Properties of QALYs,” Journal of Health Economics 16, 155–175. {% %} Bleichrodt, Han & Magnus Johannesson (1997) “An Experimental Test of a Theoretical Foundation for Rating-Scale Valuations,” Medical Decision Making 17, 208–216. {% Kirsten&I: finitely many time points %} Bleichrodt, Han & Magnus Johannesson (2001) “Time Preference for Health: A Test of Stationarity versus Decreasing Timing Aversion,” Journal of Mathematical Psychology 45, 265–282. {% doi: http://dx.doi.org/10.1287/opre.2015.1433 %} Bleichrodt, Han, Umut Keskin, Kirsten I.M. Rohde, Vitalie Spinu, & Peter P. Wakker (2015) “Discounted Utility and Present Value—A Close Relation,” Operations Research 63, 1420–1430. Link to paper This paper received the Decision Analysis Publication award of 2016 {% %} Bleichrodt, Han, Amit Kothiyal, Drazen Prelec, & Peter P. Wakker (2013) “Compound Invariance Implies Prospect Theory for Simple Prospects,” Journal of Mathematical Psychology 57, 68–77. Link to paper
Bleichrodt, Han & Marc A. Koopmanschap (1999) “Economische Evaluatie.” In Ruud Lapré, Frans F.H. Rutten & Frederik T. Schut (eds.) Algemene Economie van de Gezondheidszorg, 251–272, Elsevier/de Tijdstroom, Maarssen (in Dutch). {% Doi: 10.1007/s11238-016-9542-3 %} Bleichrodt, Han, Chen Li, Ivan Moscati, & Peter P. Wakker (2016) “Nash Was a First to Axiomatize Expected Utility,” Theory and Decision 81, 309–312. Link to paper
Bleichrodt, Han & John Miyamoto (2003) “A Characterization of Quality-Adjusted Life-Years under Cumulative Prospect Theory,” Mathematics of Operations Research 28, 181–193. {% Tradeoff method: they use it. P. 1490/1491 gives nice details about their implementation for finding indifferences. They first ask for values which give sure decisions, then narrow these down. Tradeoff method’s error propagation: p. 1495 did simulation suggesting that error propagation of the Tradeoff method is not very serious. inverse-S: they find that, doing it for health outcomes instead of monetary. The curve is more elevated/curved than for money. Table 1, p. 1488, gives a convenient listing of studies of probability weighting. They clearly find inverse-S, more than for monetary experiments. P. 1492 bottom of 2nd column: they find more bounded SA (so lower and upper SA) than monetary experiments did. Strangely enough, p. 1493/1494 finds slightly more lower SA than upper SA in one analysis, slightly less in another. So, roughly, it looks equal. P. 1494 1st column: they find approximately linear probability weighting in the middle region. P. 1495: compares fit of different parametric weighting function families. Weighting function for health is both more elevated (abstract, p. 1495; higher in Table 4) and more inverse-S (p. 1492 bottom; lower in Table 4) than commonly found for money. %} Bleichrodt, Han & José Luis Pinto (2000) “A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis,” Management Science 46, 1485–1496. {% Use medical stimuli, i.e., chronic health states with two dimensions, health state and life duration. Consider (i) Effects of varying loss aversion when scale compatibility effects are constant (ii) Effects of varying scale compatibility when loss aversion effects are constant (iii) What happens if scale compatibility goes one way, loss aversion the other? Stimuli: to get (x1, x 2) ~ (y1, y2), three of the four values are fixed and the fourth is established through choice-bracketing, e.g. (x1, x 2) ~ (y1,?) with ? to be revealed from the participant. Next, in a return question, the matching value obtained is substituted and any of the other should be substituted, as, for example, with x1 to be substituted, in (?, x2) ~ (y1, y2). Results: all effects occur, scale compatibility and loss aversion seem about equally strong for they neutralize each other when they can. Loss aversion is not constant but depends on stimuli: it seems to decrease with life duration. Suggest to do utility measurement in contexts where scale compatibility and loss aversion are minimal. %} Bleichrodt, Han & José Luis Pinto (2002) “Loss Aversion and Scale Compatibility in Two-Attribute Trade-Offs,” Journal of Mathematical Psychology 46, 315–337. {% Use Tradeoff method; empirically show that utility of life duration is concave which, as they write themselves, is not surprising in itself. The new contribution of this paper is to show it in a way not affected by violations of expected utility. Given the widespread belief in, and use of, concavity of utility of life duration, and the total absence of empirical support not distorted by violations of expected utility, this is an important result. %} Bleichrodt, Han & José Luis Pinto (2005) “The Validity of QALYs under NonExpected Utility,” Economic Journal 115, 533–550. {% %} Bleichrodt, Han & José Luis Pinto (2006) “Conceptual Foundations for Health Utility Measurement.” In Andrew Jones (ed.) The Elgar Companion to Health Economics, 347–358, Edward Elgar, Vermont. {% real incentives/hypothetical choice: of N = 300 subjects, 150 accepted an invitation for returning next week and participating in a next round of the experiment, taking about 45 minutes. Of these, 50 were randomly selected. They were offered a flat payment of €12 for that. However, 34 of the 50 did not want the payment, and preferred to participate for free (p. 716 end of §2)! This illustrates once more how well motivated people are to participate in health investigations, where several of these investigations are financed by charity donations. Many subjects have (FH0.75death) > (FH0.75X) but death < X which can be taken as a violation of stochastic dominance (or independence if death and X are not taken as outcomes but as prospects). The authors take it as preference reversal. %} Bleichrodt, Han & José Luis Pinto (2009) “New Evidence of Preference Reversals in Health Utility Measurement,” Health Economics 18, 713–726. {% %} Bleichrodt, Han, José Luis Pinto, & José Maria Abellán (2003) “A Consistency Test of the Time Trade-Off,” Journal of Health Economics 22, 1037–1052. {% inverse-S; paternalism/Humean-view-of-preference; Tradeoff method; utility elicitation; utility measurement: correct for probability distortion; SG doesn’t do well: p. 1505 has it extremely %} Bleichrodt, Han, José Luis Pinto, & Peter P. Wakker (2001) “Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility,” Management Science 47, 1498–1514. Link to paper
Bleichrodt, Han, Rogier J.D. Potter van Loon, Kirsten I.M. Rohde, & Peter P. Wakker (2013) “A Criticism of Doyle’s Survey of Time Preference: A Correction on the CRDI and CADI Families,” Judgment and Decision Making 8, 630–631. Link to paper
Bleichrodt, Han & John Quiggin (1997) “Characterizing QALYs under a General Rank Dependent Utility Model,” Journal of Risk and Uncertainty 15, 151–165. {% Tradeoff method %} Bleichrodt, Han & John Quiggin (1999) “Life-Cycle Preferences over Consumption and Health: When is Cost-Effectiveness Analysis Equivalent to Cost-Benefit Analysis?,” Journal of Health Economics 18, 681–708. {% %} Bleichrodt, Han & John Quiggin (2002) “Life-Cycle Preferences over Consumption and Health: A Reply to Klose,” Journal of Health Economics 21, 167–168. {% Tradeoff method; restricting representations to subsets %} Bleichrodt, Han, Kirsten I.M. Rohde, & Peter P. Wakker (2008) “Combining Additive Representations on Subsets into an Overall Representation,” Journal of Mathematical Psychology 52, 304–310. Link to paper
Bleichrodt, Han, Kirsten I.M. Rohde, & Peter P. Wakker (2008) “Koopmans' Constant Discounting for Intertemporal Choice: A Simplification and a Generalization,” Journal of Mathematical Psychology 52, 341–347. Link to paper
Bleichrodt, Han, Kirsten I.M. Rohde, & Peter P. Wakker (2009) “Non-Hyperbolic Time Inconsistency,” Games and Economic Behavior 66, 27–38. Link to paper
Bleichrodt, Han & Ulrich Schmidt (2002) “A Context-Dependent Model of the Gambling Effect,” Management Science 48, 802–812. {% MAUT adapted to PT, with either global reference points or within-attribute reference points. A preference foundation is given. Decision weighting and loss aversion can depend on the attribute. They give a model that is essentially addition, over attributes, of attribute-dependent PT values. Tradeoff method: used in axioms. %} Bleichrodt, Han, Ulrich Schmidt, & Horst Zank (2009) “Additive Utility in Prospect Theory,” Management Science 55, 863–873. {% Use rank-dependence in axiomatizing/justifying measures of inequality for the health domain. %} Bleichrodt, Han & Eddy van Doorslaer (2006) “A Welfare Economics Foundation for Health Inequality Measurement,” Journal of Health Economics 25, 945–957. {% inverse-S: find that because incorporating inverse-S probability weighting improves utility measurement: The consistency of QALYs is increased if probability transformation is incorporated. After that, utility curvature does not add much more. P. 253: probability transformation alone improves fit better than utility curvature alone. Power utility fits some better than exponential utility. %} Bleichrodt, Han, Jaco van Rijn, & Magnus Johannesson (1999) “Probability Weighting and Utility Curvature in QALY-Based Decision Making,” Journal of Mathematical Psychology 43, 238–260. {% http://dx.doi.org/10.1111/ecoj.12200 %} Bleichrodt, Han & Peter P. Wakker (2015) “Regret Theory: A Bold Alternative to the Alternatives,” Economic Journal 125, 493–532. Link to paper
Bleichrodt, Han, Peter P. Wakker, & Magnus Johannesson (1997) “Characterizing QALYs by Risk Neutrality,” Journal of Risk and Uncertainty 15, 107–114. Link to paper
Block, Henry David & Jacob Marschak (1960) “Random Orderings and Stochastic Theories of Responses.” In Ingram Olkin (Ed.) Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling, Stanford University Press, 97–132, Stanford, CA. {% %} Blonski, Matthias (1999) “Social Learning with Case-Based Decisions,” Journal of Economic Behavior and Organization 38, 59–77. {% proper scoring rules-correction; Gissel; Throughout, expected utility is assumed. P. 408: “Cross sections of option prices have long been used to estimate implied probability density functions (PDFs). … Unfortunately, theory also tells us that the PDFs estimated from options prices are risk-neutral. If the representative investor who determines options prices is not risk-neutral, these PDFs need not correspond to the representative investor’s (i.e., the market’s) actual forecast of the future distribution of underlying asset values.” It is reasonable that on average the subjective probabilities equal objective probabilities. This paper corrects by assuming nonlinear utility, and seeing what utility best corrects. They report RRA for both (so for exponential utility multiply the Pratt-Arrow index by the amount). Table III, p. 424, finds powers such as 4 (i.e., relative risk aversion indexes of 5) as median and mean. Table V, p. 429, has more extreme values, ranging from power 0 (ln) to power 14 for all kinds of time horizons. Table VI, p. 431, is likewise. A nice table of previous estimates is on p. 432, Table VII, with wide variation. Exponential utility seems to fit better than power. %} Bliss, Robert R. & Nikolaos Panigirtzoglou (2004) “Option-Implied Risk Aversion Estimates,” Journal of Finance 59, 407–446. {% Uses data of Wakker, Erev, & Weber (1994), does parameter fitting at an individual level. Then new prospect theory = RDU does well, better than the original ’79 prospect theory (denoted PT in this paper) and Gul’s (1991) disappointment aversion theory. Some other less well-known theories do even better. Utility is strongly concave under EU, and more weakly concave, but still concave, under nonEU theories. linear utility for small stakes: concave utility improves some over linear utility. %} Blondel, Serge (2002) “Testing Theories of Choice under Risk: Estimation of Individual Functionals,” Journal of Risk and Uncertainty 24, 251–265. {% %} Blume, Lawrence, Adam Brandenburger, & Eddie Dekel (1989) “An Overview of Lexicographic Choice under Uncertainty,” Annals of Operations Research 19, 231–246. {% %} Blumenschein, Karen, Glenn C. Blomquist, Magnus Johannesson, Nancy Horn, & Patricia Freeman (2008) “Eliciting Willingness to Pay without Bias: Evidence from a Field Experiment,” Economic Journal 118, 114–137. {% real incentives/hypothetical choice: test discrepancy between hypothetical and real choice. Subjects are considerably less willing to buy in real than hypothetical. A very easy cure is given: if in hypothetical choice a follow-up question is asked for yes answers about how sure they are, then those that are sure match well with real choices. %} Blumenschein, Karen, Magnus Johannesson, Glenn C. Blomquist, Bengt Liljas, & Richard M. O'Conor (1998) “Experimental Results on Expressed Certainty and Hypothetical Bias in Contingent Valuation,” Southern Economic Journal 65, 169–177. {% real incentives/hypothetical choice: study method of Blumenschein, Johannesson, Blomquist, Liljas, & O'Conor (1998; Southern Economic Journal 65). Do it for treatment for 172 asthma patients, which is a nicer population than students in a lab. %} Blumenschein, Karen, Magnus Johannesson, Krista K. Yokoyama, & Partricia R. Freeman (2001) “Hypothetical versus Real Willingness to Pay in the Health Care Sector: Results from a Field Experiment,” Journal of Health Economics 20, 441–457. {% %} Blyth, Colin R. (1972) “On Simpson’s Paradox and the Sure-Thing Principle,” Journal of the American Statistical Association 67, 364–366. {% %} Blyth, Colin R. (1973) “Some Probability Paradoxes in Choice from among Random Alternatives,” Journal of the American Statistical Association 67, 366–382. {% proper scoring rules: The authors apply classical test theory or, more precisely, its alternative Item Response Theory (IRT) to proper scoring rules, thus qualifying forecasters as high or low quality and events as hard or easy to predict. %} Bo, Yuanchao Emily, David V. Budescu, Charles Lewis, Philip E. Tetlock, & Barbara Mellers (2017) “An IRT Forecasting Model: Linking Proper Scoring Rules to Item Response Theory,” Judgment and Decision Making 12, 90–103. {% Seems to show that it matters whether a task is performed in the morning or evening in combination with whether one is a morning or evening person. %} Bodenhausen, Galen V. (1990) “Stereotypes as Judgmental Heuristics: Evidence of Circadian Variations in Discrimination,” Psychological Science 1, 319–322. {% %} Boere, Raymond & Peter P. Wakker (2012) “Honder Euro Polisgeld Is Snel Terugverdiend,” Interview in Algemeen Dagblad 04 Oct 2012. (National Dutch newspaper). Link to paper
Bogardus, Sidney T, jr., Eric Holmboe, & James F. Jekel (1999) “Perils, Pitfalls, and Possibilities in Talking about Medical Risk,” Journal of the American Medical Association 281, 1037–1041. {% %} Bohm, David (1980) “Wholeness and the Implicate Order.” ARK, London. {% %} Bohm, David (1985) “Unfolding Meaning - A Weekend of Dialogue with David Bohm.” Mickleton. {% real incentives/hypothetical choice: for time preferences; finds discrepancy between real/hypothetical, fewer preference reversals occur with real incentives. It seems, however, that much of the difference compared to the literature is because Bohm uses buying prices whereas most of the literature uses selling prices. Within buying prices, Bohm finds some discrepancy, but not very strong. I never studied in detail the experimental setup and incentive scheme used here. %} Bohm, Peter (1994) “Time Preference and Preference Reversal among Experienced Subjects: The Effects of Real Payments,” Economic Journal 104, 1370–1378. {% Field experiment with used cars: no pref. reversals at all (no surprise if matching cannot be done via quantitative dimension!?!?!?) This work has often been criticized for finding no preference reversals where no-one would expect them in the first place. %} Bohm, Peter (1994) “Behaviour under Uncertainty without Preference Reversal: A Field Experiment,” Empirical Economics 19, 185–200. {% Only 11% pref. reversal in real-world lotteries %} Bohm, Peter & Hans Lind (1993) “Preference Reversal, Real-World Lotteries, and Lottery-Interested Subjects,” Journal of Economic Behavior and Organization 22, 327–348. {% Take money as set of integers (cents) iso continuum. Adapt many results, such as (Theorem 4) that under EU more risk averse iff more concave utility. The latter had been proved before by Peters & Wakker (1987, Theorem 2), for completely general domains. %} Bohner, Martin & Gregory M. Gelles (2012) “Risk Aversion and Risk Vulnerability in the Continuous and Discrete Case: A Unified Treatment with Extensions,” Decisions in Ecomics and Finance 35, 1–28. {% probability elicitation: applied to experimental economics; Short summary: This paper considers standard gamble (SG; PE) measurement. The sure outcome is (10,10) (10 for you and 10 for an anonymous other person). The SG question has a good outcome (15,15) and a, for you, bad outcome (8,22). Which probability p makes you indifferent between (10,10) and (15,15)p(8,22)? I start with 2nd treatment. 2nd Treatment: the probability p refers to some objective probability determined by some random mechanism that does not arouse any emotion (at least not by the info given to the subjects). 3rd Treatment: like the 2nd, but with the payments for the other person removed. 1st Treatment: the probability p refers again to some objective probability, but it is related to an aversive event (percentage of people betraying others). This is a BDM two-stage resolution of uncertainty. In the first stage an objective probability p is chosen in an ambiguous way (in treatment 2 no info at all is given to the subjects, and in treatment 1 it is the percentage of betrayal). In the second stage it is decision under risk, choosing between (10,10) and (15,15)p(8,22). Under backward induction or isolation (in a strict sense), the subject should let the indifference p be the indifference probability of the SG/PE, so it should be the same in treatments 1 and 2. In particular, under backward induction (in a strict sense) betrayal aversion can play no role. Indeed, intuitively speaking, in treatment 2 any aversive betrayal event has happened anyhow and can no more be affected. In particular, it is no more reason to like (10,10) more than (15,15)p(8,22). Still, in the experiment the subjects just dislike the probabilities of aversive events in Treatment 1 extra and hence require a higher probability p there to make them indifferent. This means that backward induction/isolation in the strict sense must be violated. (Something that Machina (1989) argued for on, for him, normative grounds.) Conditioning on a betrayal event induces extra dislike of (15,15)p(8,22). Then betrayal aversion can come in. Also ambiguity attitude can come in (if this is considered a component separate of betrayal aversion). May be subjects dislike more, or perceive more, the ambiguity about betrayal in treatment 1 than the choice (which may be perceived as uniform) in treatment 2. Under backward induction, it can be interpreted as: violation of objective probability = one source More detailed summary: Situation 1 [Trust game]: principal, who gets bold payoffs, can choose to either get (10,10) (10 for self and 10 for agent) or move to second stage. In 2nd stage agent can choose (15,15) or (8,22) (in latter case principal gets only 8 and agent gets 22). The trust game was not played for real by the principal, but something else is done. Under backward induction, it is just a task of decision under risk with known probability, as follows: the principal is asked the minimal probability p* (objective!) at the good prize 15 (so, (15,15)p*(8,22)) to make him willing to forgo the sure prize ((10,10)) and take the risky option. This is implemented in a BDM (Becker-DeGroot-Marschak)-like implementation as follows. Each agent was asked whether he would be trustworthy (go for (15,15)) if given the chance (without any other info; they just thought it was a trust game). Then it was measured which percentage p of the agents in the sample chose to be trustworthy. Then each principal was randomly matched with an agent. If p was better than the chosen threshold p* (p > p*) then the game was played, but if p was worse (p < p*) then the sure (10,10) resulted. Under backward induction, for the principal it can be taken not as ambiguity but only as risk with known probability, where a probability equivalent question was asked for (10,10) in a lottery with (15,15) as good outcome and (8,22) as bad outcome. Then real incentives were implemented à la BDM where, however, the probability p was not chosen fully randomly from [0,1] but was determined by the agents’ responses in the sample. Under backward induction, this does not affect the incentive compatibility under the usual isolation assumption. However, ambiguity attitudes may come in regarding the probability p chosen in the BDM mechanism, which in treatment 2 is done without any info given to the subjects (so, ambiguous) and in treatment 1 through the (objective, 1st stage) probability of betrayal the 2nd stage uncertainty about which is however ambiguous. For control two other situations were considered: Situation 2: principal can choose to either get (10,10) or move to second stage. In second stage, randomness chooses: (15,15)p(8,22). Here the principals were only told that it was a probability p, but not how it was determined. It was actually determined as in Situation 1, as the probability of the agents in the sample choosing trustworthy, but principals had no knowledge of this. Situation 3: principal can choose to either get 10 or 15p8. Here the principals were only told that it was a probability p, but not how that was determined. It was actually determined as in Situation 1, as the probability of the agents in the sample choosing trustworthy. So this is like situation 2 but without payments to another agent. They find betrayal aversion: i.e., the matching probability in situation 1 is higher (showing that this objective probability is disliked more) than in the other situations. In all situations the probability regarding the decision situation of the principal can be taken as objective. In Situation 2 the only reason to be different than situation 3 then is welfare considerations regarding the payoff for the other. In Situation 1, besides the welfare considerations, there is also the (dis)like of having been betrayed yourself by your matched other or not. So not the beliefs, but only the values of the outcomes matter, formally speaking. In my preferred interpretation, the finding of betrayal aversion is a special case of source preference, be it that here both sources concern risk (objective probabilities) (in the source method risk is usually taken as one source): people just dislike uncertainty (risk in this case) having to do with betrayal, in the same way as they just like to deal with uncertainty related to their hobby of basketball rather than other uncertainties (Heath & Tversky 1991). In reality, one can, more pessimistically, expect subjects not to fully see through Situation 1 (the same way as I, each time when rereading this paper, need nontrivial time to re-understand that it is just risk) and be confused by and partly guided by beliefs in trust/betrayal still. Or it can be that backward induction is violated. %} Bohnet, Iris, Fiona Greig, Benedikt Herrmann, & Richard Zeckhauser (2008) “Betrayal Aversion: Evidence from Brazil, China, Oman, Switzerland, Turkey, and the United States,” American Economic Review 98, 294–310. {% %} Bohnet, Iris & Richard Zeckhauser (2004) “Trust, Risk and Betrayal,” Journal of Economic Behavior and Organization 55, 467–484. {% second-order probabilities to model ambiguity: paper considers ambiguity attitudes through second-order probabilities. People prefer positively-skewed second-order probability distributions, both for gains and for losses. P. 140 Table 1 gives a good impression of what goes on. All effects are weaker for losses than for gains. Download 7.23 Mb. Share with your friends:
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