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between-random incentive system
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between-random incentive system (paying only some subjects): paid 1 of every 10 subjects. losses from prior endowment mechanism: did that. Risk averse for gains, risk seeking for losses: find it. concave utility for gains, convex utility for losses: find linear utility for gains (power 0.98), somewhat convex for losses (power 0.88). The probability weighting parameter is 0.865 for gains and 0.79 for losses, so somewhat stronger for the latter. Loss aversion is 1.41. Abstract and p. 360 point out that for CE measurements of PT parameters there can be considerable collinearities (they do not use this term). This is further analyzed on p. 366 ff.. Figure 1 concerns gain prospects with only one nonzero outcome. Then the joint power of utility and probability weighting is unidentifiable. Because the parametric family chosen for w has no free power, it leads to implications for the w parameter. They show nice figures of maximum likelihood tests, showing that for CE measurements the parameters of PT strongly interact, with much collinearity. Show that there is a wide set of parameter combinations that fits the data almost as well as the optimal parameters. Figure 3b shows it for the Tversky & Kahneman (1992) data. They find PT parameters similar to other studies, confirming inverse-S (although their one-parameter T&K’92 family enhances it). P. 374: they test for stability at the individual level by using statistics that take within-subject choices as independent. It gives 1/3 of instable subjects (significant changes according to the statistic just mentioned. %} Zeisberger, Stefan, Dennis Vrecko, & Thomas Langer (2012) “Measuring the Time Stability of Prospect Theory Preferences,” Theory and Decision 72, 359–386. {% %} Zellner, Arnold (1971) “An Introduction to Bayesian Inference in Econometrics.” Wiley, New York. {% %} Zellner, Arnold (1985) “Bayesian Econometrics,” Econometrica 53, 253–269. {% Nice but no new points %} Zellner, Arnold (1995) “Bayesian and non-Bayesian Approaches to Statistical Inference and Decision-Making,” Journal of Computational and Applied Mathematics 64, 3–10. {% That every position in chess has a unique value; also uses backward induction (but only in a deterministic sense). Or so it was cited for a long time. But it seems that he considered games that can last infinitely long and did not use backward induction. He seems to have proved that if a position is winning, then it is winning in a finite number of moves. Ismail Mehmet pointed out to me in 2017 that may be Euwe (1929) was the first to use backward induction to prove that chess is determined. %} Zermelo, Ernst (1913) “Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels,” Proceedings of the Fifth International Congress of Mathematics 2, Cambridge, UK, 501–504. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value); seems to be the first to show how expected utility provides “measurable utility;” pp. 237-238 proposes both uncertainty and time aggregation as sources of cardinal utility, though not stated very clearly; explains that one should use hypothetical choices and abstraction. %} Zeuthen, Frederik (1937) “On the Determinateness of the Utility Function,” Review of Economic Studies 4, 236–239. {% Examine and discuss probability and frequency (mis)perception in many areas, including risk & uncertainty, signal detection, support theory. P. 10 3rd para points out that in experiment 1 the slope decreases with experience, which is counterintuitive. (cognitive ability related to likelihood insensitivity (= inverse-S)) P. 11 around Eq. 6 nicely relates Stevens’ power law on probability, for odds, to a one-parameter version of the LLO (linear in logodds = Einhorn-Hogarth family). The paper ends with humor: we conjecture that there are factors in each of the domains we considered that are responsible for the particular choice of probability distortion observed. We need only find out what they are.” %} Zhang, Hang & Laurence T. Maloney (2012) “Ubiquitous Log Odds: A Common Representation of Probability and Frequency Distortion in Perception, Action, and Cognition,” Frontiers in Decision Neuroscience 6, 1–14. {% ordering of subsets %} Zhang, Jiankang (1999) “Qualitative Probabilities on Lambda-Systems,” Mathematical Social Sciences 38, 11–20. {% Axiomatizes CEU (Choquet expected utility) with belief functions that are inner measures; proposes lambda-system for collection of unambiguous events, which generalizes sigma-algebra by relaxing intersection-closedness. Introduction claims that people prefer known to unknown probabilities; §§1.3 and 4.1 erroneously write that the unambiguous events in Sarin & Wakker (1992) are primitive rather than derived from preference; §4.1 sides with Nehring’s (1992) criticism of cumulative dominance. %} Zhang, Jiankang (2002) “Subjective Ambiguity, Expected Utility and Choquet Expected Utility,” Economic Theory 20, 159–181. {% %} Zhang, Jiankang & Larry G. Epstein (1995) “Expected Utility with Inner Measures,” {% Use Liu's uncertainty theory. %} Zeng, Zhiguo, Rui Kang, Meilin Wen, & Enrico Zio (2018) “Uncertainty Theory as a Basis for Belief Reliability,” Information Sciences 429, 26–36 {% Investigate how neuro-chemical factors are related to gains and losses in risky decisions, and find differences between gains and losses. %} Zhong, Songfa, Robin Chark, Richard P. Ebstein, & Soo Hong Chew (2012) “Imaging Genetics for Utility of Risks over Gains and Losses,” NeuroImage 59, 540–546. {% Studying twins, they find evidence for heritability of economic risk attitudes. %} Zhong, Songfa, Chew Soo Hong, Eric Set, Junsen S. Zhang, Hong Xue, Pak C. Sham, Richard P. Ebstein, & Salomon Israel (2009) “The Heritability of Attitude toward Economic Risk,” Twin Research and Human Genetics 12, 103–107. {% N = 350 students. Measure preference for longshot gains and losses, from one simple choice, with gains incentivized but losses not so. Find some relations with genes. %} Zhong, Songfa, Salomon Israel, Hong Xue, Richard P. Ebstein, & Chew Soo Hong (2009) “Monoamine Oxidase A Gene (MAOA) Associated with Attitude towards Longshot Risks,” PLoS ONE 4, e8516. {% losses from prior endowment mechanism; Use choice list to determine CEs (certainty equivalents) of prospects for both gains and losses, for N=350 Chinese students. From each take some blood for genotyping. Risk averse for gains, risk seeking for losses: 38% risk averse for losses, only 52% for gains. Although the introduction and so on present this paper as a study into utility, it is only a study into risk attitude and not into utility (remember that EU fails descriptively). Find that high DA tone implies high risk aversion and high 5HT tone gives less risk aversion for losses. Use random incentive system but do it several times so that there are income effects still. %} Zhong, Songfa, Salomon Israel, Hong Xue, Pak C. Sham, Richard P. Ebstein, & Soo Hong Chew (2009) “A Neurochemical Approach to Valuation Sensitivity over Gains and Losses, Proceedings of the Royal Society B 276, 4181–4188. {% %} Zhou, Lin (1994) “A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation,” Games and Economic Behavior 6, 512–526. {% %} Zhou, Lin (1994) “The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice,” Games and Economic Behavior 7, 295–300. {% %} Zhou, Lin (1995) “A Characterization of Demand Functions that Satisfy the Weak Axiom of Revealed Preference,” Economics Letters 49, 403–406. {% %} Zhou, Lin (1995) “Integral Representation of Continuous Comonotonically Additive Functionals,” Cowles Foundation, Yale University, New Haven, CT. {% %} Zhou, Lin (1995) “A Simple Choice-Based Subjective Probability Theory,” Cowles Foundation, Yale University, New Haven, CT. {% %} Zhou, Lin (1996) “A Theorem on Bayesian Utilitarianism,” Cowles Foundation, Yale University, New Haven, CT. {% Harsanyi’s aggregation %} Zhou, Lin (1997) “Harsanyi’s Utilitarianism Theorems: General Societies,” Journal of Economic Theory 72, 198–207. {% Nash bargaining solution; theorem shows that asymmetric NBS holds on closed, comprehensive, bounded from above, containing d in interior, BGs iff IIA, INV, and strict individual rationality (all more than d). %} Zhou, Lin (1997) “The Nash Bargaining Theory with Non-convex Problems,” Econometrica 65, 681–685. {% Considers DUU with a continuous state space and considers only continuous acts. Takes two-stage approach of Anscombe & Aumann (1963). Gives preference characterization for (upper-continuous capacity-) CEU (Choquet expected utility). %} Zhou, Lin (1999) “Subjective Probability Theory with Continuous Act Spaces,” Journal of Mathematical Economics 32, 121–130. {% Argue that one should not just take utility in game theory for granted but derive it from observed choice; refer to observability problem in my ’89 book! %} Zhou, Lin & Indrajit Ray (2001) “Game Theory via Revealed Preferences,” Games and Economic Behavior 37, 415–424. {% Investigates elicitability of risk measures. Elicitability is something like the possibility to elicit it using proper scoring rules. Quantile-based risk measures, such as VaR, are elicitable. Expected shortfall and, more general, all law-invariant (= probabilistically sophisticated) spectral risk measures are not elicitable unless just minus expected value. This restriction does not hold for law-invariant “coherent” risk measures. %} Ziegel, Johanna F. (2016) “Coherence and Elicitability,” Mathematical Finance 26, 901–918. {% probability communication & ratio bias: this editorial argues that 1 in X is bad way to communicate risk, following Pighin et al. (2011). Refers to the Sirota et al. meta-analysis that argues that the effect is smaller than thought, but existing. The issue of this journal has several other papers on probability communication. %} Zikmund-Fisher, Brian J. (2014) “Continued Use of 1-in-X Risk Communications Is a Systemic Problem,” Medical Decision Making 34, 412–413. {% Gives psychological background to verbal probabilities. %} Zimmer Alf C. (1984) “A Model for the Interpretation of Verbal Predictions,” International Journal of Man-Machine Studies 20, 121–134. {% The author shows that independence/separability is, essentially, the same as monotonicity if we allow outcomes to be complex things such as conditional prospects. This was also demonstrated by Marschak (1987) and LaValle (1992). %} Zimper, Alexander (2008) “Revisiting Independence and Stochastic Dominance for Compound Lotteries,” B.E. Journal of Theoretical Economics (MS #1444). {% %} Zimper, Alexander (2009) “Half Empty, Half Full and why We Can Agree to Disagree forever,” Journal of Economic Behavior and Organization 71, 283–299. {% Considers several ways of updating capacities. Applies it in economic equilibrium model. Heavy weighting of tails is accommodated by using neo-additive weighting functions. %} Zimper, Alexander (2010) “Asset Pricing in a Lucas “Fruit-Tree” Economy with Non-Additive Beliefs,” {% Shows that the law of iterated expectations can be satisfied under CEU (Choquet expected utility) if updating happens in a “rank-respecting” manner suggested by Sarin & Wakker 1998. Lapied & Toquebeuf (2013) provide a correction. %} Zimper, Alexander (2011) “Re-Examining the Law of Iterated Expectations for Choquet Decision Makers,” Theory and Decision 71, 669–677. {% updating Considers Bayesian updating for RDU maximizer under uncertainty. Assumes neo-additive weighting function. Shows that updated beliefs will mostly converge to fifty-fifty unless neo-additive is just additive and RDU is SEU. %} Zimper, Alexander (2013) “The Emergence of “Fifty–Fifty” Probability Judgments through Bayesian Updating under Ambiguity: Re-Examining the Law of Iterated Expectations for Choquet Decision Makers,” Fuzzy Sets and Systems 223, 72–88. {% Use the neo-additive function of Chateauneuf et al. in a learning/updating model where new info leads to polarization. %} Zimper, Alexander & Alexander Ludwig (2009) “On Attitude Polarization under Bayesian Learning with Non-Additive Beliefs,” Journal of Risk and Uncertainty 39, 181–212. {% DOI 10.1007/s00199-016-1007-y Nicholls, Romm, & Zimper (2015) did an experiment with Ellsberg urns where subjects could sample and learn. Strangely enough, that did not move towards EU but, if anything, made the violations worse. This paper proposes a theory on updating under ambiguity with multiple priors where there need not be convergence to EU, due to a “stubbornness” factor in the model, where priors are not removed very much after observations. %} Zimper, Alexander & Wei Ma (2017) “Bayesian Learning with Multiple Priors and Nonvanishing Ambiguity,” Economic Theory 64, 409–447. {% Christiane, Veronika & I %} Zorzi, Marco, Konstantinos Priftis, & Carlo Umiltà (2002) “Neglect Disrupts the Mental Number Line,” Nature 417, May 2002, 138–139. {% %} Zou, Liang (1986) “On the Distribution of Economic Rights under State Ownership,” Guang Ming Daily, 10 Jan. 1986 (in Chinese). {% %} Zou, Liang (1991) “The Target Incentive System vs. the Price Incentive System under Adverse Selection and the Ratchet Effect,” Journal of Public Economics 46, 51–89. {% %} Zou, Liang (1992) “Threat-Based Incentive Mechanisms under Moral Hazard and Adverse Selection,” Journal of Comparative Economics 16, 47–74. {% %} Zou, Liang (1992) “Threat-Based Implementation of Incentive Compatible Mechanisms,” Annales d’Economie et Statistique on Organization and Games 25/26, 189–204. {% %} Zou, Liang (1992) “Ownership Structure and Efficiency: An Incentive Mechanism Approach,” Journal of Comparative Economics 16, 399–431. {% %} Zou, Liang (1995) “Incentive Contracting with Hidden Choices of Effort and Risk,” Economics Letters 47, 311–316. {% %} Zou, Liang (1996) “Interest Rate Policy and Incentives of State-Owned Enterprises in the Transitional China,” Journal of Comparative Economics 23, 292–318. {% %} Zou, Liang (1997) “Investments with Downside Insurance and the Issue of Time Diversification,” Financial Analysts Journal 53, 73–79. {% %} Zou, Liang (1997) “Incentive Roles of Fringe Benefits in Compensation Contracts,” Journal of Economics 65, 181–199. {% %} Zou, Liang. (2000) “Inherent Efficiency, Security Markets, and the Pricing of Investment Strategies,” Tinbergen Institute Discussion Paper TI 2000–108/2. {% %} Zou, Liang (2001) “The Dichotomous Theory of Choice under Risk,” Economic Dept., University of Amsterdam. {% questionnaire for measuring risk aversion; %} Zuckerman, Marvin & D. Michael Kuhlman (2000) “Personality and Risk-Taking: Common Biosocial Factors,” Journal of Personality 68, 999–1029. {% Seems to cite Markowitz on Markowitz himself, irrationally, investing his retirement savings fifty-fifty in bonds and equity. %} Zweig, Jason (1988) “Five Investment Lessons from America’s Top Pension Fund,” 8Money, January, 115–118. {% “Het gevoel is belangrijker dan het verstand: met passie, bevlogenheid en overgave kan het cynisme van alledag worden overleefd.” English translation by Wakker: Feelings are more important than the mind: with passion, enthusiasm, and devotion the cynicism of everyday can be survived. (Claim of Dutch Ph.D. dissertation at the University of Amsterdam.) %} Zwiet, Channah Shanon (1998). {% Consider infinite sequences of outcomes (interpreted as intertemporal), and rank-dependent representation + exchangeability, so temporal ordering plays no role (rank-discounted utilitarian approach). Provide preference foundation for it, mostly by a comonotonic stationarity. Mathematical problem is how to do for infinite sequences, where symmetry can generate impossibility results. Results on inequality aversion, dictatorship.| Here is a detailed explanation: It is easiest to understand this model first for finitely many timepoints/generations. In fact, let us first do decision under uncertainty, where RDU (often called CEU (Choquet expected utility)) is better understood, and then extend it to the case of this paper. Assume that there are n states of nature in S = {s1,…,sn}, and x = (x1, …, xn) is the prospect yielding $xj if state of nature sj occurs. We consider a rank-dependent evaluation, as in Wakker (2010). We will do reversed rank-ordering to stay close to the paper. Wakker (2010 §7.6) explains, for risk, that reversed or not reversed ranking does not matter, and the same holds for uncertainty. I strongly advise everyone to do nonreversed ranking, but for clarifying this paper consider reversed ranking still. We take a weighting function W with W() = 0 and W(S) = 1 (the latter relaxed soon). If x1 ... xn, then RDU(x1,…,xn) = j=1;n jU(xj) where the weight j is W{(sj,…,s1} W{sj1,…,s1}. (My book does it for non-reversed ranking x1 … xn, but this is an arbitrary convention as just explained.) If not x1 ... xn, then we have to reorder the outcomes into x[1], …, x[n] with x[1] ... x[n]. Then RDU(x1,…,xn) = j=1;n [j]U(x[j]) where [j] = W{(s[j],…,s[1]} W{s[j1],…,s[1]}. For example, if n = 3, (x1,x2,x3) = (5,7,1), then x[1] = x3 = 1, x[2] = x1 = 5, and x[3] = x2 = 7. The convention is that W(S) = 1, but this is not important and is just normalization. We can allow it to be any value > 0, and will do so. Only point to keep in mind is that a constant act = (,…,) is evaluated by W(S)(U) rather than by U(). Now assume that W(E) = 1 + 1 + … + j1 whenever E contains j states, such as E = {s1, …, sj} or E = {snj+1, …, sn}. Here 0. If x1 ... xn, then RDU(x1,…,xn) = U(x1) + 1U(x2) + ... +j1U(xj). Rank dependence allows dependence of the weights on the rank, with different weighting for the best outcome than for the worst outcome. This happens here. For < 1, outcomes are weighted more as they are ranked worse. Such pessimism can be seen to be equivalent to W being concave for this reversed rank-ordering. Now assume that sj does not refer to a state of nature, but to a generation. Then we can use the same evaluation as above. Now overweighting the lowest outcome does not reflect pessimism, but preference for equity: the poorer a person is, the more weight is given to this person. It reflects a desire for fairness. That rank dependence can be used this way to capture fairness in welfare (if sj is a person iso a state of nature) has been known for a long time, and has been used in several papers. Wakker (2010, Appendix D, Interpretation D.2) discusses it. This is what Zuber & Asheim do, for generations. A generation is not weighted more as it is nearer to the present, but as it is poorer, for fairness reasons. So has nothing to do with discounting, but reflects fairness. The smaller , the more fairness concern. The authors extend the model to the case of infinite generations, which brings some mathematical complications but does not affect the concepts. %} Zuber, Stéphane & Geir B. Asheim (2012) “Justifying Social Discounting: The Rank-Discounted Utilitarian Approach,” Journal of Economic Theory 147, 1572–1601. {% Find that more than half of the variance in risk aversion can be ascribed to genetic factors. %} Zyphur, Michael J., Jayanth Narayanan, Richard D. Arvey, & Gordon J. Alexander (2009) “The Genetics of Economic Risk Preferences,” Journal of Behavioral Decision Making 22, 367–377. Download 7.23 Mb. Share with your friends:
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