Lecture IV

1. Lecture IV Methodological inquiry on preferences reversal

2. Wrap up of the previous lecture • Preferences reversal consists of a violation of transitivity axiom, procedure invariance or both. • Evidence supporting the characterization of preferences reversal as a violation of procedure invariance. • Explanatory hypothesis: preferences formation is a contingent form of information processing. • To understand if preferences reversal can be an evidence of endogenous preferences we must be sure that the phenomenon at stake is real and not an artifact.

3. Epistemological framework. Data-phenomenon distinction applied to preferences reversal • Data are what we observe in an empirical inquiry. • Phenomenon is a relational concept that requires a hypothesis to organize data (Bogen and Woodward 1988). • A scientific phenomenon is inferred from data and is not observable. • Data are not susceptible of theoretical explanation and systematic prediction while scientific phenomena do are (Ibidem). • Empirical data on price-choice reversals (Guala 2005). These data – in themselves – are compatible with an unrestricted set of causes. • Explanatory hypothesis: preferences are a contingent form of information processing. • Inference of the scientific phenomenon of preferences reversal. • The truth of the inference and the possibility of testing the hypothesis depends on the reliability of the preferences elicitation methods (Ibidem).

4. Some implication of the data-phenomena distinction • Phenomena cannot be explained through data, because they are idiosyncratic: the causal imputation would be ambiguous. • Data play the role of evidence for the phenomena. • The causal attribution is to be referred to the pattern emerging from data. • Data of price-choice reversal are not explanatory of the phenomenon of preferences reversal. • Price-choice reversals are evidence of preference reversal. • The cause (preferences responsiveness to the cue dimension of the stimulus) is attributed to the pattern emerging from data.

5. Phenomenic instances and ideal-type phenomena • In a specific empirical inquiry we infer phenomena from data. • The empirical inquiry is replicated to test for the phenomenon robustness. • We might have different causal explanations that might be ranked according to their relevance. • Taxonomy of patterns that are a phenomenic instance of the same ideal-type phenomenon. • Inference of preference reversal from price-choice reversal data. • Replication of the experiments to test for PR robustness. • Different explanations based either on violation of transitivity or procedure invariance: the latter is the relevant feature. • Taxonomy of PR patterns that are instances of the same ideal-type phenomenon of PR.

6. Further complication.Preferences are not directly observable • Revealed preferences theory (Samuelson 1938): preferences defined in terms of choices that in turn are defined in terms of consequent outcomes. • Economic theory is only about observable facts (i.e. pricing and choosing). • Preferences are not directly observable. • Preferences reversal requires techniques of indirect observation (i.e. elicitation methods).

7. Artifacts • The interpretation of observable data is an artifact when it is either the illusion of the instrument of observation orthe result of the instruments(Grether and Plott 1979). • I case: artifacts are not real at all, II case: artifact are a constructed reality. • Preferences reversal can be an artifact in the sense of being an illusion. • An artifact is a misleading connection between data and phenomena. • The elicitation methods result to be unreliable: the explanatory hypothesis cannot be tested. • Price-choice reversal data are misleadingly connected to preferences reversal phenomenon. • The elicitation methods (reports of subjects’ choices and pricing) is not reliable. • The explanatory hypothesis of preferences sensitivity to the cue dimension of the external stimulus cannot be tested. • We cannot attribute an unambiguous cause to the observed behavior.

8. Elicitation methods. Becker-DeGroot-Marschak (BDM) mechanism • A subject is asked to state the reservation price s over a lottery and then an offer b is generated by a random process (Becker, DeGroot, Marschak 1964). • The subjects receives the offer if b > s, otherwise the lottery is played and the subject receives the resulting outcome. • Stating the real selling price is a weakly dominant strategy. • BDM controls that the cash equivalent of a lottery reflects subject’s true preferences.

9. Elicitation methods. Random Lottery Selection (RLS) mechanism • Subjects are asked to perform choice and pricing tasks. When asked to perform several tasks in sequence subjects might change their preferences because of the change in their wealth (income effect). • If subjects repeatedly play the P bet such as to increase their income, then they will be more willing to go for a riskier lottery (the $ bet) in the pricing task. • Subjects are rewarded according to a single task selected at random so as to neutralize income effect.

10. Artifact for misspecified incentives and income effect • Misspecified incentives: subjects can bid in a strategic way so as to not always reveal their true valuation of the bets. • Preferences reversal is a misleading inference from price-choices reversal. Reversals of preferences are illusory. • Income effect: subject might price higher the risky prospect as their wealth increases. • Price-choice reversals do not imply reversals at the level of preferences.

11. Replication of preferences reversal • Grether and Plott (1979) replicated Slovic and Lichtenstein (1971) results by using BDM and RLS. • The aim of the experiment was to control if preferences reversal was an artifact due to misspecified incentives (BDM) or income effect (RLS). • Preferences reversal resulted to be a robust and systematic phenomenon wrt BDM and RLS. • Can preference reversal phenomenon be an artifact of BDM and RLS?

12. Holt’s argument • Preferences reversal might occur when individuals violate independence axiom but not transitivity (Holt 1986). • Independence axiom: x > y → (x, p; z, 1 - p) > (y, p; z, 1 - p). The axioms allows for an expected utility representation linear in probability. • In a PR experiment subjects perform several tasks randomly selected through RLS mechanism. If the task is a choice one it is simply plaid out, while if the task is a pricing one BDM mechanism is implemented. • Let us consider the case of price elicitation and choices in sequence. • Subjects might perceive the PR experiment as a two stages lottery. • If reduction principle is applied but not independence than subjects preferring (pricing) the $ bet to the P bet might reverse choices. • RLS and BDM produce the artifact of preferences reversal as a violation of independence axiom.

13. Procedure • Implementation of BDM. • Random selection of only one lottery to be used to determine subject’s payoff. • We will have random payments of selling prices elicited through BDM.

14. Choices with independence axiom • Xp = P bet and X$ = $ bet; xp and x$ the respective random payments. • P > $ iff E {U (w + xp)} > E {U (w + x$)} • Elicitation of price through BDM • B (r; X) lottery; b(rp; X); b(r$; X) random payment • Decision problem: selling price r$ and rp and a random variable x ε (x$, xp). • EU(.) = 1/3 E{U (w + x)} + 1/3 E {U (w + b (r$; X$))} + 1/3 E {U (w + b (rp; Xp))} • The function is separable, linear in lotteries probabilities and the choices can be made independently.

15. Implications • The selected random variable x ε (x$, xp) is the truly preferred lottery. • Selling prices reveal subjects’ true willingness to accept valuations. • RLS and BDM control for income effects if preferences satisfy independence axiom.

16. Choice without the independence axiom • The elicitation of prices precedes the lotteries choices. • r$ and rp are the elicited selling prices. • Xp and X$ are the lotteries to be chosen in the final stage. • The final task is a choice between compound lotteries.

17. Choices without independent axiom

18. Implications • If independence axiom does not hold we do not have any restriction on the choices between the two compounds lotteries. • The bet chosen in the final stage might be different wrt the bet priced higher in the first stage. • The selling price might not be the lowest price expressing subjects’ true WTA valuations.

19. Apologetic defense of RCT • Independence axiom presupposes transitivity otherwise it is redundant when applied to non well ordered preferences relation. • Transitivity has direct normative justification while independence axiom does not (Guala 2000). • Theories of generalized expected utility without independence axiom (Machina 1982, Yaari 1987). • Preferences reversal are an illusion (artifact) due to the violation of independence axiom which in turn is determined by BDM and RLS mechanisms. • Holt’s argument is an ex post rationalization of empirical evidence and not an empirical test. • Holt’s argument does not grasp any causal nexus explaining preferences reversal in terms of non-independent choices. • Holt’s argument is devoid of empirical content. • Holt’s argument can be assessed on the empirical level to the extent that we derive from it an empirical hypothesis.

20. Predictive hypothesis • Subjects prefer an even chance to play either $ or P over the option of playing P and over the option of playing $. • Observation of random reversal of preferences. • The hypothesis aims at denying the systematic occurrence of preferences reversal. Is that true?

21. Circularity problem • BDM and RLS work if and only if expected utility axioms are satisfied (Becker, DeGroot, Marschak 1964). • BDM and RLS are instrument to test the descriptive accuracy of the axioms. • Preference reversal is an inconsistency with EUT, but the instruments are constructed on the hypothesis EUT is correct. • Preference reversal cannot be regarded as an artifact of BDM and RLS.

22. Triangulation method • If the commonly used measurement methods are not completely reliable, we should use several different procedures. • Evidence obtained through different measurement methods is a strong support for the existence of a phenomenon. • The reliability of a measurement is a function of different techniques delivering the same results. • If BDM and RLS are not completely reliable, then we should use different incentive mechanisms to reproduce PR. • If we still obtain price-choice reversal data, then we have a strong support to infer PR phenomenon. • On these grounds the explanatory hypothesis (preferences are responsive to the cue dimension of a stimulus) has a chance to be true.

23. Tversky, Slovic and Kahneman experiment • Preferences reversal concerns inconsistent orders and not inconsistent selling prices. • Preferences reversal is inconsistent with decision theory and not just with independence axiom (Cox and Epstein 1989). • It is needed to elicit ordering rather than true selling price (Tversky et al.1990). • Subject were asked to price lotteries in each pair separately and then they faced the choice task. • Subjects were told that only one lottery among the highest priced and the chosen one would have been randomly selected. • Observation of PR without BDM and RLS mechanism.

24. Predicted patterns of reversals • Standard pattern of reversal: H > L and CL> X > CH • Intransitivity: L > X and X > H, yielding L > X > H > L • Overpricing of L (OL): X > H and X > L yielding CL > X > L • Underpricing of H (UH): H > X and L > X, yielding H > X > CH. • Both OL and UH: H > X and X > L yielding H > X > CH and CL > X > L

25. Diagnosis

26. Testing the mixed strategy hypothesis • Students were presented with six pairs of P and $ bet. • For each pair they were given three options: 1) select the P bet (pure strategy); 2) select the $ bet (pure strategy); 3) let the experimenter select either P or $ (mixed strategy). • The mixed strategy was not selected therefore preferences reversal is not a violation of independence axiom. • This is an empirical assertion that denies the explanatory power of Holt’s argument and not its logical cogency.

27. Preferences reversal is a real-lab phenomenon • Preferences reversal is observable through different procedures (Camerer 1995). • The lab-reality of the phenomenon is a function of the repeating checking procedures implemented to control for experimental mistakes. • If the phenomenon is real, then the truth-value of the explanatory hypothesis can be tested.

28. Conclusions • Methodological problem of inferring from price-choice reversal data to the phenomenon of preferences reversal. • If the inference is incorrect, then the phenomenon at stake is an artifact and the explanatory hypothesis (preferences responsiveness to the cue dimension of external stimuli) is no testable. • Triangulation method and lab-reality of preferences reversal. • The truth-value of the explanatory hypothesis can be tested.

29. References Becker, G., DeGroot, M., Marschak, J., 1964. Measuring utility by a single-response sequential method. Behavioral Science 9, 226–236. Bogen J. and Woodward J., Saving the phenomena, Philosophical Review, 97: 303-352. Grether D.M. and Plott C., Economic Theory of Choice and the Preference Reversal Phenomenon, The American Economic Review, 69, 4: 623-638. Guala F. (2005), Methodology of Experimental Economics. Cambridge University press. Holt C. A., Preference Reversals and the Independence Axiom, The American Economic Review, Vol. 76, No. 3 (Jun., 1986), pp. 508-515 Samuelson P. (1938), A note on the pure theory of consumer’s behaviour. Economica 17: 61-72.