Min and Maxinduced rankings: an experimental study
 Amélie Vrijdags
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Abstract
The current paper is the first to report an experimental study of “Min and Maxinduced rankings” (MMIR), i.e., a family of set rankings that require preferences over sets to be induced from comparison of the best and/or worst elements within those sets. These MMIR do not perform well in predicting preferences over simple sets of monetary outcomes. In this paper, we investigate the axiomatic underpinnings of these models by means of pairwise choice experiments. From this investigation, some important conclusions can be drawn: Axioms that prevent rankings to be based on totalgoodness, as well as monotonicity conditions (ensuring that replacing a set element with a better one results in a better set) cannot be refuted. Axioms that rule out any utilization of the relative difference in the values of the outcomes and axioms that prevent rankings to be based on averagegoodness are all systematically violated. The Uniform Expected Utility (UEU) criterion seems to meet the apparent shortcomings of the MMIR. Some frequently occurring preference patterns, however, suggest that a significant portion of the participants uses neither a Min or Maxinduced ranking, nor UEU, but some other unspecified decision rule, possibly characterized by the tendency to prefer a diversification of uncertainty.
 Arlegi, R. (2001). Rational evaluation of actions under complete uncertainty. Working paper. Dept. of Economics, University of California, Riverside.
 Arlegi R. (2003) A note on Bossert, Pattanaik and Xu’s choice under complete uncertainty: Axiomatic characterizations of some decision rules. Economic Theory 22: 219–225 CrossRef
 Arlegi R. (2007) Sequentially consistent rules of choice under complete uncertainty. Journal of Economic Theory 135: 131–143 CrossRef
 Arrow K.J., Hurwicz L. (1972) An optimality criterion for decisionmaking under ignorance. In: Carter C., Ford J. (Eds.), Uncertainty and expectations in economics: Essays in honour of G.L.S. Shackle. Basil Blackwell, Oxford, pp 1–11
 Barberà S., Bossert W., Pattanaik P.K. (2004) Ranking sets of objects. In: Barberà S., Hammond P., Seidl C. (Eds.), Handbook of utility theory. Volume 2 Extensions. Kluwer Academic Publishers, Dordrecht, pp 893–977 CrossRef
 Birnbaum M.H. (2004) Test of rankdependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting. Organizational Behaviour and Human Decision Processes 95: 40–65 CrossRef
 Birnbaum M.H. (2008) New tests of cumulative prospect theory and the priority heuristic: Probabilityoutcome tradeoff with branch splitting. Judgment and Decision Making 3: 304–316
 Birnbaum M.H., Bahra J. (2007) Gain–loss separability and coalescing in risky decision making. Management Science 53: 1016–1028 CrossRef
 Birnbaum M.H., Gutierrez R.J. (2007) Testing for intransitivity of preferences predicted by a lexicographic semiorder. Organizational Behavior and Human Decision Processes 104: 96–112 CrossRef
 Birnbaum M.H., Schmidt U. (2008) An experimental investigation of violations of transitivity in choice under uncertainty. Journal of Risk and Uncertainty 37: 77–91 CrossRef
 Birnbaum M.H., Schmidt U. (2010) Testing transitivity in choice under risk. Theory and Decision 69: 599–617 CrossRef
 Bossert W., Pattanaik P.K., Xu Y. (2000) Choice under complete uncertainty: Axiomatic characterization of some decision rules. Economic Theory 16: 295–312 CrossRef
 Cohen M., Jaffray J.Y. (1980) Rational behavior under complete ignorance. Econometrica 48: 1281–1299 CrossRef
 Czerlinski, J., Gigerenzer, G., & Goldstein, D. G. (1999). How good are simple heuristics? In G. Gigerenzer, P. Todd, & The ABC Research Group (Eds.), Simple heuristics that make us smart (pp. 97–118). New York: Oxford University Press.
 Dawes R.M. (1979) The robust beauty of improper linear models in decision making. American Psychologist 34: 571–582 CrossRef
 DeMiguel V., Garlappi L., Uppal R. (2009) Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?. Financial Studies 22: 1915–1953 CrossRef
 Ellsberg D. (1961) Risk, ambiguity and the savage axioms. Quarterly Journal of Economics 75: 643–669 CrossRef
 Gigerenzer, G., & Goldstein, D. G. (1999). Betting on one good reason: The take the best heuristic. In G. Gigerenzer, P. Todd, & The ABC Research Group (Eds.), Simple heuristics that make us smart (pp. 75–95). New York: Oxford University Press.
 Gigerenzer, G., Selten, R. (Eds.). (2001) Bounded rationality: The adaptive toolbox. MIT Press, Cambridge, MA
 Gilboa I., Schmeidler D. (1989) Maxmin expected utility with a nonunique prior. Journal of Mathematical Economics 18: 141–153 CrossRef
 Gravel N., Marchant T., Sen A. (2012) Uniform expected utility criteria for decision making under ignorance or objective ambiguity. Journal of Mathematical Psychology 56: 297–315 CrossRef
 Harless D.W., Camerer C.F. (1994) The predictive utility of generalized expected utility theories. Econometrica 62: 1251–1290 CrossRef
 Hey J.D., Orme C. (1994) Investigating generalizations of expected utility theory using experimental data. Econometrica 62: 1291–1326 CrossRef
 Jaffray J.Y. (1989) Linear utility theory for belief functions. Operations Research Letters 8: 107–112 CrossRef
 Kelsey D. (1993) Choice under partial uncertainty. International Economic Review 34: 297–308 CrossRef
 Luce R.D., Raiffa H. (1957) Games and decisions. Wiley, New York
 Maskin E. (1979) Decisionmaking under ignorance with implications for social choice. Theory and Decision 11: 319–337 CrossRef
 Milnor J. (1954) Games against nature. In: Thrall R., Coombs C., Davis R. (Eds.), Decision processes. Wiley, New York, pp 49–59
 Nitzan S., Pattanaik P.K. (1984) Medianbased extensions of an ordering over a set to the power set: An axiomatic characterization. Journal of Economic Theory 34: 252–261 CrossRef
 Pattanaik P.K., Peleg B. (1984) An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set. Social Choice and Welfare 1: 113–122 CrossRef
 Payne J.W., Bettman J.R., Johnson J.E. (1988) Adaptive strategy selection in decision making. Journal of Experimental Psychology 14: 534–552
 Russo J.E., Dosher B.A. (1983) Strategies for multiattribute binary choice. Journal of Experimental Psychology: Learning, Memory and Cognition 9: 676–696 CrossRef
 Savage J.L. (1956) The foundations of statistics. Wiley, New York
 Simon H.A. (1955) A behavioral model of rational choice. The Quarterly Journal of Economics 69: 99–118 CrossRef
 Simon H.A. (1956) Rational choice and the structure of the environment. Psychological Review 63: 129–138 CrossRef
 Simon H.A. (1990) Invariants of human behavior. Annual Review of Psychology 41: 1–19 CrossRef
 Sopher B., Gigliotti G. (1993) Intransitive cycles: Rational choices or random error? An answer based on estimation of error rates with experimental data. Theory and Decision 35: 311–336 CrossRef
 von Neumann J., Morgenstern O. (1947) Theory of games and economic behavior. Princeton University Press, Princeton, NJ
 Vrijdags A. (2010) An experimental investigation of transitivity in set ranking. Theory and Decision 68: 213–232 CrossRef
 Title
 Min and Maxinduced rankings: an experimental study
 Journal

Theory and Decision
Volume 75, Issue 2 , pp 233266
 Cover Date
 20130801
 DOI
 10.1007/s112380129339y
 Print ISSN
 00405833
 Online ISSN
 15737187
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Decision making
 Set ranking
 Complete uncertainty
 Axiom tests
 Industry Sectors
 Authors

 Amélie Vrijdags ^{(1)}
 Author Affiliations

 1. Department of Data Analysis, Ghent University, Henri Dunantlaan 1, 9000, Ghent, Belgium