Abstract
We use money-metric utility functions as a cardinal utility to define a binary similarity relation between alternatives. That relation is taken into account in ranking opportunity sets, with information about diversity of alternatives being used to reduce the size of large opportunity sets. We provide characterization results for generalizations of several rules proposed for finite sets of alternatives.
Substantial improvements have been made thanks to two anonymous referees.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aizpurua, J.M., Nieto, J., Uriarte, J.R.: Choice procedure consistent with similarity relations. Theory Decis. 29, 235–254 (1990)
Alcantud, J.C.R., Manrique, A.: Continuous representation by a money-metric function. Math. Soc. Sci. 41, 365–373 (2001)
Ballester, M.A., De Miguel, J.R.: Extending an order to the power set: the leximax criterion. Soc. Choice Welf. 21, 63–71 (2003)
Binder, C.: Preference and similarity between alternatives. RMM-Journal 5, 120–132 (2014)
Bossert, W., Pattanaik, P.K., Xu, Y.: Ranking opportunity sets: an axiomatic approach. J. Econ. Theory 63, 326–345 (1994)
Honkapohja, S.: Representing consumer’s tastes in terms Mckenzie expenditure functions: a tribute to Aami Nyberg on his 60th birthday. Acta Academiae Oeconomicae Helsingiensis Series A 52, 31–44 (1987)
Hu, Y.C.: Recommendation using neighborhood methods with preference-relation-based similarity. Inf. Sci. 284, 18–30 (2014)
Lauwers, L., Potoms, T., Vázquez, C.: Addendum to: “Ranking opportunity sets on the basis of similarities of preferences: a proposal”. Math. Soc. Sci. 88, 1–2 (2017)
Mckenzie, L.: Demand theory without a utility index. Rev. Econ. Stud. 24, 185–189 (1957)
Mehta, G.B.: Metric utility functions. J. Econ. Behav. Organ. 26, 289–298 (1995)
Mehta, G.B.: Preference and utility. In: Barberá, S., Hammond, P., Seidl, C. (eds.) Handbook of Utility Theory, pp. 1–47. Kluwer Academic Publishers, Dordrecht (1998)
Mesiar, R.: Fuzzy set approach to the utility, preference relations, and aggregation operators. Eur. J. Oper. Res. 176, 414–422 (2007)
Pattanaik, P.K., Xu, Y.: On diversity and freedom of choice. Math. Soc. Sci. 40, 123–130 (2000)
Rubinstein, A.: Similarity and decision-making under risk (Is there a utility theory resolution to the Allais paradox?). J. Econ. Theory 46, 145–153 (1988)
Samuelson, P.A.: Complementary: an essay on the 40th anniversary of the Hicks-Allen revolution in demand theory. J. Econ. Lit. 12(4), 1255–1289 (1974)
Sen, A.K.: Welfare, preference and freedom. J. Econ. 50, 15–29 (1991)
Vázquez, C.: Ranking opportunity sets on the basis of similarities of preferences: a proposal. Math. Soc. Sci. 67, 23–26 (2014)
Weymark, J.: Money-metric utility functions. Int. Econ. Rev. 28, 219–232 (1985)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Vázquez, C. (2020). Ranking Opportunity Sets Taking into Account Similarity Relations Induced by Money-Metric Utility Functions. In: Bosi, G., Campión, M., Candeal, J., Indurain, E. (eds) Mathematical Topics on Representations of Ordered Structures and Utility Theory. Studies in Systems, Decision and Control, vol 263. Springer, Cham. https://doi.org/10.1007/978-3-030-34226-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-34226-5_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34225-8
Online ISBN: 978-3-030-34226-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)