Abstract
In this work we generalize classical Decision Theory by considering that a preference relation might not be total. Incomplete preferences may be helpful to represent those situations where, due to lack of information, the decision maker would like to maintain different options alive and defer the final decision. In particular, we show that, when totality is pulled out, different formalizations of classical Decision Theory become not equivalent. We provide a hierarchical characterization of such formalizations and show that some derived properties of classical Decision Theory, such as justification, no longer hold. Consequently, whenever profitable, justification has to be reintroduced into the theory as an independent axiom.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Anisetti, M., Ardagna, C.A., Bonatti, P.A., Damiani, E., Faella, M., Galdi, C., Sauro, L.: E-Auctions for multi-cloud service provisioning. In: Proc. of the IEEE International Conf. on Services Computing, SCC 2014, Anchorage, AK, USA, 27 June–2 July 2014
Aumann, R.J.: Subjective programming. Econometric Res. Prog. Re-search memorandum vol. 22, Princeton University (1961). Also in Shelly, M.W., Bryan, G.L., (eds.) Human judgments and optimality. Wiley, New York (1964)
Aumann, R.J.: Utility Theory without the Completeness Axiom. Econometrica 30(3), 445–462 (1962)
Bonatti, P.A., Faella, M., Galdi, C., Sauro, L.: Towards a mechanism for incentivating privacy. In: Atluri, V., Diaz, C. (eds.) ESORICS 2011. LNCS, vol. 6879, pp. 472–488. Springer, Heidelberg (2011)
Bonatti, P.A., Faella, M., Sauro, L.: Partial preferences for mediated bargaining. In: Proc. of the 2nd International Workshop on Strategic Reasoning, SR14, Grenoble, France, 5–6 April 2014
Bonatti, P.A., Faella, M., Galdi, C., Sauro, L.: Auctions for partial heterogeneous preferences. In: Proc. of Mathematical Foundations of Computer Science 2013–38th International Symposium, MFCS 2013, Klosterneuburg, Austria, 26–30 August 2013
Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H.H.: CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements. Journal of Articial Intelligence Research 21, 135–191 (2004)
Dubra, J., Maccheroni, F., Ok, E.A.: Expected utility theory without the completeness axiom. Journal of Economic Theory 115(1), 118–133 (2004)
Myerson, R.B.: Game Theory: Analysis of Conict. Harvard University Press (1997)
van Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press (1994)
Savage, L.J.: The Foundations of Statistics. Wiley, NewYork (1954)
Simon, H.: A Behavioral Model of Rational Choice. Q. J. Econ. 69(1), 99–118 (1955). doi:10.2307/1884852
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Sauro, L. (2015). On the Hierarchical Nature of Partial Preferences. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds) PRIMA 2015: Principles and Practice of Multi-Agent Systems. PRIMA 2015. Lecture Notes in Computer Science(), vol 9387. Springer, Cham. https://doi.org/10.1007/978-3-319-25524-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-25524-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25523-1
Online ISBN: 978-3-319-25524-8
eBook Packages: Computer ScienceComputer Science (R0)