We approach the problem of preference aggregation by endowing both individuals and coalitions with partially-ordered or incomplete cardinal preferences. Consistency across preferences for coalitions comes in the form of the Extended Pareto Rule: if two disjoint coalitions A and B prefer x to y, then so does the coalition A [ B. The Extended Pareto Rule has important consequences for the social aggregation of individual preferences. Restricting attention to the case of complete individual preferences, and assuming complete preferences for some pairs of agents (interpersonal comparisons of utility units), we discover that the Extended Pareto Rule imposes a " no arbitrage " condition in the terms of utility comparison between agents. Furthermore, if all the individuals and pairs have complete preferences and certain non-degeneracy conditions are met, then we witness the emergence of a complete preference ordering for coalitions of all sizes. The corresponding utilities are a weighted sum of individual utilities, with the n ¡ 1 independent weights obtained from the preferences of n ¡ 1 pairs forming a spanning tree in the group.
[1]
Martin Shubik,et al.
Game Theory in Economics: Chapter 4, Preferences and Utility
,
1974
.
[2]
M. Fleming,et al.
A Cardinal Concept of Welfare
,
1952
.
[3]
Amartya Sen,et al.
Interpersonal Comparison and Partial Comparability: A Correction
,
1972
.
[4]
Rubin Saposnik.
SOCIAL CHOICE WITH CONTINUOUS EXPRESSION OF INDIVIDUAL PREFERENCES
,
1975
.
[5]
R. Aumann.
UTILITY THEORY WITHOUT THE COMPLETENESS AXIOM
,
1962
.
[6]
Amrita Dhillon.
Extended Pareto rules and relative utilitarianism
,
1998
.
[7]
Charles R. Plott,et al.
A Welfare Function Using "Relative Intensity" of Preference
,
1971
.
[8]
David Schmeidler,et al.
Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture
,
1977
.
[9]
J. Harsanyi.
Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility
,
1955
.