Preferences, Summation, and Social Welfare Functions

This paper gives a necessary and sufficient condition for the following proposition, in which ⪯ and ⪯ i for i = 1,…, n are weak orders on a finite set X. There are real-valued functions f 1 , f 2 ,…, f n on X such that, for all x and y in X and i in {1,…,n}x⪯ i y if and only if f i (x) ≤ f i (y), and x ⪯ y if and only if f l (x) + ⋯ + f n (x) ≤ f l (y) + ⋯ + f n (y). The condition can be viewed as an extension of a simple unanimity or dominance condition.

• 저널Management Science · 16(3) · 179–186
• 토픽Game Theory and Voting Systems · Economics and Econometrics
• DOI10.1287/mnsc.16.3.179
• 저자Peter C. Fishburn