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The greatest unhappiness of the least number

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Walter Bossert
Walter Bossert
Walter Bossert
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Kotaro Suzumura
Kotaro Suzumura
Kotaro Suzumura
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Abstract

We propose an alternative articulation of the Benthamite greatest-happiness-of-the-greatest-number principle. With ordinally measurable and interpersonally non-comparable utilities, the rule chooses those feasible alternatives that maximize the number of individuals who end up with their greatest element. This rule is tantamount to the plurality rule. Furthermore, in the spirit of Rawls’s maximin principle, we propose the greatest-unhappiness-of-the-least-number principle. In analogy to the greatest-happiness principle, the least-unhappiness principle is formally equivalent to the anti-plurality rule. Our main result is a characterization of the least-unhappiness principle.
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Soc Choice Welf (2016) 47:187–205
DOI 10.1007/s00355-016-0951-6
The greatest unhappiness of the least number
Walter Bossert1·Kotaro Suzumura2
Received: 8 December 2015 / Accepted: 6 February 2016 / Published online: 22 February 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract We propose an alternative articulation of the Benthamite greatest-happiness-
of-the-greatest-number principle. With ordinally measurable and interpersonally
non-comparable utilities, the rule chooses those feasible alternatives that maximize
the number of individuals who end up with their greatest element. This rule is tanta-
mount to the plurality rule. Furthermore, in the spirit of Rawls’s maximin principle,
we propose the greatest-unhappiness-of-the-least-number principle. In analogy to the
greatest-happiness principle, the least-unhappiness principle is formally equivalent to
the anti-plurality rule. Our main result is a characterization of the least-unhappiness
principle.
This paper is dedicated to John Roemer with our compliments, who has been one of the major
contributors on theories of justice in such various disciplines as economics, philosophy, and political
science; see, for example, Roemer (1996). We thank Thierry Marchant and several seminar audiences for
their comments and suggestions. Financial support from a Grant-in-Aid for Specially Promoted Research
from the Ministry of Education, Culture, Sports, Science and Technology of Japan for the Project on
Economic Analysis of Intergenerational Issues (Grant number 22000001), the Fonds de Recherche sur la
Société et la Culture of Québec, and the Social Sciences and Humanities Research Council of Canada is
gratefully acknowledged.
BWalter Bossert
walter.bossert@videotron.ca
Kotaro Suzumura
ktr.suzumura@gmail.com
1Centre Interuniversitaire de Recherche en Economie Quantitative (CIREQ), P.O. Box 6128,
Station Downtown, Montreal, QC H3C 3J7, Canada
2School of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku,
Tokyo 169-8050, Japan
123
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... Another prominent example is the plurality voting rule. As discussed in Bossert and Suzumura (2016), this voting procedure can also be viewed as an expression of Bentham's (1776) greatest-happiness-of-the-greatest-number principle if Bentham's dictum is given an ordinalist interpretation. That Bentham himself may have been an ordinalist is suggested in a citation by Mitchell in his "Bentham's felicific calculus" (Mitchell 1937, p. 184), according to which Bentham states that " 'Tis in vain to talk of adding quantities which after the addition will continue distinct as they were before, one man's happiness will never be another man's happiness: a gain to one man is no gain to another: you might as well pretend to add 20 apples to 20 pears". ...
... The equity-oriented counterpart of the greatest-happiness principle is the greatestunhappiness-of-the-least-number principle; see, again, Bossert and Suzumura (2016). ...
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