The importance of incompleteness

• DOI: http://doi.org/10.1111/ijet.12145
• Date: 01 March 2018
• Published date: 01 March 2018
• Author: Amartya Sen

The importance of incompleteness

Amartya Sen

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Kotaro Suzumura can be seen as the most complete social choice theorist the subject has ever

had. No area of social choice has failed to benefit from Suzumura’s penetrating analyses. Among

the many important contributions made by Suzumura is the use of the idea of incompleteness of

evaluation in his analysis of consistency, particularly in the form of what has come to be called

‘‘Suzumura consistency’’. In this paper I explore the need for allowing – and incorporating –

incompleteness of preferences in choice theory in general and social choice in particular. This is

followed by a number of critical enquiries. Why is incompleteness important? How does it arise

as an essential part of rational reflections? What are its implications (i) for prudential decisions,

and (ii) for ethical judgments? Finally, how should making room for incompleteness influence

theories of justice?

Key words Suzumura, Suzumura consistency, incompleteness, partial ordering, justice, global

justice

JEL classification D01, D63, D71

Accepted 22 December 2017

1 Introduction

Kotaro Suzumura can be seen as the most complete social choice theorist the subject has ever had.

There is no area of social choice that has failed to benefit from Suzumura’s penetrating insights and

far-reaching analyses. The birth of the subject might go back to the Marquis de Condorcet in the

eighteenth century and the establishment of the modern discipline of social choice theory to Kenneth

Arrow’s pioneering departure in 1950, but every branch of what is now a very large discipline bears

the strong imprint of Suzumura’s creativity. The entire subject would be very different today, but for

(and here I speak with well-grounded pride) my friend Kotaro’s outstanding work.

2 Suzumura consistency

Among the many important contributions made by the most complete of all social choice theorists is

the use of the idea of incompleteness of evaluation in his analysis of consistency, particularly in the

form of what has come to be called in the choice literature ‘‘Suzumura consistency.’’ Suzumura

consistency takes us towards maximality, rather than full optimality. Suzumura consistency is a

weaker demand than having a transitive ordering, but the difference disappears when the ranking is

complete (the rather trivial requirement of reflexivity that each xis taken to be as good as itself 

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Department of Economics, Harvard University, Cambridge, MA, USA. Email: asen@fas.harvard.edu

doi: 10.1111/ijet.12145

International Journal of Economic Theory 14 (2018) 9–20 ©IAET 9

International Journal of Economic Theory