“Acceptable social rules would tend to take notice of a variety of other relevant facts in judging the division of the cake: who is poorer than whom, who gains how much in terms of welfare or of the basic ingredients of living, how is the cake being “earned” or “looted” and so on. The insistence that no other information is needed (and that other information, if available, could not influence the decisions to be taken) makes these rules not very interesting for economic decision making. Given this recognition, the fact that there is also a problem of inconsistency—in dividing a cake through votes — may well be seen not so much as a problem, but as a welcome relief from the unswerving consistency of brutal and informationally obtuse procedures.”
Sen is aware that his reasoning is not strict (vide his use of “primarily” and “also”) but, still, he makes the suggestion, which is erroneous.
Indeed, the spirit of “impossibility” is not, I believe, the right way of seeing Arrow’s “impossibility theorem.” [footnote] Arrow provides a general approach to thinking about social decisions based on individual conditions, and his theorem—and a class of other results established after his pioneering work — show that what is possible and what is not may turn crucially on what information is taken into effective account in making social decisions. Indeed, through informational broadening, it is possible to have coherent and consistent criteria for social and economic assessment. The “social choice” literature (as this field of analytical exploration is called), which has resulted from Arrow’s pioneering move, is as much a world of possibility as of conditional impossibilities. [footnote]”
This quote just repeats the error - and adds a string of perceptions to sweeten the cake. The footnotes are references to his “Collective choice and social welfare”, his Handbook contribution and the Nobel lecture, Sen (1999b), and add no news, for us, to the essence discussed here. Indeed, the obviously relevant Nobel lecture just repeats the error.
Hence, Sen basically does not understand the problem. I do value his work on social choice since it was a useful guide to me in making Arrow’s result accessible, and in seeing the various perspectives of it. As Newton is reported to have said: “Standing on the shoulders of giants, we can look further.” I cannot wait till Sen writes me that he enjoys my solution !
Addendum: Mas-colell, Whinston and Green, “Microeconomic Theory”
Andreu Mas-colell, Michael Whinston and Jerry Green ’s 1995 “Microeconomic Theory” is just wonderful. A great book. Generally speaking, though, since they erroneously write: “Either we must give up the hope that social preferences could be rational in the sense introduced in Chapter 1 (i.e. that society behaves as an individual would) or we must accept dictatorship.” (p780). And the subsequent discussion indeed leads the student in the bogs and misdirections so typical of 20th century ‘social choice theory’. The math is OK, but concerns something like the question of how many angels can dance on a pin’s head - and the whole induces the student to become wary of social decision making. (To be sure: I appreciate the other qualities, and have used the book for sections of my Economics Pack.)
35. Without time, no morality
Summary
Theory shows that voting is subject to paradoxes, while it also appears that a voting result is caused as much by the procedure as by the voters’ preferences. From a moral point of view, the choice of the procedure then is the major issue. A key insight is that morality presumes time. In a static world everything is given and there is no place for individuals who have to ponder their moral choices. The real world is dynamic however and the most challenging voting paradoxes concern budget changes. The paper develops a new “Borda Fixed Point” mechanism that provides a better protection to surprises by such budget changes. Under dynamics, Donald Saari’s argument on symmetry is less convincing.