‘there is no social choice mechanism which satisfies a number of seemingly reasonable conditions’.
(4) I am a bit shocked by Mueller’s (1989, p406-407) discussion of Arrow’s general view. One would expect a more critical attitude, but finds instead:
“The Arrow and Sen theorems (...) raise fundamental questions about the possibility of establishing collective choice procedures satisfying minimally appealing normative properties (...) But the negative side should not be overemphasized. We have suggested that both sorts of paradoxes might be avoided with the use of cardinal, interpersonally comparable utility information. Arrow explicitly eschewed the use of such information, and the independence of irrelevant alternatives [thus Pairwise Decision Making / TC] axiom was imposed to rule out voting procedures that might make use of such information (... But it) is possible that the citizens may be trusted to make these comparisons in an ethically acceptable way.”
Well, interpersonal comparison of course occurs, minimally, when we assign votes to people, assign rights to put topics on ballot, and the like. So interpersonal comparison is not as bad as many economists seem to think. But my solution to Arrow’s difficulty does not rely on cardinality and cardinal comparison. So, disappointingly, Mueller both accepts the idea that Arrow would cause ‘questions’ about the possibility of social choice, and he comes with a wildly wrong conclusion. This is supposed to be a modern textbook !
(5) What is important, is that the development of economic theory and the development of real economies have been hindered by the confusion generated by the standard explanation. Where decision makers were divided, some interested in social welfare and others not, the latter group was provided with decisive gunpowder - and beware of people who have an ideology and even wield a mathematical theorem to prove their lunacy. Generations of students have been taught by Nobel Prize laureats that research into social welfare would be subject to impossibilities. Creative energy has been directed to enlarging the impossibilities rather than to devising structures that might improve practical situations. Practical research into social choice functions and parameters has been aborted, all with reference to a misunderstood theorem !
Economic research also leads to a suggestion of a constitutional amendment, see Colignatus (1996b) and the appendix. I hope that this present chapter helps to clarify that this kind of research is a useful type of economics.
(6) This analysis also clarifies a confusion about the relation of constitutions to the SWF. While many economists argued that constitutions could not be reasonable or morally acceptable, they did accept the Bergson-Samuelson SWF, even though the latter was derived from the former - and nobody seems to care about this inconsistency. Which is now removed, since the properties of the constitution are projected into the SWF.
(7) It is relevant to note that I gave this analysis earlier, in Colignatus (1990c, 1992a). This chapter is almost 99% the same as 1997b, and a a rephrasing of the main principles. I have had no success so far in getting a publication, neither at the CPB nor in a journal. [109]
Conclusion
Arrow’s Theorem has given some problems in the literature, see the quotes above. We have achieved the following solution: