Fred D’Agostino on Arrow’s Theorem - Dictionary of Arguments
Gaus I 242
Arrow’s Theorem/pluralism/diversity/D’Agostino: Consider a collection of individuals, each of whom has well-behaved preferences (or judgements) over a domain of alternative social arrangements. The problem of collective choice is to specify a procedure, meeting (at least) minimal conditions of fairness, that will deliver a rating of these alternative arrangements, based on individuals' assessments, that is sufficiently determinate to warrant the selection of one of them as the collectively binding arrangement for this group.
Arrow: What Arrow shows, and what much subsequent tinkering has confirmed, is that there is no formal procedure of amalgamation that can be relied on for this purpose (see Arrow, 1979(1); and, for helpful commentary, see Mueller, 1989(2), and Sen, 1970(3)). In so far as a procedure fairly recognizes the antecedent assessments of the various individuals, it will, on certain profiles of assessments, fail to achieve determinacy, and, hence, will fail to identify a collectively binding social arrangement.
D’Agostino: I tried elsewhere (D' Agostino, 1996)(4) to show that this result provides a model for theorizing about ideals, such as 'public reason', that are, at least nowadays, directly associated with liberalism per se (see also Gaus, 1996(5); and D' Agostino and Gaus, 1998(6)).
Democracy/diversity/procedures/Arrow/D’Agostino: the point of Arrow's Theorem is not that formal procedures never work, but rather that they don't always work. And this point is ethico-politically significant for two reasons. 2) When we apply a procedure in concrete circumstances, we typically will not be able to tell, antecedently, whether or not it will work in these circumstances.
2) Even if we can determine that it will not work in these circumstances, we have, according to Arrow's Theorem, no alternative procedure (of the same type) to use instead, except, of course, another that also will not work.
Three Individuals (A, B, C)
Gaus I 243
and three possible social arrangements (S1 , S2, S3),
and (...) individuals' assessments of these arrangements. Given [a specific problematic] 'profile' of preferences (or deliberative judgements) [chosen for the sake of the argument], no merely 'mechanical' procedure of combination will produce a non-arbitrary (and hence legitimately
collectively binding) ranking of the alternative social arrangements:
Table I of preferences
S1: A 1st – B 3rd – C 2nd
S2: A 2nd – B 1st – C 3rd
S 3: A 3rd – B 2nd - C 1st
S1/S2 then S3: Winner: S3
S1/S3 then S2: Winner: S2
S2/S3 then S1: Winner S1
Problem/D’Agostino: (...) it is clear that, on this profile of preferences, a collectively binding choice can be determined mechanically only on an ethico-politically arbitrary basis - e.g. by fixing the order in which alternatives are compared. (The alternative to such arbitrariness is simple indeterminacy: none of the options can be identified as the collectively binding best for the group.) Cf. >Chaos Theorem/Social Choice Theory.
Elections/democracy/solutions: (...) once such diversity among individuals' assessments is 'managed', exactly the indeterminacy of such formal procedures as voting (and other modes of amalgamation) disappears. Suppose, for instance, that through some programme of socialization and education, individuals' assessments are sufficiently 'homogenized' that one of the alternative social arrangements that individuals are assessing is 'dominant' in the sense that it is best from all
relevant points of view. In this case, we might have the configuration in Table II of preferences.
Table II of preferences
S1: A 1st – B 1st – C 1st
S2: A 2nd – B 3rd – C 3rd
S 3: A 3rd – B 2nd - C 2nd
Given this configuration, there would be no difficulty with collective choice, either statically or dynamically. There is a unique collectively best option whose identification as such is not dependent on arbitrary factors and whose selection as such cannot be destabilized (so long as individuals' assessments themselves remain constant).
Value monism/pluralism//D‘Agostino: Of course, Arrow's Theorem, and its extensions, can be read as an argument for monism. Arrow courts chaos in providing, as pluralists would insist, for the recognition of diversity. (For D’Agostino’s solution see >Diversity/Liberalism.)
1. Arrow, Kenneth (1979) 'Values and collective decision making'. In Frank Hahn and Martin Hollis, eds, Philosophy and Economic Theory. Oxford: Oxford University Press.
2. Mueller, Dennis (1989) Public Choice 11. Cambridge: Cambridge University Press.
3. Sen, Amartya (1970) Collective Choice and Social Welfare. San Francisco: Holden-Day.
4. D'Agostino, Fred (1996) Free Public Reason. Oxford: Oxford University Press.
5. Gaus, Gerald (1996) Justificatory Liberalism. Oxford: Oxford University Press.
6. D' Agostino, Fred and Gerald Gaus, eds (1998) Public Reason. Aldershot: Dartmouth.
D’Agostino, Fred 2004. „Pluralism and Liberalism“. In: Gaus, Gerald F. & Kukathas, Chandran 2004. Handbook of Political Theory. SAGE Publications_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Gerald F. Gaus
Handbook of Political Theory London 2004