Social Choice Theory on Chaos Theorem - Dictionary of Arguments
Gaus I 243
Chaos Theorem/Social choice theory/D’Agostino: ((s) This is a special case of problems arising from the situation described by >Arrows Theorem):
Arrow’s theorem/Example: e.g.,
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 S 1: Winner S 1
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.
Chaos theorem: (...) unless there are strong constraints on 'profiles', it is possible to establish a very general result, known in the literature of social choice as the chaos theorem, according to which, as Melvin Hinich and Michael Munger put it, 'it is possible to construct an agenda, or sequence of comparisons of pairs of alternatives, that leads to any alternative .. Choosing an agenda implies a choice of an outcome' (1997(1): 160—1). The situation is 'chaotic', in particular, because the procedure fails to provide any legitimate basis for distinguishing the alternatives
among which individuals are imagined as choosing.
Dynamic cycling: This situation is also, of course, chaotic dynamically, in the sense that any coalition to fix a particular procedure, and thus a particular outcome, can be destabilized. (This is called 'cycling' in the social choice literature.)
Example: Consider Table I of preferences. Both B and C prefer S3 to Sl , and hence could form a coalition against A to fix the agenda (Sl/S2 then S3) that will deliver S3 as the overall result. But both A and B prefer S2 to S3 and, indeed, since B ranks S2 first, A could plausibly appeal to B to abandon her coalition with C and join him in a coalition against C; and so on ad nauseam
(see Mueller, 1989(2): ch. 11.5). >Arrow’sTheorem/D’Agostino.
1. Hinich, Melvin and Michael Munger (1997) Analytical Politics. Cambridge: Cambridge University Press.
2. Mueller, Dennis (1989) Public Choice 11. Cambridge: Cambridge University Press.
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.
|Social Choice Theory
Gerald F. Gaus
Handbook of Political Theory London 2004