POLI 100E, Interest Group Politics: Topics 3 and 4

The Geometry of Pluralism

1. For Pluralism to work -- that is, to produce public
   policy that reflects the multiplicity of interests taking
   part in the bargaining process -- there must be multiple
   distinct policy dimensions.
   
   In terms of a geometric (spatial) voting model this means
   that, given a specific group/individal, the public policy
   will be close to that group/individual on some dimensions
   but distant on other dimensions reflecting the tradeoffs
   made during the bargaining process.

   
   Ideal Point:    Xi. = (Xi1, Xi2, Xi3, ... , Xin)
   Policy Outcome: Oj. = (Oj1, Oj2, Oj3, ... , Ojn)
   
        on some dimensions, k, |Xik-Ojk| is small; 
        on some dimensions, h, |Xih-Ojh| is large  
   

2. However, if this is true, social choice theory tells
   us that we will encounter "problems" (see below)
   because multidimensionality allows
   cyclical majorities in legislatures.
   
   For example, suppose there are 3 Alternatives:
   A, B, and C,
   
   and three voting blocs in the legislature of equal size.
   The preferences are:
   
   Bloc 1 (33%): A > B > C
   Bloc 2 (33%): B > C > A
   Bloc 3 (33%): C > A > B
   
   
   1. Binary Voting, A vs. B first Vote, Winner Against C
      
      
   2. Binary Voting, A vs. C first Vote, Winner Against B
      
      
   3. Binary Voting, B vs. C first Vote, Winner Against A
      
      
3. In the geometric (spatial) model of choice, Richard McKelvey
   in his landmark paper "Intransitivities in Multidimensional Voting
   Models and Some Implications for Agenda Control," Journal of
   Economic Theory, 1976, 12:472-482, showed that if someone
   controlled the agenda, that is, what alternatives were
   to be voted on in an assembly and in what order, then any
   outcome was possible, even one remote from all the members
   of the voting body.
   
   McKelvey's "Chaos" Theorem
   
   
4. McKelvey always emphasized that his results were
   due to the fact that social choice took place in a
   highly abstract environment with no institutions.
   
   
5. If a small amount of institutional structure
   is added to these abstract models -- for example,
   restricting individual preferences -- then this tends
   to produce stable sets of outcomes.
   
   
6. Pluralism vs. Social Choice Theory: The
   irony here is that pluralism heaven is one where no permanent
   majority can form. Cross-cutting divisions of society that
   produce different majorities on different issues are regarded
   as good under pluralism but produce cycling in Social
   Choice Theory.
   
   
7. This raises the question: How Multi-Dimensional is actual
   Policy Making in Congress and the U.S. State Legislatures?