The Liberal Paradox: Rights in Social Choice and Judgment Aggregation

Generally, research on collective decision making is interested in finding aggregation rules which limit the influence of any particular individual or subgroup (cf. anonimity etc.). At the same time, a libertarian would hold that any aspect within what we may consider an individual's private sphere should be decided by herself and herself alone.

As Sen (1970) pointed out, such libertarian demands may be inconsistent with upholding the Pareto principle. To understand his famous liberal paradox, consider a situation in which two individuals A and B have to make a collective choice on the color of their houses (which they can paint either white or yellow). Suppose that both prefer yellow for their own houses but really care more about the color of the other's house color which they would rather have in white.

 

Denoting social states by (color of A's house, color of B's house), we have

A: (y,w) > (w,w) > (y,y) > (w,y) and  B: (w,y) > (w,w) > (y,y) > (y,w).

Given all other aspects are fixed, a libertarian rule should let individuals decide the color of their own houses. In particular, the social ranking would have to respect B's preference for (y,y) over (y,w) and A's preference for (y,w) over (w,w). Thus, socially,

(y,y) > (y,w) > (w,w)

in conflict with the Pareto rule - seeing that both A and B prefer (w,w) to (y,y).

 

On a related note (cf. Dietrich & List, 2008), granting (expert) rights in judgment aggregation clashes with requiring precedures to respect unanimous consent. For example, in a version of the doctrinal paradox (see below), consider the following sets of individual judgments:

judge 1: {¬A, ¬B, ¬(A Λ B)} judge 2: {A, ¬B, ¬(A Λ B)} judge 3: {¬A, B, ¬(A Λ B)}.

 

If judge 1 is considered an expert on A, judge 2 an expert on B, - i.e., we grant locally dictatorial decision making power on these issues - we collectively judge A and B to be true. This, however, is inconsistent with unanimous agreement on ¬(A Λ B).

 

Inspired by the above the literature on rights has dealt with relexations of both the Pareto principle and libertarian claims to avoid the paradox. At the same time, researchers have challenged Sen's consequentialist formulation of rights and proposed a procedural formulation of rights in game forms. While this strand of literature has clarified that there is seldom a problem with the existence of rights per se, Sen's paradox resurfaces as inefficiency of equilibria in games of rights exercise.

Claudio Kretz: claudio.kretz∂kit.edu