ECONOMY

hervé moulin 379
4 The Complementarity of Endstate
and Procedural Justice
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We develop the commonplace “means matter as well as ends” in the context of the
general model of Section 2.
Procedural justice is not concerned with the strategic properties of the procedure.
Whether or not the game has a zero, many, or single equilibrium outcome does not
matter. Even irrational actions by the agents are of no concern: my negative freedom
includes the privilege of being unpredictable (Berlin 1969). A serious objection to
this position comes from the familiar concept of efficiency, also known as Pareto
optimality. An outcome z (endstate) is Pareto optimal (efficient) if there exists no
otherfeasibleoutcomewhichisweaklypreferredtoz by all agents, and strictly
preferred to z by at least one agent. This is the only rationality test of the endstate
that is common to all doctrines of the social order derived from methodological
individualism.
In our model, the requirement of efficiency means that upon playing the game G,
an efficient outcome should result. This forces our attention to the strategic properties
of G. In particular,
suppose that the game G has no equilibrium for some profile of individual
characteristics. This precludes rational behavior by the participants: anything can
happen, including inefficiencies. A typical example is majority voting when the
majority relation has a cycle. Where we stop in the cycle may be a matter of
pure luck, or of who is able to control the agenda of the relevant committee. The
cycles of the majority relation encompass large subsets of inefficient outcomes so
there is the very real possibility of an inefficient endstate. This point is emphatically
demonstrated by McKelvey’s theorem (McKelvey 1976) in the spatial voting
context.
symmetrically, suppose our game G has a large set of equilibrium outcomes,
then the selection of a particular endstate is a difficult coordination problem.
If the coordination fails, inefficiency is to be expected. The standard example
is the division of a surplus by means of the Nash demand game. Each player
independently requests a share of a dollar. If the demands are compatible, they
are satisfied; otherwise everyone goes home empty handed. Any division of the
dollar between the players is a legitimate (and efficient) equilibrium of the game.
However, the definition of the game does not help the participants to coordinate
their demands on a particular division of the dollar. If they choose their demands
independently, chances are they will not be compatible, resulting in an inefficient
endstate.
To meet the compelling requirement of endstate efficiency, the game form must
have a unique equilibrium outcome (or at least a small set of such outcomes), moreover
this outcome must pass the test of Pareto optimality.