ECONOMY

378 social choice
discovery of the necessary information. Yet in the context of endstate justice, neither
the design of G, nor the behavior of its players has any normative content. The
judgement of justice is entirely ex post, oblivious to the means by which the endstate
is reached.
Procedural justice: fair play. Procedural justice is a judgement on the game form G
itself, independent of the way the game is subsequently played by the agents, and of
the particular endstate that results. The normative discussion is limited to the rules of
the game (the procedure); no outcome (endstate) can be called unfair if the rules have
been scrupulously observed while the game was played, just as a fair lottery cannot
produce an unfair outcome. This time the judgement of justice is entirely ex ante; it
bears only on the means regardless of the ends.
Consider Divide and Choose. If we deem this procedure fair to divide a certain
cake among two given agents, then it does not matter if the Divider plays the game
well or not. If she has some idea about the preferences of the Chooser, she may be
able to obtain a share worth more than one half (to her), provided her expectation of
the chooser’s behavior is correct; if she is wrong and ends up with a share worth less
than one half, she can only blame herself, not the procedure.
Naturally, a fair procedure may yield an unfair endstate, and a fair endstate may
result from an unfair procedure.
Examples of the former include provision of a public good by voluntary subscription,
where a single agent often ends up bearing the entire cost of the good (see
Ledyard, this volume). Indeed, if Ann likes the good enough that she is willing to
pay the full price of the public good, every other agent will gladly get a free ride and
this is a Nash equlibrium configuration. Another instance is when fair competition
results in a blatantly unfair endstate. The canonical example is the celebrated “gloves
market” with 101 owners of a right glove and 100 owners of a left glove. Assume a
pair of gloves is worth $1 but a single glove is worthless. If the price of a right glove is
positive, there is excess supply of these gloves; a price of zero for the right gloves is the
only way to balance demand and supply. Then the owners of a left glove each get one
right glove so that the competitive equilibrium gives all the surplus to the left glove
owners.
Examples of the latter include the choice of the “just” candidate by a benevolent
dictator; or the envy-free division of the cake between two agents by the Divide and
Choose game form. In this asymmetric game form, the Divider cuts the pie in two
shares among which the Chooser picks the one she prefers. In this game both agents
can guarantee that their share is at least as valuable (to them) as the other share: the
Divider can cut to shares of equal value to him.
Endstate justice and procedural justice pursue similar goals. They look for
“solutions” to simple problems of resource allocations and justify these solutions
by a suitable set of axioms (normative requirements). Under procedural justice this
solution is a distribution of rights, a game form; under endstate justice it is a social
choice function, associating an outcome deemed just to every profile of individual
characteristics.