ECONOMY

380 social choice
A good example where these demanding properties are met is the exchange and
distribution of private goods in a competitive environment: many agents with convex
preferences each with a “small” initial endowment relative to the market size. The
set of (efficient) competitive allocations is then small and coincides with the set
of equilibrium outcomes under a variety of strategic scenarios, both cooperative
(core stability) and non-cooperative (market bidding games) (see e.g. Mas-Colell,
Whinston, and Green 1990).
On the other hand, many procedures commonly used to allocate certain scarce
resources display either a unique but inefficient equilibrium outcome, or a large or
empty set of such equilibria.
Examples of the former include the exploitation of common property resources
under free access (Hardin 1968), and the provision of public goods by voluntary
subscription, the classic exposition of which is by Olson (1965) (seealsoLedyard,
this volume).
Examples of the latter include voting by a qualified majority: the quota is the
relative size of the majority required to pass a motion. With a small quota of 51 per
cent, we only require simple majority and cycles are likely to appear: in this case there
is no equilibrium when coalitions of agents can easily coordinate their actions. If the
quota is large, say 90 per cent, then the equilibrium set is likely to be large: there are
many outcomes z that cannot be defeated by any other outcome z ′ because this would
require that 90 per cent of the voters prefer z ′ to z. (See Nakamura 1979.)
We can speak of private ownership as the natural system of rights when the issue
is to produce and exchange private goods, because the resulting trading game has all
the desirable strategic features, namely a small set of efficient equilibrium outcomes.
But for many important resource allocation problems, no natural system of rights, no
canonical game form stands out to our attention. Examples include:
the quota (size of the qualified majority) we should require to amend the constitution;
how we should regulate access to common property exhaustible resources, so as
to avoid the tragedy of the commons;
how we should produce and trade under decreasing marginal costs, as is the case
for “natural monopolies;”
how we should share costs under widespread externalities.
The point is that any reasonable answer to these questions must take into account
the endstate consequences of the procedure, which procedural justice alone is deliberately
ignoring.
We turn to the central objections to “pure” endstate justice and return to the implementation
problem alluded to in Section 3. As some of the individual characteristics
included in R i are privately known only to the concerned agent (and perhaps to
some of her fellow citizens), the mechanism designer relies on a game form to elicit
these private characteristics, either directly by asking each agent to simply report this
piece of information, or indirectly by designing a game form of which the equilibrium
outcome (or outcomes) is (are) just in the endstate sense. Such a game form,