ECONOMY

386 social choice
technology leads to severe inefficiencies due to the free rider problem in the former
model, and to the tragedy of the commons in the latter.
The most interesting characterization results combine (group) strategy-proofness
with normative requirements of fairness, in particular the fundamental horizontal
equity (often called anonymity), requiring that equal messages yield equal allocations.
An anonymous group strategy-proof game form always produces an “envy-free”
allocation (Moulin 1993). The nature of the results (positive, negative, or neutral)
depends much on the nature of the good produced by the shared technology. In
the provision of a pure public good problem we have negative or at best neutral
results: for instance, strategy-proofness is not compatible with the natural standalone
lower bound, computed as the welfare level of an agent who pays the full cost
of the public good (Saijo 1991; Serizawa1999). On the other hand, the production
of a private good yields strikingly positive results: the serial cost-sharing method
emerges as uniquely fair, (group) strategy-proof, and not too inefficient (Moulin and
Shenker 1992; Shenker1995). This method can also be adapted to the provision of an
excludable public good—a non-rival private good (Deb and Razzolini 1999; Moulin
1994; Olszewski2004). A general characterization of (group) strategy-proof social
choice functions that does not use simplifying requirements of fairness may not be
too far from our reach (Leroux 2004; Moulin 1999a).
7 Concluding Comments
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Group strategy-proofness is a tractable requirement in a number of specialized
allocation problems: majority voting with single-peaked preferences, uniform
rationing of a single commodity, assignment of indivisble goods and matching,
serial cost-sharing of a private or excludable public good with increasing marginal
cost. Yet the initial negative results continue to place tight limits on the flexibility
that the strategy-proofness property allows to the mechanism designer. In many
cases we must settle for a less demanding equilibrium concept, hence a less plausible
prediction of implementation, in order to secure an efficient and endstatejust
outcome. The question is now to strike a compromise between two conflicting
objectives:
we want a simple mechanism, with natural message spaces, easily understandable
rules, and a fair distribution of rights (as required by procedural justice).
we want a mechanism implementing the desired social choice function in a
manner as strategically robust as possible (as required by endstate justice).
The precise nature of this trade-off is still far from clear at this point of a research
effort that started nearly three decades ago. For recent surveys of the implementation
problem, the reader may consult Moore (1992) and Jackson (2001).