ECONOMY

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Endstate justice: fair outcome. Endstate justice is a judgment on the profile
(R 1 ,...,R n ) of individual characteristics and the state of the world z, deciding
whether this particular endstate is equitable at this particular profile. The equity
criteria bear on the individual welfare levels, as well as on the endstate.
The most popular criterion is an index of collective utility, aggregating cardinal
measures of individual welfare (Blackorby and Bossert, this volume). An alternative
route eschews cardinal measures of welfare and relies only on the profile of ordinal
preference orderings, together with some physical characteristics of the endstate. A
very influential instance of this ordinal interpretation of endstate justice is the test of
“No Envy.” We are dividing a given bundle of resources (a “cake”) among participants
endowed with identical property rights over the resources, and different preferences
over the various shares of resources. Everyone cares only about the share she receives.
We say that a particular division of the cake is “envy free” if no participant prefers
the share of someone else to her own share. For instance, the outcome of the Divide
and Choose procedure is envy free if the Divider prudently cuts two pieces of equal
value (to him). For very general division problems, a systematic way to obtain an
envy free and Pareto optimal allocation is to endow each participant with an equal
share of the resources and compute a competitive equilibrium from these egalitarian
property rights. See Moulin and Thomson 1997 for a review of the No Envy test and of
competing ordinal interpretations of endstate justice in microeconomic fair division
problems.
In some important problems of fair division, individual characteristics capture
the pattern of responsibilities in the production of a joint surplus or cost. A typical
example involves a scholar delivering lectures in several different cities: the question
is to divide fairly her total travel cost between her successive hosts. We know the cost
of her entire trip, as well as the (presumably lower) cost of all trips in which she
would have visited only a subset of the original cities. The celebrated formula known
as the “Shapley value” proposes to compute the cost share of each city as follows:
order the cities arbitrarily and compute the incremental cost share of a given city (the
cost of adding this city to the set of cities preceding it in the given order); then take
the average of these incremental shares over all orderings, each with equal probability.
The normative properties of the Shapley value, and of several extensions and variants,
are the subject of much axiomatic research (see Moulin 2002; Moulin and Sprumont
2005;Sprumont1998;Thomson2003).
The normative statement of endstate justice is oblivious to any particular procedure
we may use to implement a particular endstate. The information about
individual characteristics relevant to the computation of a just endstate is private
to each participant, and must be somehow retrieved from these agents. As
discussed in the following sections, this elicitation process is not straightforward,
because rational selfish agents cannot be expected to report their private information
truthfully, if they can improve their welfare by not doing so. This is the familiar
“incentive compatibility” issue: because crucial information is dispersed, the
process of gathering it to determine a just endstate is a strategic game G, exactly
as in the previous section. This game must be carefully designed to allow proper