Egalitarian equivalence (EE) is a criterion of fair division.
In an egalitarian-equivalent division, there exists a certain "reference bundle"
The EE fairness principle is usually combined with Pareto efficiency.
: An allocation is called PEEEA if it is both Pareto-efficient and egalitarian-equivalent.
The EE criterion was introduced by Elisha Pazner and David Schmeidler in 1978.
[1] [2] Previously, the main fairness criterion in economics has been envy-freeness (EF).
EF has the merit that it is an ordinal criterion --- it can be defined based only on individual preference-relations; it does not need to compare utilities of different agents, or to assume that the agents' utility functions are normalized.
However, EF might be incompatible with Pareto efficiency (PE).
In particular, in a standard economy with production, there may be no allocation which is both PE and EF.
[3] EE, like EF, is an ordinal criterion --- it can be defined based only on individual preference-relations.
Pazner and Schmeidler informally describe a PEEEA as follows: As a special case, assume that there is a finite number of homogeneous divisible goods.
Note that the maximin principle depends on numeric utility.
Herve Moulin describes this special case of the EE rule as follows:[4]: 242 The following example is based on.
[4]: 240–243 The question is how to divide the 100 units of capacity in each road among the 100 agents?
The utilities of the AB and BC agents are as above, but the utility of the AC agents when getting x units of AB and y units of BC is now (x+y)/2.
Note that it is normalized such that their utility from having a unit of each resource is 1.
To summarize: in this example, a divider who believes in the importance of egalitarian-equivalence must choose between equitability and envy-freeness.
[1] However, with three or more agents, the set of PE allocations that are both EE and EF might be empty.
[6] In the special case in which the reference bundle contains a constant fraction of each good, the PEEEA rule has some more desirable properties:[4]: 248–251 However, it is lacking some other desirable properties: In some settings, the PEEEA rule is equivalent to the Kalai-Smorodinsky bargaining solution.