The Decreasing Demand procedure is a procedure for
fair item allocation
Fair item allocation is a kind of the fair division problem in which the items to divide are ''discrete'' rather than continuous. The items have to be divided among several partners who potentially value them differently, and each item has to be gi ...
. It yields a
Pareto-efficient
In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse ...
division that maximizes the rank of the agent with the lowest rank. This corresponds to the
Rawlsian justice criterion of taking care of the worst-off agent.
The procedure was developed by Dorothea Herreiner and
Clemens Puppe
Clemens Dieter Puppe (*14 April 1960 in Heidelberg) is a German economist. He is known for his contributions to individual and collective decision theory (social choice theory).
Clemens Puppe is Professor at Karlsruhe Institute of Technology (K ...
.
Description
Each agent is supposed to have a linear ranking on all bundles of items.
The agents are queried in a round-robin fashion: each agent, in turn, reports his next bundle in the ranking, going from the best to the worst.
After each report, the procedure checks whether it is possible to construct a complete partition of the items based on the reports made so far. If it is possible, then the procedure stops and returns one such partition. If there is more than one partition, then a Pareto-efficient one is returned.
The procedure produces "balanced" allocations, that is, allocations which maximize the rank in the preference ordering of the bundle obtained by the worst-off agent.
Limitations
The procedure requires the agents to rank bundles of items. This is feasible when the number of items is small, but may be difficult when the number of items is large, since the number of bundles grows exponentially with the number of items.
The procedure does not guarantee
envy-freeness
Envy-freeness, also known as no-envy, is a criterion for fair division. It says that, when resources are allocated among people with equal rights, each person should receive a share that is, in their eyes, at least as good as the share received by ...
; see
envy-free item assignment
Envy-free (EF) item allocation is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle that they believe to be at least as good as the bundle of any other agent.
Since the items are ...
for procedures that do guarantee it. However, for two agents, if an envy-free allocation exists, it will be found.
Axiomatization
The allocation returned by the Decreasing Demand procedure - the maximin-rank allocation - satisfies certain natural axioms when there are two agents:
* Pareto-efficiency;
* Anonymity;
* Envy-freeness-if-possible;
* Monotonicity w.r.t. changes in the preferences (more different preferences means a higher utility).
See also
*
Undercut procedure The undercut procedure is a procedure for fair item assignment between two people. It provably finds a complete envy-free item assignment whenever such assignment exists. It was presented by Brams and Kilgour and Klamler and simplified and extende ...
and
envy-graph procedure
The envy-graph procedure (also called the envy-cycles procedure) is a procedure for fair item allocation. It can be used by several people who want to divide among them several discrete items, such as heirlooms, sweets, or seats in a class.
Ideal ...
- two additional procedures based on the ordinal ranking of bundles.
References
{{reflist
Fair division protocols