A given set of agents jointly own and operate a decreasing returns to scale technology (with a single input and a single output). They all contribute some input and receive some of the output. What first best allocation is equitable? We discuss three allocation mechanisms. The Equal Benefits solution gives every agent the same benefit, computed at the supporting price. The Equal Returns solution equalizes returns (output shares/input contributions) across agents. The Constant Returns Equivalent solution gives every agent his indirect utility level at some common price of output relative to input. A lower and an upper bound on individual welfares play a key role in these axiomatic characterization results.

Journal Article The Proportional Veto Principle Get access Hervé Moulin Hervé Moulin CEREMADE Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 48, Issue 3, July 1981, Pages 407–416, https://doi.org/10.2307/2297154 Published: 01 July 1981 Article history Received: 01 June 1980 Accepted: 01 March 1981 Published: 01 July 1981

A binary choice problem with side-payments and quasi-linear utilities is considered. We study two compensation rules, called social choice functions. The egalitarian rule divides equally the surplus above the average utility level. The laissez-faire rule chooses an efficient decision but performs no transfer. Egalitarianism is characterized by a monotonicity axiom called Agreement: no two agents ever disagree in comparing two distinct preferences of a third one. Laissez-fairism is characterized by the No Subsidy axiom: a coalition would not be worse off if the other agents were not present.

In a rationing problem, each agent demands a quantity of a certain commodity and the available resources fall short of total demand. A rationing method solves this problem at every level of resources and individual demands. We impose three axioms: Consistency—with respect to variations of the set of agents—Upper Composition and Lower Composition—with respect to variations of the available resources. In the model where the commodity comes in indivisible units, the three axioms characterize the family of priority rules, where individual demands are met lexicographically according to an exogeneous ordering of the agents. In the (more familiar) model where the commodity is divisible, these three axioms plus Scale Invariance—independence of the measurement unit—characterize a rich family of methods. It contains exactly three symmetric methods, giving equal shares to equal demands: these are the familiar proportional, uniform gains, and uniform losses methods. The asymmetric methods in the family partition the agents into priority classes; within each class, they use either the proportional method or a weighted version of the uniform gains or uniform losses methods.

The author considers fair division when monetary compensations are feasible and utilities are quasi-linear. Four axioms are discussed: individual rationality, resource monotonicity, population solidarity, and the stand alone test. The latter views the utility from consuming all the goods as an upper bound on every coalition's actual (joint) utility. Under efficiency, the four axioms show little compatibility. However, when the goods have enough substitutability in everyone's preferences, the Shapley value of the surplus sharing game satisfies all four axioms. An example is the optimal assignment of indivisible goods when every agent consumes only one good.

In an economy with one public and one private good, egalitarian-equivalent cost sharing consists of finding the highest public good level, x*, such that consuming x* for free yields a feasible utility distribution. The corresponding feasible allocation (typically unique), called egalitarian-equivalent, is in the core of the economy. Conversely, any cost sharing method satisfying Pareto optimality, cost monotonicity (nobody suffers a utility loss if the production technology improves upon, ceteris paribus), and individual rationality (no single-agent coalition objects) or no private transfers (no agent receives a positive amount of private good), must select an egalitarian-equivalent allocation in every economy.

The concept of a dominance solvable voting scheme is presented as a weakening of the strategy-proofness requirement: it relies on successive elimination of dominated strategies and generalizes the well known concept of "sophisticated voting." Dominance solvable decision schemes turn out to contain many usual voting procedures such as voting by veto, kingmaker, and voting by binary choices. The procedure of voting by elimination is proved to be an anonymous dominance solvable voting scheme which always selects an efficient alternative.

A group of peers must choose one of them to receive a prize; everyone cares only about winning, not about who gets the prize if someone else. An award rule is impartial if one's message never influences whether or not one wins the prize. We explore the consequences of impartiality when each agent nominates a single (other) agent for the prize. On the positive side, we construct impartial nomination rules where both the influence of individual messages and the requirements to win the prize are not very different across agents. Partition the agents in two or more districts, each of size at least 3, and call an agent a local winner if he is nominated by a majority of members of his own district; the rule selects a local winner with the largest support from nonlocal winners, or a fixed default agent in case there is no local winner. On the negative side, impartiality implies that ballots cannot be processed anonymously as in plurality voting. Moreover, we cannot simultaneously guarantee that the winner always gets at least one nomination, and that an agent nominated by everyone else always wins.

The authors consider the problem of cost sharing in the case of a fixed group of agents sharing a one input, one output technology with decreasing returns. They introduce and analyze the serial cost sharing method. Among agents endowed with convex and monotonic preferences, serial cost sharing is dominance solvable and its unique Nash equilibrium is also robust to coalitional deviations. The authors show that no other smooth cost sharing mechanism yields a unique Nash equilibrium at all preference profiles.