Lars-Gunnar Svensson

Large Indivisibles: An analysis with respect to price equilibrium and fairness

An exchange economy is considered in which there are a finite number of individuals, the same number of indivisibles, and a fixed amount of a divisible good. Each individual consumes exactly one of the indivisibles and a certain quantity of the divisible good. The existence of prices corresponding to Pareto-efficient allocations is proved. It is also shown that this economy possesses fair allocations, income-fair allocations, coalition-fair allocations, and Pareto-efficient egalitarian-equivalent allocations. IN THIS STUDY the effect of including large indivisibles in an exchange economy will be analyzed. The analysis will be carried out with respect to the existence of price equilibrium and with respect to the existence of different forms of fairness. The economy consists of a finite number of individuals, the same number of indivisibles, and a fixed amount of a divisible good. It is assumed that each individual consumes exactly one of the indivisibles and some quantity of the divisible good. We may interpret the indivisibles as being professions or houses. The relationship between price equilibrium and a Pareto-efficient allocation is well-known and proved in a number of cases under different assumptions about preferences and commodities. For a standard economy see, e.g., Debreu [5]. In case of nonconvexities, which may also describe a certain type of indivisibility, we may have an exact relationship in economies with a continuum of individuals (see, e.g., Hildenbrand [11]), but otherwise an approximate relationship obtains. The degree of approximation depends on the degree of nonconvexities in preferences, and not on the number of individuals (see, e.g., Arrow and Hahn [1]). We will prove the existence of prices characterizing a Pareto-efficient allocation in a case where the indivisibles play an essential role and where approximate results would be too approximate. The indivisibles may be considered large for the individual compared to his total consumption. The theory of fairness has developed considerably during the seventies. Different kinds of concepts of fairness have been introduced and analyzed; see Daniel [41, Foley [81, Pazner and Schmeidler [121, and Schmeidler and Vind [141, among others. Normally, these authors have considered models with divisible goods or an infinite number of individuals. For exchange economies the existence of fair allocations (an envy-free and Pareto-efficient allocation) has been proved in

Queue Allocation of Indivisible Goods

A model with a finite number of indivisible goods (houses) and the same number of individuals is considered. The allocation of houses among the individuals according to a queue order is analysed. First an allocation mechanism is constructed where it is a dominant strategy for the individuals to truthfully report their preferences. Second it is demonstrated that in order to obtain the desired allocation, the individuals must not in general report their complete ranking of the houses, but only their maximal elements in recursively defined choice sets.Financial support from Jan Wallanders Foundation for Research in the Social Sciences is gratefully acknowledged.

Non-manipulable assignment of individuals to positions revisited

This paper investigates an allocation rule that fairly assigns at most one indivisible object and a monetary compensation to each agent, under the restriction that the monetary compensations do not exceed some exogenously given upper bound. A few properties of this allocation rule are stated and the main result demonstrates that the allocation rule is coalitionally strategy-proof.

Strategy-proof voting on the full preference domain

In analyses of strategy-proof voting, two results feature prominently: the dictatorial characterization contained in the Gibbard-Satterthwaite theorem and the voting by committees characterization in the Barbera-Sonnenschein-Zhou theorem. The two theorems are based on voting procedures defined on the domain of strict preferences. In the present study, we derive corresponding results for voting schemes defined on the full domain of weak preferences and obtain a characterization by means of a combination of sequential dictatorship and voting by extended committees.

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set

Least manipulable Envy-free rules in economies with indivisibilities

{A_{1}\times \cdots \times A_{m}}

Fairness, the Veil of Ignorance and Social Choice

. The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods Ak is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set