Fair Allocation of Indivisible Goods and Criteria of Justice

Abstract

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Fair Allocation of Indivisible Goods

“…In particular, in the context of assignment problems, i.e., when each agent can only receive at most a single good, states that are both efficient and envy-free are known to always exist. This has been shown by Alkan et al [1]. When agents can obtain (and express preferences over) bundles consisting of several goods, there is in general no such guarantee [31].…”

“…1 In this section, we recall the classical Knaster procedure, show how to adapt it to define a payment scheme, and prove a convergence theorem showing that this scheme guarantees outcomes that are both efficient and proportional.…”

“…When agents can obtain (and express preferences over) bundles consisting of several goods, there is in general no such guarantee [31]. But the assumption of quasi-linearity of money is very important here: in this setting, the existence of EEF states can be proven by an argument similar to the one used by Alkan et al [1], appealing to the Duality Theorem [17], as demonstrated by Beviá [2]. When all valuation functions are supermodular, then we can give a very simple existence argument for EEF states, which does not rely on the Duality Theorem.…”

“…There has been some work on procedures for finding EEF states in the social choice literature [1,20,18], albeit with little or no attention to computational issues. The work of Haake et al [18] is particularly interesting.…”

“…The literature on cake-cutting, for instance, is concerned with divisible goods [5,27]. As for indivisible goods, we can distinguish assignment problems [1], where each agent can consume at most a single good, from more general settings where each agent may receive a set (or bundle) of goods [2,31]. If agents can receive sets of goods, and if their preferences over the goods are not additively separable, then fair division becomes a combinatorial optimisation problem.…”