Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness

Moshe Babaioff, Noam Manaker Morag

Abstract

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.

On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness

Abstract

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.

Paper Structure

This paper contains 40 sections, 32 theorems, 91 equations.

Table of Contents

  1. Introduction
  2. Our Main Result: Ordinal Mechanism Characterization
  3. Implications of Our Main Results
  4. Characterization Results for Cardinal Preferences
  5. Fairness of Truthful Mechanisms
  6. Future Work
  7. Additional Related Work
  8. Mechanism Design for Indivisible Goods
  9. Fair Allocation of Indivisible Goods
  10. The Ordinal Model
  11. Preferences
  12. Mechanisms
  13. Serial-Quota Mechanisms
  14. A Characterization for Strict Ordinal Preferences
  15. Monotonicity
  16. ...and 25 more sections

Key Result

Theorem 1

Let $f$ be a mechanism that allocates a set ${\mathcal{M}}$ of $m$ goods among $n$ agents with preferences from some permutations-closed class of strict preferences ${\mathcal{P}}$ that contains the lexicographic preferences (${\mathcal{P}}\in{\mathcal{F}}_{\neq}({\mathcal{M}})$), when not all goods

Theorems & Definitions (90)

  • Theorem 1
  • Lemma 1
  • Corollary 1
  • Definition 1: Strict preferences
  • Definition 2: Permuted preference
  • Definition 3: Lexicographic preferences
  • Definition 4: Order consistency
  • Definition 5
  • Definition 6: Allocation mechanism
  • Definition 7: Partition mechanism
  • ...and 80 more