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Strategy-proof and fair reallocation with single-peaked preferences

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Abstract

We consider the strategy-proof rules for reallocating individual endowments of an infinitely divisible good when agents’ preferences are single-peaked. In social endowment setting, the seminal work established by Sprumont (Econometrica 59:509–519, 1991) proves that the uniform rule is the unique one which satisfies strategy-proofness, efficiency, and envy-freeness. However, the uniform rule is not so appealing in our model since it disregards the differences in individual endowments. In other words, the uniform rule is not individually rational. In this paper, we propose a new rule named the uniform proportion rule. First, we prove that it is the unique rule which satisfies strategy-proofness, efficiency, and envy-freeness on proportion and we show that it is individually rational. Then, we show that our rule is indeed a member of the class of sequential allotment rules characterized by Barberà et al. (Games Econ Behav 18:1–21, 1997).

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Notes

  1. An agent is a demander (respectively, supplier) whenever his endowment is strictly less (respectively, greater) than his peak. The formal definition is given in Sect. 2.

  2. The concept of envy-freeness in terms of allotment changes, called fair net trade, was formulated by Kolm (1972) and Schmeidler and Vind (1972) in the more general context of exchange economies.

  3. See also Klaus et al. (1997), Klaus (2001), and Moreno (2002).

  4. There are many interesting axiomatic studies on the uniform rule, for example, Ching (1992, 1994), Mizobuchi and Serizawa (2006), Sakai and Wakayama (2012) and Sönmez (1994).

  5. By feasibility, \( \lambda \) can be precisely computed as \( \lambda = \frac{E - \sum _ {i \in N^{*}(R)}p(R_i)}{\sum _ {j \notin N^{*}(R)}e_j}\).

  6. See Klaus et al. (1997) and Hashimoto and Wakayama (2021).

  7. This is based on the idea of an anonymous referee.

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Acknowledgements

We would like to thank an associate editor, two anonymous referees, Yuji Fujinaka, Kazuhiko Hashimoto, Osamu Hayashida, Kosuke Hirose, Tomoyuki Kamo, Toshiji Miyakawa, Akitoshi Muramoto, Shohei Tamura and Takuma Wakayama for helpful suggestions and comments. This research was partially supported by JSPS KAKENHI Grant Number 21K01384.

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  1. Faculty of Economics, Tohoku University, Sendai, Miyagi, 980-8576, Japan

    Zhen Zhao & Shinji Ohseto

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  1. Zhen Zhao
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  2. Shinji Ohseto
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Correspondence to Zhen Zhao.

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Zhao, Z., Ohseto, S. Strategy-proof and fair reallocation with single-peaked preferences. Soc Choice Welf 58, 791–800 (2022). https://doi.org/10.1007/s00355-021-01374-3

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