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Dichotomous preferences and the possibility of Arrovian social choice

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Abstract

Consider an individual whose judgments are always based on a fundamental criterion such as a political ideology or a religious doctrine. In a choice situation, he always prefers any alternative that is compatible with the criterion to any that is not. When individuals are allowed to have preference spaces restricted in this manner, we investigate Arrow-consistent domains. We observe that a diversity of attitudes is essential in order to escape an Arrovian impossibility.

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Notes

  1. For a set A, ∣A∣ denotes its cardinality.

  2. This condition is restricted by the numbers of individuals and alternatives. For example, it is easy to check that when the number of individuals is two and the number of alternatives is nine, there is no dichotomous net.

  3. It is also possible to consider the case when G 1 and G 2 intersect. However, we do not deal with this case here to simplify the discussion.

  4. Arguments similar to this lemma can be found in Kalai et al. (1979) and Le Breton and Weymark (2002).

  5. The basic line of our proof is due to Fishburn (1976) and Suzumura and Xu (2004, Theorem 4).

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Authors and Affiliations

  1. Faculty of Economics and IGSSS, Yokohama National University, 79-3 Tokiwadai Hodogaya-ku, Yokohama, 240-8501, Japan

    Toyotaka Sakai

  2. Faculty of Economics, Hannan University, 5-4-33, Amamihigashi, Matsubara, Osaka, 580-8502, Japan

    Masaki Shimoji

Authors
  1. Toyotaka Sakai
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  2. Masaki Shimoji
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Corresponding author

Correspondence to Toyotaka Sakai.

Additional information

This paper received the Kanematsu Fellowship from RIEB, Kobe University in May 2002. We are much indebted to two anonymous referees of this journal, three anonymous referees of the Kanematsu Fellowship, Jun Iritani, William Thomson, and John Weymark for helpful comments. We also thank Takashi Kamihigashi, Tetsuya Kishimoto, Ryo-ichi Nagahisa, Hiroaki Nagatani, Tadashi Sekiguchi, Koji Shimomura, Tomoichi Shinotsuka, Koichi Suga, Makoto Tanaka, Ken Urai, and participants at the Kobe-Osaka Joint Seminar in Mathematical Economics at Osaka University in March 2001, the meeting of the Japanese Economic Association at Hiroshima Syudo University in May 2001, the Far Eastern Meeting of the Econometric Society in Kobe in July 2001, the Seventh Decentralization Conference at Waseda University in October 2001, the Sixth International Meeting of the Society for Social Choice and Welfare at Caltech in July 2002 for valuable suggestions. The first version was written while we were graduate students in Economics at Kobe University.

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Sakai, T., Shimoji, M. Dichotomous preferences and the possibility of Arrovian social choice. Soc Choice Welfare 26, 435–445 (2006). https://doi.org/10.1007/s00355-005-0028-4

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  • DOI: https://doi.org/10.1007/s00355-005-0028-4

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