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Majoritarian Group Actions

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PRIMA 2015: Principles and Practice of Multi-Agent Systems (PRIMA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9387))

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Abstract

In this paper, we introduce a logic to reason about group actions for groups that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The logic of action that we use here for modelling group actions is based on a substructural propositional logic that allows for preventing inconsistent outcome. Agency is modeled by means of a “bringing-it-about” modal logic with coalitions. We show that, in this way, it is possible to obtain a consistent model of agency of groups that are defined in an aggregative manner.

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References

  1. Avron, A.: The semantics and proof theory of linear logic. Theor. Comput. Sci. 57, 161–184 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Boella, G., Pigozzi, G., Slavkovik, M., van der Torre, L.: Group intention is social choice with commitment. In: De Vos, M., Fornara, N., Pitt, J.V., Vouros, G. (eds.) COIN 2010. LNCS, vol. 6541, pp. 152–171. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Campbell, D.E., Kelly, J.S.: A strategy-proofness characterization of majority rule. Economic Theory 22(3), 557–568 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chellas, B.: Modal Logic: An Introduction. Cambridge University Press (1980)

    Google Scholar 

  5. Elgesem, D.: The modal logic of agency. Nordic J. Philos. Logic 2(2) (1997)

    Google Scholar 

  6. Endriss, U., Grandi, U., Porello, D.: Complexity of judgment aggregation. Journal of Artificial Intelligence Research 45, 481–514 (2012)

    MathSciNet  MATH  Google Scholar 

  7. Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50(1), 1–101 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Girard, J.-Y.: Linear logic: its syntax and semantics. In: Proceedings of the Workshop on Advances in Linear Logic, pp. 1–42. Cambridge University Press, New York (1995)

    Google Scholar 

  9. Governatori, G., Rotolo, A.: On the Axiomatisation of Elgesem’s Logic of Agency and Ability. Journal of Philosophical Logic 34, 403–431 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. List, C.: Three kinds of collective attitudes. Erkenntnis 79(9), 1601–1622 (2014)

    Article  MathSciNet  Google Scholar 

  11. List, C., Pettit, P.: Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18(1), 89–110 (2002)

    Article  Google Scholar 

  12. List, C., Pettit, P.: Group Agency. The possibility, design, and status of corporate agents. Oxford University Press (2011)

    Google Scholar 

  13. List, C., Puppe, C.: Judgment aggregation: a survey. In: Handbook of Rational and Social Choice. Oxford University Press (2009)

    Google Scholar 

  14. Moulin, H., Peleg, B.: Cores of effectivity functions and implementation theory. Journal of Mathematical Economics 10(1), 115–145 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ono, H.: Substructural logics and residuated latticesan introduction. Springer (2003)

    Google Scholar 

  16. Paoli, F.: Substructural logics: a primer, vol. 13. Springer Science & Business Media (2002)

    Google Scholar 

  17. Pauly, M.: A modal logic for coalitional power in games. J. Log. Comput. 12(1), 149–166 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Porello, D.: Ranking judgments in arrow’s setting. Synthese 173(2), 199–210 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Porello, D.: A proof-theoretical view of collective rationality. In: IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3–9, 2013 (2013)

    Google Scholar 

  20. Porello, D., Endriss, U.: Ontology merging as social choice: Judgment aggregation under the open world assumption. Journal of Logic and Computation 24(6), 1229–1249 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. Porello, D., Troquard, N.: A resource-sensitive logic of agency. In ECAI 2014–21st European Conference on Artificial Intelligence, August 18–22, 2014, Prague, Czech Republic - Including Prestigious Applications of Intelligent Systems (PAIS 2014), pp. 723–728 (2014)

    Google Scholar 

  22. Porello, D., Troquard, N.: Non-normal modalities in variants of linear logic (2015). CoRR, abs/1503.04193

    Google Scholar 

  23. Rubinstein, A.: Economics and language: Five essays. Cambridge University Press (2000)

    Google Scholar 

  24. Troelstra, A.S.: Lectures on Linear Logic. CSLI Publications (1992)

    Google Scholar 

  25. Troquard, N.: Reasoning about coalitional agency and ability in the logics of “bringing-it-about”. Autonomous Agents and Multi-Agent Systems 28(3), 381–407 (2014)

    Article  Google Scholar 

  26. Tuomela, R.: Social ontology: Collective intentionality and group agents. Oxford University Press (2013)

    Google Scholar 

  27. Urquhart, A.: Semantics for relevant logics. J. Symb. Log. 37(1), 159–169 (1972)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory for Applied Ontology, ISTC-CNR, Trento, Italy

    Daniele Porello

Authors
  1. Daniele Porello
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Corresponding author

Correspondence to Daniele Porello .

Editor information

Editors and Affiliations

  1. Jinan University, Guangzhou, China

    Qingliang Chen

  2. Università di Bologna, Bologna, Italy

    Paolo Torroni

  3. Inria - Sophia Antipolis-Méditerran, Sophia Antipolis, France

    Serena Villata

  4. National Taiwan University, Taipei, Taiwan

    Jane Hsu

  5. Università di Bologna, Bologna, Italy

    Andrea Omicini

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Porello, D. (2015). Majoritarian Group Actions. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds) PRIMA 2015: Principles and Practice of Multi-Agent Systems. PRIMA 2015. Lecture Notes in Computer Science(), vol 9387. Springer, Cham. https://doi.org/10.1007/978-3-319-25524-8_26

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  • DOI: https://doi.org/10.1007/978-3-319-25524-8_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25523-1

  • Online ISBN: 978-3-319-25524-8

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