Skip to main content
SpringerLink
Log in

A Probabilistic Approach to Voting, Allocation, Matching, and Coalition Formation

  • Chapter
  • First Online:
The Future of Economic Design

Part of the book series: Studies in Economic Design ((DESI))

Abstract

Randomisation and time-sharing are some of the oldest methods to achieve fairness. I make a case that applying these approaches to social choice settings constitutes a powerful paradigm that deserves an extensive and thorough examination. I discuss challenges and opportunities in applying these approaches to settings including voting, allocation, matching, and coalition formation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The argument for the existence of such a lottery invokes von Neumann’s minimax theorem.

  2. 2.

    For further discussion on probabilistic approaches to circumvent impossibility results in voting, we refer to the survey by Brandt (2017).

  3. 3.

    Any fractional bipartite matching can be represented as a convex combination of discrete matchings via Birkhoff’s algorithm.

References

  • Aharoni, R., & Fleiner, T. (2003). On a lemma of scarf. Journal of Combinatorial Theory Series B, 87, 72–80.

    Article  Google Scholar 

  • Akbarpour, M., & Nikzad, A. (2017). Approximate random allocation mechanisms. Technical report 422777, SSRN.

    Google Scholar 

  • Anshelevich, E., & Postl, J. (2016). Randomized social choice functions under metric preferences. In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI) (pp. 46–59). AAAI Press.

    Google Scholar 

  • Anshelevich, E., Bhardwaj, O., & Postl, J. (2015). Approximating optimal social choice under metric preferences. In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI) (pp. 777–783).

    Google Scholar 

  • Athanassoglou, S., & Sethuraman, J. (2011). House allocation with fractional endowments. International Journal of Game Theory, 40(3), 481–513.

    Article  Google Scholar 

  • Aziz, H., & Klaus, B. (2019). Random matching under priorities: stability and no envy concepts. Social Choice and Welfare.

    Google Scholar 

  • Aziz, H., & Stursberg, P. (2014). A generalization of probabilistic serial to randomized social choice. In Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI) (pp. 559–565). AAAI Press.

    Google Scholar 

  • Aziz, H., Brandt, F., & Brill, M. (2013). On the tradeoff between economic efficiency and strategy proofness in randomized social choice. In Proceedings of the 12th International Conference on Autonomous Agents and Multi-agent Systems (AAMAS) (pp. 455–462). IFAAMAS.

    Google Scholar 

  • Aziz, H., Brandt, F., Brill, M., & Mestre, J. (2014). Computational aspects of random serial dictatorship. ACM SIGecom Exchanges, 13(2), 26–30.

    Article  Google Scholar 

  • Aziz, H., Bogomolnaia, A., & Moulin, H. (2017). Fair mixing: the case of dichotomous preferences. Working paper.

    Google Scholar 

  • Aziz, H., Luo, P., & Rizkallah, C. (2018). Rank maximal equal contribution: A probabilistic social choice function. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI) (pp. 910–916).

    Google Scholar 

  • Bogomolnaia, A., & Moulin, H. (2001). A new solution to the random assignment problem. Journal of Economic Theory, 100(2), 295–328.

    Article  Google Scholar 

  • Bogomolnaia, A., & Moulin, H. (2004). Random matching under dichotomous preferences. Econometrica, 72(1), 257–279.

    Article  Google Scholar 

  • Brandl, F. (2013). Efficiency and incentives in randomized social choice. Master’s thesis, Technische Universität München.

    Google Scholar 

  • Brandl, F., Brandt, F., & Hofbauer, J. (2015). Incentives for participation and abstention in probabilistic social choice. In Proceedings of the 14th International Conference on Autonomous Agents and Multi-agent Systems (AAMAS) (pp. 1411–1419). IFAAMAS.

    Google Scholar 

  • Brandl, F., Brandt, F., & Seedig, H. G. (2016). Consistent probabilistic social choice. Econometrica, 84(5), 1839–1880.

    Article  Google Scholar 

  • Brandt, F. (2017). Rolling the dice: Recent results in probabilistic social choice. In U. Endriss (Ed.), Trends in computational social choice (chap. 1, pp. 3–26). AI Access.

    Google Scholar 

  • Brandt, F. (2019). Collective choice lotteries: Dealing with randomization in economic design. In J.-F. Laslier, H. Moulin, R. Sanver, & W. S. Zwicker (Eds.), The future of economic design. Springer-Verlag. Forthcoming.

    Google Scholar 

  • Budish, E., Che, Y.-K., Kojima, F., & Milgrom, P. (2013). Designing random allocation mechanisms: Theory and applications. American Economic Review, 103(2), 585–623.

    Article  Google Scholar 

  • Cabannes, Y. (2004). Participatory budgeting: A significant contribution to participatory democracy. Environment and Urbanization, 16(1), 27–46.

    Article  Google Scholar 

  • Chen, Y., Lai, J. K., Parkes, D. C., & Procaccia, A. D. (2013). Truth, justice, and cake cutting. Games and Economic Behavior, 77(1), 284–297.

    Article  Google Scholar 

  • Cho, W. J. (2016). Incentive properties for ordinal mechanisms. Games and Economic Behavior, 95, 168–177.

    Article  Google Scholar 

  • Dogan, B., & Yildiz, K. (2016). Efficiency and stability of probabilistic assignments in marriage problems. Games and Economic Behavior, 95, 47–58.

    Article  Google Scholar 

  • Fain, B., Goel, A., & Munagala, K. (2016). The core of the participatory budgeting problem. In Web and Internet Economics - 12th International Conference, WINE 2016, Montreal, Canada, Proceedings (pp. 384–399). 11–14 Dec 2016.

    Google Scholar 

  • Kesten, O., & Unver, U. (2015). A theory of school choice lotteries. Theoretical Economics, 543–595.

    Google Scholar 

  • Manjunath, V. (2016). Fractional matching markets. Games and Economic Behavior, 100, 321–336.

    Article  Google Scholar 

  • Manlove, D. F. (2013). Algorithmics of matching under preferences. Hackensack: World Scientific Publishing Company.

    Book  Google Scholar 

  • Procaccia, A. D. (2010). Can approximation circumvent Gibbard-Satterthwaite? In Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI) (pp 836–841). AAAI Press.

    Google Scholar 

  • Procaccia, A. D., & Tennenholtz, M. (2013). Approximate mechanism design without money. ACM Transactions on Economics and Computation, 1(4), 1–26.

    Article  Google Scholar 

  • Stone, P. (2011). The luck of the draw: The role of lotteries in decision making. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Teo, C.-P., Sethuraman, J., & Tan, W.-P. (2001). Gale-shapley stable marriage problem revisited: Strategic issues and applications. Management Science, 49(9), 1252–1267.

    Article  Google Scholar 

  • Young, H. P. (1994). Equity: In theory and practice. Princeton: Princeton University Press.

    Google Scholar 

Download references

Acknowledgements

The author is supported by a Julius Career Award and a UNSW Scientia Fellowship. He thanks Gabrielle Demange, Jörg Rothe, Nisarg Shah, Paul Stursberg, Etienne Billette De Villemeur, and Bill Zwicker for useful feedback. He thanks all of his collaborators on this topic in particular Florian Brandl, Felix Brandt, and Bettina Klaus for several insightful discussions. Finally he thanks Hervé Moulin and Bill Zwicker for encouraging him to write the chapter.

Author information

Authors and Affiliations

  1. UNSW Sydney and Data61 CSIRO, Sydney, NSW, Australia

    Haris Aziz

Authors
  1. Haris Aziz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haris Aziz .

Editor information

Editors and Affiliations

  1. CNRS - Paris School of Economics, Paris, France

    Jean-François Laslier

  2. University of Glasgow, Glasgow, UK

    Hervé Moulin

  3. Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, Paris, France

    M. Remzi Sanver

  4. Union College, Schenectady, NY, USA

    William S. Zwicker

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Aziz, H. (2019). A Probabilistic Approach to Voting, Allocation, Matching, and Coalition Formation. In: Laslier, JF., Moulin, H., Sanver, M., Zwicker, W. (eds) The Future of Economic Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-030-18050-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation