Collective Choice Lotteries

Dealing with Randomization in Economic Design

  • Chapter
  • First Online:
The Future of Economic Design

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

Abstract

Randomization is playing an ever increasing role in economic design with examples ranging from fair allocation to matching markets to voting. I propose and briefly discuss three interdisciplinary and interrelated research questions that deserve further attention: (i) when are collective choice lotteries acceptable, (ii) how do agents compare lotteries, and (iii) how can randomized rules be implemented.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 ship** worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    For further philosophical discussions of using lotteries to achieve fairness, see, for example, Broome (1991); Nissan-Rozen (2012).

  2. 2.

    For a related discussion of the benefits and challenges of randomization, see Haris Aziz’s piece in this volume (Aziz 2019).

  3. 3.

    For other approaches to come up with coherent collective decisions when individual decision-makers violate traditional decision-theoretic assumptions, see Regenwetter et al. (2009) and Danan et al. (2016).

References

  • Aziz, H. (2019). A probabilistic approach to voting, allocation, matching, and coalition formation. In J.-F. Laslier, H. Moulin, R. Sanver, & W. S. Zwicker (Eds.), The Future of Economic Design. Berlin: Springer.

    Google Scholar 

  • Aziz, H., Brandt, F., & Brill, M. (2013). The computational complexity of random serial dictatorship. Economics Letters, 121(3), 341–345.

    Article  Google Scholar 

  • Aziz, H., Brandl, F., & Brandt, F. (2015). Universal Pareto dominance and welfare for plausible utility functions. Journal of Mathematical Economics, 60, 123–133.

    Article  Google Scholar 

  • Aziz, H., Brandl, F., Brandt, F., & Brill, M. (2018). On the tradeoff between efficiency and strategyproofness. Games and Economic Behavior, 110, 1–18.

    Article  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 

  • Bogomolnaia, A., Moulin, H., & Stong, R. (2005). Collective choice under dichotomous preferences. Journal of Economic Theory, 122(2), 165–184.

    Article  Google Scholar 

  • Brandl, F., & Brandt, F. (2019). Arrovian aggregation of convex preferences. Working paper.

    Google Scholar 

  • Brandl, F., Brandt, F., & Hofbauer, J. (2019). Welfare maximization entices participation. Games and Economic Behavior. 14, 308–314.

    Google Scholar 

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

    Article  Google Scholar 

  • Brandt, F., & Sandholm, T. (2005). On correctness and privacy in distributed mechanisms. Revised selected papers from the 7th AAMAS Workshop on Agent-Mediated Electronic Commerce (AMEC) (Vol. 3937, pp. 212–225)., Lecture Notes in Artificial Intelligence (LNAI).

    Google Scholar 

  • Brandt, F., Hofbauer, J., & Suderland, M. (2017). Majority graphs of assignment problems and properties of popular random assignments. Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (pp. 335–343). IFAAMAS.

    Google Scholar 

  • Broome, J. (1991). Fairness. Proceedings of the Aristotelian Society, New Series, 91, 81–101.

    Google Scholar 

  • Butler, D., & Pogrebna, G. (2018). Predictably intransitive preferences, Judgment and Decision Making. 13(3), 217–236.

    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 

  • Danan, E., Gajdos, T., Hill, B., & Tallon, J.-M. (2016). Robust social decisions. American Economic Review, 106(9), 2407–2425.

    Article  Google Scholar 

  • Dobzinski, S., & Dughmi, S. (2013). On the power of randomization in algorithmic mechanism design. SIAM Journal on Computing, 42(6), 2287–2304.

    Article  Google Scholar 

  • Dowlen, O. (2009). Sorting out sortition: A perspective on the random selection of political officers. Political Studies, 57(2), 298–315.

    Article  Google Scholar 

  • Ehlers, L., Peters, H., & Storcken, T. (2002). Strategy-proof probabilistic decision schemes for one-dimensional single-peaked preferences. Journal of Economic Theory, 105(2), 408–434.

    Article  Google Scholar 

  • Fischer, F., & Klimm, M. (2015). Optimal impartial selection. SIAM Journal on Computing, 44(5), 1263–1285.

    Article  Google Scholar 

  • Fishburn, P. C. (1988). Nonlinear preference and utility theory. The Johns Hopkins University Press.

    Google Scholar 

  • Fishburn, P. C. (1984a). Probabilistic social choice based on simple voting comparisons. Review of Economic Studies, 51(4), 683–692.

    Article  Google Scholar 

  • Fishburn, P. C. (1984b). SSB utility theory: An economic perspective. Mathematical Social Sciences, 8(1), 63–94.

    Article  Google Scholar 

  • Gibbard, A. (1977). Manipulation of schemes that mix voting with chance. Econometrica, 45(3), 665–681.

    Article  Google Scholar 

  • Goodwin, B. (2005). Justice by lottery (1st ed. 1992). Chicago: University of Chicago Press.

    Google Scholar 

  • Guerrero, A. (2014). Against elections: The lottocratic alternative. Philosophy and Public Affairs, 42(2), 135–178.

    Article  Google Scholar 

  • Headlam, J. W. (1933). Election by Lot at Athens. Cambridge: Cambridge University Press.

    Google Scholar 

  • Nisan, N., & Ronen, A. (2001). Algorithmic mechanism design. Games and Economic Behavior, 35(1), 166–196.

    Article  Google Scholar 

  • Nissan-Rozen, I. (2012). Doing the best one can: A new justification for the use of lotteries. Erasmus Journal for Philosophy and Economics, 5(1), 45–72.

    Article  Google Scholar 

  • Regenwetter, M., Grofman, B., Popova, A., Messner, W., Davis-Stober, C. P., & Cavagnaro, D. R. (2009). Behavioural social choice: a status report. Philosophical Transactions of the Royal Society, 364(1518), 833–843.

    Google Scholar 

  • Saban, D., & Sethuraman, J. (2015). The complexity of computing the random priority allocation matrix. Mathematics of Operations Research, 40(4), 1005–1014.

    Google Scholar 

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

    Google Scholar 

Download references

Acknowledgements

This material is based on work supported by the Deutsche Forschungsgemeinschaft under grant BR 2312/12-1. I am grateful to Florian Brandl, Ashley Piggins, Marcus Pivato, and Bill Zwicker for helpful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Felix Brandt .

Editor information

Editors and Affiliations

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

Brandt, F. (2019). Collective Choice Lotteries. 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_9

Download citation

Publish with us

Policies and ethics

Navigation