Skip to main content
Log in

Multi-agent soft constraint aggregation via sequential voting: theoretical and experimental results

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables (i.e., features). These scenarios are very common when candidates are described by feature vectors, such as cars, or houses, or any complex product. We assume agents to compactly express their preferences over the candidates via soft constraints. This is a compact way to model preferences which naturally models variables domains, and relationship among variables. To aggregate the preferences of the agents, we consider a sequential procedure that asks the agents to vote on one variable at a time. At each step, all agents express their preferences over the domain of a variable; based on such preferences, a voting rule is used to select one value for that variable. When all variables have been considered, the selected values constitute the returned variable assignment, that is, the elected candidate. We study several properties of this procedure (such as Condorcet consistency, anonymity, neutrality, monotonicity, consistency, efficiency, participation, independence of irrelevant alternatives, non dictatorship, and strategy-proofness), by relating them to corresponding properties of the adopted voting rules used for each variable. Moreover, we perform an experimental study on a special kind of soft constraints, namely fuzzy constraints. The experimental study shows that the proposed sequential procedure yields a considerable saving in time with respect to a non-sequential approach, while the winners satisfy the agents just as well, independently of the variable ordering, and of the presence of coalitions of agents.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. Notice that a soft profile consists of a collection of SCSPs over the same set of variables, while a profile (as in the classical social choice setting) is a collection of total orderings over a set of candidates.

  2. Notice that the preference values 0 and 1 mentioned here are the preference values 0 and 1 of the preference structure \(S = \langle A, +, \times , 0, 1 \rangle \) of the SCSPs that we consider, i.e., they are the worst and the best preference value that can be associated by a constraint to an assignment of values to variables.

References

  1. Arrow, K. J. (1951). Social choice and individual values. New York: Wiley.

    MATH  Google Scholar 

  2. Arrow, K. J., Sen, A. K., & Suzumura, K. (2002). Handbook of social choice and welfare. Amsterdam: North-Holland.

    MATH  Google Scholar 

  3. Bacchus, F., & Grove, A. (1995). Graphical models for preference and utility. In Proceedings of UAI, 1995, pp. 3–10.

  4. Bessiere, C. (2005). Constraint propagation. In F. Rossi, P. V. Beek, & T. Walsh (Eds.), Handbook of constraint programming. Amsterdam: Elsevier.

    Google Scholar 

  5. Boutilier, C., Brafman, R. I., Domshlak, C., Hoos, H. H., & Poole, D. (2004). CP-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. JAIR, 21, 135–191.

    Article  MathSciNet  MATH  Google Scholar 

  6. Boutilier, C., Goldszmidt, M., & Sabata, B. (1999). Sequential auctions for the allocation of resources with complementarities. In Proceedings of IJCAI 1999.

  7. Brafman, R. I., Rossi, F., Salvagnin, D., Venable, K. B., & Walsh, T. (2010). Finding the next solution in constraint- and preference-based knowledge representation formalisms. In Proceedings of KR 2010.

  8. Conitzer, V., Sandholm, T., & Lang, J. (2007). When are elections with few candidates hard to manipulate. JACM, 54(3), 1–33.

    Article  MathSciNet  MATH  Google Scholar 

  9. Conitzer, V., & Xia, L. (2012). Paradoxes of multiple elections: An approximation approach. In Proceedings of KR 2012.

  10. Dechter, R. (2003). Constraint processing. Burlington: Morgan Kaufmann.

    MATH  Google Scholar 

  11. Dechter, R. (2005). Tractable structures for CSPs. In F. Rossi, P. V. Beek, & T. Walsh (Eds.), Handbook of constraint programming. Amsterdam: Elsevier.

    Google Scholar 

  12. Faliszewski, P., Hemaspaandra, E., & Hemaspaandra, L. A. (2009). How hard is bribery in elections? JAIR, 35, 485–532.

    Article  MathSciNet  MATH  Google Scholar 

  13. Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41(3), 587–601.

    Article  MathSciNet  MATH  Google Scholar 

  14. Gonzales, C., Perny, P., & Queiroz, S. (2008). Preference aggregation with graphical utility models. In Proceedings of AAAI, 2008, pp. 1037–1042.

  15. Kelly, J. S. (1978). Arrow impossibility theorems. New York: Academic Press.

    MATH  Google Scholar 

  16. Lang, J., Mengin, J., & Xia, L. (2012). Aggregating conditionally lexicographic preferences on multi-issue domains. In Proceedings of CP, 2012, pp. 973–987.

  17. Lang, J., & Xia, L. (2009). Sequential composition of voting rules in multi-issue domains. Mathematical Social Sciences, 57, 304–324.

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, X., & Truszczynski, M. (2013). Aggregating conditionally lexicographic preferences using answer set programming solvers. In Proceedings of international conference on algorithmic decision theory (ADT-13).

  19. Maran, A., Maudet, N., Pini, M.S., Rossi, F., & Venable, K.B. (2013). A framework for aggregating influenced CP-nets and its resistance to bribery. In Proceedings of AAAI 2013.

  20. Mattei, N., Pini, M. S., Venable, K. B., & Rossi, F. (2012). Bribery in voting over combinatorial domains is easy. In Proceedings of AAMAS, 2012, pp. 1407–1408.

  21. Mattei, N., Pini, M. S., Venable, K. B., & Rossi, F. (2013). Bribery in voting with CP-nets. Annals of Mathematics and Artificial Intelligence., 68, 135–160.

    Article  MathSciNet  MATH  Google Scholar 

  22. Mattei, N., & Walsh, T. (2013). Preflib: A library of preference data. In Proceedings of ADT 2013. Springer

  23. Maudet, N., Pini, M. S., Venable, K. B., & Rossi, F. (2012). Influence and aggregation of preferences over combinatorial domains. In Proceedings of AAMAS 2012, pp. 1313–1314.

  24. May, K. (1952). A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica, 20, 680–684.

    Article  MathSciNet  MATH  Google Scholar 

  25. Meseguer, P., Rossi, F., & Schiex, T. (2005). Soft constraints. In F. Rossi, P. V. Beek, & T. Walsh (Eds.), Handbook of constraint programming. Amsterdam: Elsevier.

    Google Scholar 

  26. Mittal, S., & Frayman, F. (1989). Toward a generic model of configuration tasks. In Proceedings of IJCAI 1989, pp. 1395–1401.

  27. Pini, M. S., Rossi, F., & Venable, K. B. (2013). Bribery in voting with soft constraints. In Proceedings of AAAI 2013.

  28. Pini, M. S., Rossi, F., & Venable, K. B. (2013). Resistance to bribery when aggregating soft constraints. In Proceedings of AAMAS, 2013, pp. 1301–1302.

  29. Pozza, G. D., Pini, M. S., Rossi, F., & Venable, K. B. (2011). Multi-agent soft constraint aggregation via sequential voting. In Proceedings of IJCAI, 2011, pp. 172–177.

  30. Pozza, G. D., Rossi, F., & Venable, B. (2011). Multi-agent soft constraint aggregation: A sequential approach. In Proceedings of ICAART, 2011, pp. 277–282.

  31. Purrington, K., & Durfee, E. H. (2007). Making social choices from individuals’ CP-nets. In Proceedings of AAMAS, 2007, pp. 1122–1124.

  32. Satterthwaite, M. (1975). Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Economic Theory, 10, 187–217.

    Article  MathSciNet  MATH  Google Scholar 

  33. Schiex, T. (1992). Possibilistic constraint satisfaction problems or “how to handle soft constraints?” In Proceedings of UAI, 1992, pp. 268–275.

  34. Taylor, A. (2005). Social choice and the mathematics of manipulation. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  35. Xia, L., & Conitzer, V. (2010). Strategy-proof voting rules over multi-issue domains with restricted preferences. In Proceedings of WINE, 2010, pp. 402–414.

  36. Xia, L., Conitzer, V., & Lang, J. (2008). Voting on multiattribute domains with cyclic preferential dependencies. In Proceedings of AAAI, 2008, pp. 202–207.

  37. Xia, L., Conitzer, V., & Lang, J. (2010). Aggregating preferences in multi-issue domains by using maximum likelihood estimators. In Proceedings of AAMAS, 2010, pp. 399–408.

Download references

Acknowledgements

This work has been partially supported by the strategic project “KIDNEY—Incorporating patients preferences in kidney transplant decision protocols” funded by the University of Padova. We would like to thank Giorgio Dalla Pozza for his contribution to a first version of the experimental part of this work, that he carried on as part of his Master thesis project.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cristina Cornelio.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was conducted while Cristina Cornelio and Francesca Rossi were at the University of Padua, Italy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cornelio, C., Pini, M.S., Rossi, F. et al. Multi-agent soft constraint aggregation via sequential voting: theoretical and experimental results. Auton Agent Multi-Agent Syst 33, 159–191 (2019). https://doi.org/10.1007/s10458-018-09400-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10458-018-09400-y

Keywords

Navigation