Skip to main content
SpringerLink
Log in

Optimal Group Manipulation in Facility Location Problems

  • Conference paper
  • First Online:
Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

Included in the following conference series:

Abstract

We address optimal group manipulation in multi-dimensional, multi-facility location problems. We focus on two families of mechanisms, generalized median and quantile mechanisms, evaluating the difficulty of group manipulation of these mechanisms. We show that, in the case of single-facility problems, optimal group manipulation can be formulated as a linear or second-order cone program, under the \(L_1\)- and \(L_2\)-norms, respectively, and hence can be solved in polynomial time. For multiple facilities, we show that optimal manipulation is NP-hard, but can be formulated as a mixed integer linear or second-order cone program, under the \(L_1\)- and \(L_2\)-norms, respectively. Despite this hardness result, empirical evaluation shows that multi-facility manipulation can be computed in reasonable time with our formulations.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

    Anonymity is critical, as dictatorial mechanisms belong to the class of GMMs and are group strategy-proof.

  2. 2.

    Barberà et al.’s [2] characterizations do not preclude the existence of group strategy-proof mechanisms when specific cost functions are used. However, it is still meaningful to study the group manipulation of GMMs and QMs due to their simplicity and intuitive nature, their (individual) strategy proofness, and their flexibility. Indeed, these are the only “natural” such mechanisms for multi-dimensional, multi-FLPs of which we are aware.

  3. 3.

    NP-hardness refers to the corresponding decision problem (as is colloquially understood for optimization problems): is there a misreport that gives the manipulators total cost less than epsilon (for any fixed epsilon). This implies NP-hardness of existence (set cost to truthful cost).

References

  1. Ballester, M.Á., Rey-Biel, P.: Does uncertainty lead to sincerity? simple and complex voting mechanisms. Soc. Choice Welf. 33(3), 477–494 (2009)

    Article  MathSciNet  Google Scholar 

  2. Barberà, S., Gul, F., Stacchetti, E.: Generalized median voter schemes and committees. J. Econ. Theory 61(2), 262–289 (1993)

    Article  MathSciNet  Google Scholar 

  3. Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: The computational difficulty of manipulating an election. Soc. Choice Welf. 6(3), 227–241 (1989)

    Article  MathSciNet  Google Scholar 

  4. Black, D.: On the rationale of group decision-making. J. Polit. Econ. 56(1), 23–34 (1948)

    Article  Google Scholar 

  5. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  6. Clarke, E.H.: Multipart pricing of public goods. Public Choice 11(1), 17–33 (1971)

    Article  Google Scholar 

  7. Conitzer, V., Sandholm, V.: Nonexistence of voting rules that are usually hard to manipulate. In: Proceedings of the Twenty-first National Conference on Artificial Intelligence (AAAI 2006), pp. 627–634, Boston (2006)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Erdélyi, G., Lackner, M., Pfandler, A.: The complexity of nearly single-peaked consistency. In: Proceedings of the Fourth International Workshop on Computational Social Choice (COMSOC 2012), Kraków, Poland (2012)

    Google Scholar 

  10. Escoffier, B., Lang, J., Öztürk, M.: Single-peaked consistency and its complexity. In: Proceedings of the Eighteenth European Conference on Artificial Intelligence (ECAI 2008), Patras, Greece, pp. 366–370 (2008)

    Google Scholar 

  11. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A.: The complexity of manipulative attacks in nearly single-peaked electorates. In: Proceedings of the Thirteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2011), Groningen, The Netherlands, pp. 228–237 (2011)

    Google Scholar 

  12. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: The shield that never was: societies with single-peaked preferences are more open to manipulation and control. In: Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 118–127. ACM (2009)

    Google Scholar 

  13. Faliszewski, P., Procaccia, A.D.: AI’s war on manipulation: are we winning? AI Mag. 31(4), 53–64 (2010)

    Article  Google Scholar 

  14. Friedgut, E., Kalai, G., Nisan, N.: Elections can be manipulated often. In: Proceedings of the 49th Annual IEEE Symposium on the Foundations of Computer Science (FOCS 2008), Philadelphia, pp. 243–249 (2008)

    Google Scholar 

  15. Galand, L., Cornaz, D., Spanjaard, O.: Bounded single-peaked width and proportional representation. In: Proceedings of the Fourth International Workshop on Computational Social Choice (COMSOC 2012), Kraków, Poland (2012)

    Google Scholar 

  16. Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41(4), 587–601 (1973)

    Article  MathSciNet  Google Scholar 

  17. Gormley, I.C., Murphy, T.B.: A latent space model for rank data. In: Airoldi, E.M., Blei, D.M., Fienberg, S.E., Goldenberg, A., Xing, E.P., Zheng, A.X. (eds.) ICML 2006. LNCS, vol. 4503, pp. 90–102. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)

    Article  MathSciNet  Google Scholar 

  19. Isaksson, M., Kindler, G., Mossel, E.: The geometry of manipulationa quantitative proof of the gibbard-satterthwaite theorem. Combinatorica 32(2), 221–250 (2012)

    Article  MathSciNet  Google Scholar 

  20. Lu, T., Tang, P., Procaccia, A.D., Boutilier, C.: Bayesian vote manipulation: optimal strategies and impact on welfare. In: Proceedings of the Twenty-eighth Conference on Uncertainty in Artificial Intelligence (UAI 2012), Catalina, CA, pp. 543–553 (2012)

    Google Scholar 

  21. Majumdar, D., Sen, A.: Ordinally Bayesian incentive compatible voting rules. Econometrica 72(2), 523–540 (2004)

    Article  MathSciNet  Google Scholar 

  22. Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, New York (1995)

    MATH  Google Scholar 

  23. Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)

    Article  MathSciNet  Google Scholar 

  24. Moulin, H.: On strategy-proofness and single peakedness. Public Choice 35(4), 437–455 (1980)

    Article  Google Scholar 

  25. Poole, K.T., Rosenthal, H.: A spatial model for legislative roll call analysis. Am. J. Polit. Sci. 29(2), 357–384 (1985)

    Article  Google Scholar 

  26. Procaccia, A.D., Rosenschein, J.S.: Junta distributions and the average-case complexity of manipulating elections. J. Artif. Intell. Res. 28, 157–181 (2007)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. Schummer, J., Vohra, R.V.: Mechanism design without money. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.) Algorithmic Game Theory, pp. 243–265. Cambridge University Press, Cambridge (2007)

    Chapter  Google Scholar 

  29. Sui, X., Boutilier, C., Sandholm, T.: Analysis and optimization of multi-dimensional percentile mechanisms. In: Proceedings of the Twenty-third International Joint Conference on Artificial Intelligence (IJCAI 2013), Beijing (2013)

    Google Scholar 

  30. Sui, X., Francois-Nienaber, A., Boutilier, C.: Multi-dimensional single-peaked consistency and its approximations. In: Proceedings of the Twenty-third International Joint Conference on Artificial Intelligence (IJCAI 2013), Beijing (2013)

    Google Scholar 

  31. Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finance 16(1), 8–37 (1961)

    Article  MathSciNet  Google Scholar 

  32. Walsh, T.: Where are the really hard manipulation problems? the phase transition in manipulating the veto rule. In: Proceedings of the Twenty-first International Joint Conference on Artificial Intelligence (IJCAI 2009), Pasadena, CA, pp. 324–329 (2009)

    Google Scholar 

  33. Xia, L., Conitzer, V.: A sufficient condition for voting rules to be frequently manipulable. In: Proceedings of the Ninth ACM Conference on Electronic Commerce (EC 2008), Chicago, pp. 99–108 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, 6 King’s College Road, Toronto, ON, Canada

    Xin Sui & Craig Boutilier

Authors
  1. Xin Sui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Craig Boutilier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin Sui .

Editor information

Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Sui, X., Boutilier, C. (2015). Optimal Group Manipulation in Facility Location Problems. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23114-3_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation