Jump to ContentJump to Main Navigation
Show Summary Details
More options …

The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan

2 Issues per year


IMPACT FACTOR 2017: 0.220
5-year IMPACT FACTOR: 0.328

CiteScore 2017: 0.28

SCImago Journal Rank (SJR) 2017: 0.181
Source Normalized Impact per Paper (SNIP) 2017: 0.459

Mathematical Citation Quotient (MCQ) 2017: 0.09

Online
ISSN
1935-1704
See all formats and pricing
More options …

Structural Control in Weighted Voting Games

Anja Rey / Jörg Rothe
Published Online: 2018-07-18 | DOI: https://doi.org/10.1515/bejte-2016-0169

Abstract

Inspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given player’s Shapley–Shubik or probabilistic Penrose–Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.

Keywords: algorithmic game theory; weighted voting games; structural control; power indices; computational complexity

PACS: I.2.11 Distributed Artificial Intelligence–Multiagent Systems; J.4 Social and Behavioral Sciences–Economics

References

  • Aziz, H., Y. Bachrach, E. Elkind, and M. Paterson. 2011. “False-Name Manipulations in Weighted Voting Games.” Journal of Artificial Intelligence Research 40: 57–93.CrossrefGoogle Scholar

  • Bachrach, Y., and E. Elkind. 2008. “Divide and Conquer: False-Name Manipulations in Weighted Voting Games. In Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 975–982. IFAAMAS.

  • Bachrach, Y., and E. Porat. 2010. “Path Disruption Games. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 1123–1130. IFAAMAS.

  • Banzhaf III, J. 1965. “Weighted Voting Doesn’t Work: A Mathematical Analysis.” Rutgers Law Review 19: 317–343.Google Scholar

  • Bartholdi III, J., C. Tovey, and M. Trick. 1989. “The Computational Difficulty of Manipulating an Election.” Social Choice and Welfare 6 (3): 227–241.CrossrefGoogle Scholar

  • Bartholdi III, J., C. Tovey, and M. Trick. 1992. “How Hard is it to Control an Election? Mathematical Computer Modelling 16 (8/9): 27–40.

  • Baumeister, D., G. Erdélyi, O. Erdélyi, and J. Rothe. 2012. “Control in Judgment Aggregation. In Proceedings of the 6th European Starting AI Researcher Symposium, pp. 23–34. IOS Press.

  • Baumeister, D., G. Erdélyi, O. Erdélyi, and J. Rothe. 2015a. “Complexity of Manipulation and Bribery in Judgment Aggregation for Uniform Premise-Based Quota Rules.” Mathematical Social Sciences 76: 19–30.CrossrefGoogle Scholar

  • Baumeister, D., G. Erdélyi, and J. Rothe. 2015b. “Judgment Aggregation, Chapter 6.” In Economics and Computation. An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division, edited by J. Rothe, pp. 361–391. Springer-Verlag.

  • Baumeister, D. and J. Rothe. 2015. “Preference Aggregation by Voting, Chapter 4.” In Economics and Computation. An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division, edited by J. Rothe, pp. 197–325. Springer-Verlag.

  • Beigel, R., L. Hemachandra, and G. Wechsung. 1989. “On the Power of Probabilistic Polynomial Time: PNP [log] ⊆ PP.” In Proceedings of the 4th Structure in Complexity Theory Conference, pp. 225–227. IEEE Computer Society Press.

  • Brandt, F., V. Conitzer, and U. Endriss. 2013. “Computational Social Choice.” In Multiagent Systems, 2nd ed. edited by G. Weiß, pp. 213–283. MIT Press.

  • Brandt, F., V. Conitzer, U. Endriss, J. Lang, and A. Procaccia, eds. 2016. Handbook of Computational Social Choice. Cambridge University Press.Google Scholar

  • Chalkiadakis, G., E. Elkind, and M. Wooldridge. 2011. Computational Aspects of Cooperative Game Theory. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan and Claypool Publishers.

  • Conitzer, V., and T. Walsh. 2016. “Barriers to Manipulation in Voting, Chapter 6.” In Handbook of Computational Social Choice edited by F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. Procaccia, pp. 127–145. Cambridge University Press.

  • Deng, X., and C. Papadimitriou. 1994. “On the Complexity of Comparative Solution Concepts.” Mathematics of Operations Research 19 (2): 257–266.CrossrefGoogle Scholar

  • Dubey, P., and L. Shapley. 1979. “Mathematical Properties of the Banzhaf Power Index.” Mathematics of Operations Research 4 (2): 99–131.CrossrefGoogle Scholar

  • Elkind, E., D. Pasechnik, and Y. Zick. 2013a. “Dynamic Weighted Voting Games.” In Proceedings of the 12th International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 515–522. IFAAMAS.

  • Elkind, E., T. Rahwan, and N. Jennings. 2013b. “Computational Coalition Formation.” In Multiagent Systems, 2nd ed. edityed by G. Weiß, pp. 329–380. MIT Press.

  • Elkind, E., and J. Rothe. 2015. “Cooperative Game Theory, Chapter 3.” In Economics and Computation. An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division, edited by J. Rothe, pp. 135–193. Springer-Verlag.

  • Endriss, U. 2013. “Sincerity and Manipulation Under Approval Voting.” Theory and Decision 74 (3): 335–355.CrossrefGoogle Scholar

  • Endriss, U. 2016. “Judgment Aggregation, Chapter 17.” In Handbook of Computational Social Choice edited by F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. Procaccia, pp. 399–426. Cambridge University Press.

  • Endriss, U., U. Grandi, and D. Porello. 2012. “Complexity of Judgment Aggregation.” Journal of Artificial Intelligence Research 45: 481–514.CrossrefGoogle Scholar

  • Faliszewski, P., E. Hemaspaandra, and L. Hemaspaandra. 2009a. How Hard is Bribery in Elections? Journal of Artificial Intelligence Research 35: 485–532.Google Scholar

  • Faliszewski, P., E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. 2009b. “Llull and Copeland Voting Computationally Resist Bribery and Constructive Control.” Journal of Artificial Intelligence Research 35: 275–341.CrossrefGoogle Scholar

  • Faliszewski, P. and L. Hemaspaandra. 2009. “The Complexity of Power-Index Comparison.” Theoretical Computer Science 410 (1): 101–107.CrossrefGoogle Scholar

  • Faliszewski, P. and J. Rothe. 2016. “Control and Bribery in Voting, Chapter 7.” In Handbook of Computational Social Choice, edited by F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. Procaccia, pp. 146–168. Cambridge University Press.

  • Felsenthal, D., and M. Machover. 1995. “Postulates and Paradoxes of Relative Voting Power – A Critical Re-Appraisal.” Theory and Decision 38 (2): 195–229.CrossrefGoogle Scholar

  • Fortnow, L., and N. Reingold. 1996. “PP is Closed Under Truth-Table Reductions.” Information and Computation 124 (1): 1–6.CrossrefGoogle Scholar

  • Freixas, J., and M. Pons. 2008. “Circumstantial Power: Optimal Persuadable Voters.” European Journal of Operational Research 186: 1114–1126.CrossrefGoogle Scholar

  • Garey, M., and D. Johnson. 1979. “Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company.

  • Gill, J. 1977. “Computational Complexity of Probabilistic Turing Machines.” SIAM Journal on Computing 6 (4): 675–695.CrossrefGoogle Scholar

  • Hemaspaandra, E., L. Hemaspaandra, and J. Rothe. 1997a. “Exact Analysis of Dodgson Elections: Lewis Carroll’s 1876 Voting System is Complete for Parallel Access to NP.” Journal of the ACM 44 (6): 806–825.CrossrefGoogle Scholar

  • Hemaspaandra, E., L. Hemaspaandra, and J. Rothe. 1997b. “Raising NP Lower Bounds to Parallel NP Lower Bounds.” SIGACT News 28 (2): 2–13.CrossrefGoogle Scholar

  • Hemaspaandra, E., L. Hemaspaandra, and J. Rothe. 2007. “Anyone But Him: The Complexity of Precluding an Alternative.” Artificial Intelligence 171 (5–6): 255–285.CrossrefGoogle Scholar

  • Loreggia, A., N. Narodytska, F. Rossi, B. Venable, and T. Walsh. 2015. “Controlling Elections by Replacing Candidates or Votes (Extended Abstract).” In Proceedings of the 14th International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 1737–1738. IFAAMAS.

  • Myerson, R. 1980. “Conference Structures and Fair Allocation Rules.” International Journal of Game Theory 9 (3): 169–182.Crossref

  • Nisan, N., T. Roughgarden, E. Tardos, and V. Vazirani. 2007. Algorithmic Game Theory. Cambridge University Press.Google Scholar

  • Papadimitriou, C. 1995. Computational Complexity, 2nd ed. Addison-Wesley.Google Scholar

  • Papadimitriou, C., and S. Zachos. 1983. “Two Remarks on the Power of Counting.” In Proceedings of the 6th GI Conference on Theoretical Computer Science (Lecture Notes in Computer Science #145), pp. 269–276. Springer-Verlag.

  • Peleg, B., and P. Sudhölter. 2007. Introduction to the Theory of Cooperative Games, 2nd ed. Springer-Verlag.Google Scholar

  • Penrose, L. 1946. “The Elementary Statistics of Majority Voting.” Journal of the Royal Statistical Society 109 (1): 53–57.CrossrefGoogle Scholar

  • Prasad, K., and J. Kelly. 1990. “NP-Completeness of Some Problems Concerning Voting Games.” International Journal of Game Theory 19 (1): 1–9.CrossrefGoogle Scholar

  • Rahwan, T., T. Michalak, and M. Wooldridge. 2014. “A Measure of Synergy in Coalitions. Technical Report arXiv: 1404.2954.v1 [cs.GT], ACM Computing Research Repository (CoRR).

  • Rey, A., and J. Rothe. 2014. “False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time.” Journal of Artificial Intelligence Research 50: 573–601.CrossrefGoogle Scholar

  • Rey, A., J. Rothe, and A. Marple. 2017. “Path-Disruption Games: Bribery and a Probabilistic Model.” Theory of Computing Systems 60 (2): 222–252.CrossrefGoogle Scholar

  • Rothe, J. 2005. Complexity Theory and Cryptology. An Introduction to Cryptocomplexity. EATCS Texts in Theoretical Computer Science. Springer-Verlag.

  • Rothe, J. ed. 2015. Economics and Computation. An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division. Springer Texts in Business and Economics. Springer-Verlag.

  • Shapley, L., and M. Shubik. 1954. “A Method of Evaluating the Distribution of Power in a Committee System.” American Political Science Review 48 (3): 787–792.CrossrefGoogle Scholar

  • Shoham, Y., and K. Leyton-Brown. 2009. Multiagent Systems. Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press.

  • Toda, S. 1991. “PP is as hard as the polynomial-time hierarchy.” SIAM Journal on Computing 20 (5): 865–877.CrossrefGoogle Scholar

  • Zick, Y. 2013. “On Random Quotas and Proportional Representation in Weighted Voting Games.” In Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pp. 432–438. AAAI Press/IJCAI.

  • Zick, Y., A. Skopalik, and E. Elkind. 2011. “The Shapley Value as a Function of the Quota in Weighted Voting Games.” In Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 490–496. AAAI Press/IJCAI.

  • Zuckerman, M., P. Faliszewski, Y. Bachrach, and E. Elkind. 2012. “Manipulating the Quota in Weighted Voting Games.” Artificial Intelligence 180–181:1–19.Google Scholar

About the article

Published Online: 2018-07-18


Citation Information: The B.E. Journal of Theoretical Economics, Volume 18, Issue 2, 20160169, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2016-0169.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in