research-article

Generalized Decision Scoring Rules: Statistical, Computational, and Axiomatic Properties

Author:

Lirong XiaAuthors Info & Claims

EC '15: Proceedings of the Sixteenth ACM Conference on Economics and Computation

Pages 661 - 678

https://doi.org/10.1145/2764468.2764518

Published: 15 June 2015 Publication History

Abstract

We pursue a design by social choice, evaluation by statistics and computer science paradigm to build a principled framework for discovering new social choice mechanisms with desirable statistical, computational, and social choice axiomatic properties. Our new framework is called generalized decision scoring rules (GDSRs), which naturally extend generalized scoring rules [Xia and Conitzer 2008] to arbitrary preference space and decision space, including sets of alternatives with fixed or unfixed size, rankings, and sets of rankings. We show that GDSRs cover a wide range of existing mechanisms including MLEs, Chamberlin and Courant rule, and resolute, irresolute, and preference function versions of many commonly studied voting rules. We provide a characterization of statistical consistency for any GDSR w.r.t. any statistical model and asymptotically tight bounds on the convergence rate. We investigate the complexity of winner determination and a wide range of strategic behavior called vote operations for all GDSRs, and prove a general phase transition theorem on the minimum number of vote operations for the strategic entity to succeed. We also characterize GDSRs by two social choice normative properties: anonymity and finite local consistency.

References

[1]

Altman, A. and Tennenholtz, M. 2010. An axiomatic approach to personalized ranking systems. Journal of the ACM 57, 4. Article 26.

Digital Library

[2]

Arrow, K. J. 1950. A difficulty in the concept of social welfare. Journal of Political Economy 58, 4, 328--346.

[3]

Azari Soufiani, H., Parkes, D. C., and Xia, L. 2012. Random utility theory for social choice. In Proceedings of NIPS. Lake Tahoe, NV, USA, 126--134.

[4]

Azari Soufiani, H., Parkes, D. C., and Xia, L. 2013. Preference Elicitation For General Random Utility Models. In Proceedings of UAI. Bellevue, Washington, USA.

[5]

Azari Soufiani, H., Parkes, D. C., and Xia, L. 2014. Statistical decision theory approaches to social choice. In Proceedings of NIPS. Montreal, Quebec, Canada.

[6]

Bartholdi, III, J., Tovey, C., and Trick, M. 1989a. The computational difficulty of manipulating an election. Social Choice and Welfare 6, 3, 227--241.

[7]

Bartholdi, III, J., Tovey, C., and Trick, M. 1989b. Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare 6, 157--165.

[8]

Bartholdi, III, J., Tovey, C., and Trick, M. 1992. How hard is it to control an election? Math. Comput. Modelling 16, 8--9, 27--40. Formal theories of politics, II.

Digital Library

[9]

Betzler, N., Niedermeier, R., and Woeginger, G. 2011. Unweighted coalitional manipulation under the Borda rule is NP-hard. In Proceedings of IJCAI. 55--60.

Digital Library

[10]

Brandt, F. 2009. Some remarks on Dodgson's voting rule. Mathematical Logic Quarterly 55, 460--463.

[11]

Braverman, M. and Mossel, E. 2008. Noisy Sorting Without Resampling. In Proceedings of SODA. Philadelphia, PA, USA, 268--276.

Digital Library

[12]

Caragiannis, I., Procaccia, A., and Shah, N. 2013. When do noisy votes reveal the truth? In Proceedings of EC. Philadelphia, PA.

Digital Library

[13]

Cary, D. 2011. Estimating the margin of victory for instant-runoff voting. In Proceedings of 2011 EVT/WOTE Conference.

Digital Library

[14]

Chamberlin, J. R. and Courant, P. N. 1983. Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule. The American Political Science Review 77, 3, 718--733.

[15]

Chierichetti, F. and Kleinberg, J. 2012. Voting with Limited Information and Many Alternatives. In Proceedings of SODA. Kyoto, Japan, 1036--1055.

Digital Library

[16]

Condorcet, M. d. 1785. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: L'Imprimerie Royale.

[17]

Conitzer, V., Rognlie, M., and Xia, L. 2009. Preference functions that score rankings and maximum likelihood estimation. In Proceedings of IJCAI. Pasadena, CA, USA, 109--115.

Digital Library

[18]

Conitzer, V. and Sandholm, T. 2005. Common voting rules as maximum likelihood estimators. In Proceedings of UAI. Edinburgh, UK, 145--152.

[19]

Conitzer, V., Sandholm, T., and Lang, J. 2007. When are elections with few candidates hard to manipulate? Journal of the ACM 54, 3, 1--33.

Digital Library

[20]

Cook, W. J., Gerards, A. M. H., Schrijver, A., and Tardos, E. 1986. Sensitivity theorems in integer linear programming. Mathematical Programming 34, 3, 251--264.

Digital Library

[21]

Davies, J., Katsirelos, G., Narodytska, N., Walsh, T., and Xia, L. 2014. Complexity of and Algorithms for the Manipulation of Borda, Nanson and Baldwin's Voting Rules. Artificial Intelligence 217, 20--42.

Digital Library

[22]

Dwork, C., Kumar, R., Naor, M., and Sivakumar, D. 2001. Rank aggregation methods for the web. In Proceedings of WWW. 613--622.

Digital Library

[23]

Elkind, E., Faliszewski, P., and Slinko, A. 2010. Good rationalizations of voting rules. In Proceedings of AAAI. Atlanta, GA, USA, 774--779.

[24]

Faliszewski, P., Hemaspaandra, E., and Hemaspaandra, L. A. 2009. How hard is bribery in elections? Journal of Artificial Intelligence Research 35, 485--532.

Digital Library

[25]

Faliszewski, P., Hemaspaandra, E., and Hemaspaandra, L. A. 2010. Using complexity to protect elections. Communications of the ACM 53, 74--82.

Digital Library

[26]

Faliszewski, P. and Procaccia, A. D. 2010. AI's war on manipulation: Are we winning? AI Magazine 31, 4, 53--64.

[27]

Fishburn, P. C. 1977. Condorcet social choice functions. SIAM Journal on Applied Mathematics 33, 3, 469--489.

[28]

Friedgut, E., Kalai, G., and Nisan, N. 2008. Elections can be manipulated often. In Proceedings of FOCS. 243--249.

Digital Library

[29]

Ghosh, S., Mundhe, M., Hernandez, K., and Sen, S. 1999. Voting for movies: the anatomy of a recommender system. In Proceedings of AGENTS. 434--435.

Digital Library

[30]

Greene, W. H. 2011. Econometric Analysis 7th Ed. Prentice Hall.

[31]

Hemaspaandra, E., Hemaspaandra, L. A., and Rothe, J. 1997. Exact analysis of dodgson elections: Lewis carroll's 1876 voting system is complete for parallel access to np. Journal of the ACM 44, 806--825.

Digital Library

[32]

Hoeffding, W. 1963. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58, 301, 13--30.

[33]

Horn, R. A. and Johnson, C. R. 1985. Matrix Analysis. Cambridge University Press.

Digital Library

[34]

enstra19Lenstra, H. W. 1983. Integer programming with a fixed number of variables. Mathematics of Operations Research 8, 538--548.

Digital Library

[35]

Lu, T. and Boutilier, C. 2011. Learning mallows models with pairwise preferences. In Proceedings of ICML. Bellevue, WA, USA, 145--152.

[36]

Magrino, T. R., Rivest, R. L., Shen, E., and Wagner, D. 2011. Computing the Margin of Victory in IRV Elections. In Proceedings of 2011 EVT/WOTE Conference.

Digital Library

[37]

Mallows, C. L. 1957. Non-null ranking model. Biometrika 44, 1/2, 114--130.

[38]

Mao, A., Procaccia, A. D., and Chen, Y. 2013. Better human computation through principled voting. In Proceedings of AAAI. Bellevue, WA, USA.

[39]

Monroe, B. L. 1995. Fully Proportional Representation. The American Political Science Review 89, 4, 925--940.

[40]

Mossel, E., Procaccia, A. D., and Racz, M. Z. 2013. A Smooth Transition From Powerlessness to Absolute Power. Journal of Artificial Intelligence Research 48, 1, 923--951.

[41]

Mossel, E. and Racz, M. Z. 2012. A quantitative Gibbard-Satterthwaite theorem without neutrality. In Proceedings of STOC.

Digital Library

[42]

Nurmi, H. 1987. Comparing voting systems. Springer.

[43]

Obraztsova, S. and Elkind, E. 2011. On the complexity of voting manipulation under randomized tie-breaking. In Proceedings of IJCAI. Barcelona, Catalonia, Spain, 319--324.

Digital Library

[44]

Pennock, D. M., Horvitz, E., and Giles, C. L. 2000. Social choice theory and recommender systems: Analysis of the axiomatic foundations of collaborative filtering. In Proceedings of AAAI. Austin, TX, USA, 729--734.

Digital Library

[45]

Porello, D. and Endriss, U. 2013. Ontology Merging as Social Choice: Judgment Aggregation under the Open World Assumption. Journal of Logic and Computation.

[46]

Pritchard, G. and Wilson, M. C. 2009. Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour. Mathematical Social Sciences 1, 35--57.

[47]

Procaccia, A. D., Reddi, S. J., and Shah, N. 2012. A maximum likelihood approach for selecting sets of alternatives. In Proceedings of UAI.

[48]

Procaccia, A. D. and Rosenschein, J. S. 2007. Junta distributions and the average-case complexity of manipulating elections. Journal of Artificial Intelligence Research 28, 157--181.

Digital Library

[49]

Raman, K. and Joachims, T. 2014. Methods for Ordinal Peer Grading. In Proceedings of KDD. New York, NY, USA, 1037--1046.

Digital Library

[50]

Rothe, J. and Schend, L. 2013. Challenges to Complexity Shields That Are Supposed to Protect Elections Against Manipulation and Control: A Survey. Annals of Mathematics and Artificial Intelligence 68, 1--3, 161--193.

Digital Library

[51]

Xia, L. 2012. Computing the margin of victory for various voting rules. In Proceedings of EC. Valencia, Spain, 982--999.

Digital Library

[52]

Xia, L. 2013. Generalized Scoring Rules: A Framework That Reconciles Borda and Condorcet. ACM SIGecom Exchanges 12, 1, 42--48.

Digital Library

[53]

Xia, L. and Conitzer, V. 2008. Generalized scoring rules and the frequency of coalitional manipulability. In Proceedings of EC. Chicago, IL, USA, 109--118.

Digital Library

[54]

Xia, L. and Conitzer, V. 2009. Finite local consistency characterizes generalized scoring rules. In Proceedings of IJCAI. Pasadena, CA, USA, 336--341.

Digital Library

[55]

Xia, L. and Conitzer, V. 2011. A maximum likelihood approach towards aggregating partial orders. In Proceedings of IJCAI. Barcelona, Catalonia, Spain, 446--451.

Digital Library

[56]

Xia, L., Zuckerman, M., Procaccia, A. D., Conitzer, V., and Rosenschein, J. 2009. Complexity of unweighted coalitional manipulation under some common voting rules. In Proceedings of IJCAI. Pasadena, CA, USA, 348--353.

Digital Library

[57]

Young, H. P. 1975. Social choice scoring functions. SIAM Journal on Applied Mathematics 28, 4, 824--838.

[58]

Zuckerman, M., Procaccia, A. D., and Rosenschein, J. S. 2009. Algorithms for the coalitional manipulation problem. Artificial Intelligence 173, 2, 392--412.

Digital Library

Cited By

Xia L(2022)Learning and Decision-Making from Rank DataundefinedOnline publication date: 11-Mar-2022
Xia LRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)The semi-random satisfaction of voting axiomsProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3540726(6075-6086)Online publication date: 6-Dec-2021
Doucette JTsang AHosseini HLarson KCohen R(2019)Inferring true voting outcomes in homophilic social networksAutonomous Agents and Multi-Agent Systems10.1007/s10458-019-09405-133:3(298-329)Online publication date: 1-May-2019
Show More Cited By

Index Terms

Generalized Decision Scoring Rules: Statistical, Computational, and Axiomatic Properties
1. Applied computing
  1. Law, social and behavioral sciences
    1. Economics
2. Computing methodologies
  1. Artificial intelligence
    1. Distributed artificial intelligence
      1. Multi-agent systems

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cover image ACM Conferences

EC '15: Proceedings of the Sixteenth ACM Conference on Economics and Computation

June 2015

852 pages

ISBN:9781450334105

DOI:10.1145/2764468

General Chair:
Tim Roughgarden
Stanford University, USA
,
Program Chairs:
Michal Feldman
Tel Aviv University, Israel
,
Michael Schwarz
Google, USA

Copyright © 2015 ACM.

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Published: 15 June 2015

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EC '15: ACM Conference on Economics and Computation

June 15 - 19, 2015

Oregon, Portland, USA

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EC '15 Paper Acceptance Rate 72 of 220 submissions, 33%;

Overall Acceptance Rate 664 of 2,389 submissions, 28%

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Cited By

Xia L(2022)Learning and Decision-Making from Rank DataundefinedOnline publication date: 11-Mar-2022
Xia LRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)The semi-random satisfaction of voting axiomsProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3540726(6075-6086)Online publication date: 6-Dec-2021
Doucette JTsang AHosseini HLarson KCohen R(2019)Inferring true voting outcomes in homophilic social networksAutonomous Agents and Multi-Agent Systems10.1007/s10458-019-09405-133:3(298-329)Online publication date: 1-May-2019
Xia L(2017)Improving group decision-making by artificial intelligenceProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171837.3172034(5156-5160)Online publication date: 19-Aug-2017
Pivato M(2017)Epistemic democracy with correlated votersJournal of Mathematical Economics10.1016/j.jmateco.2017.06.00172(51-69)Online publication date: Oct-2017

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