Finite Local Consistency Characterizes Generalized Scoring Rules

An important problem in computational social choice concerns whether it is possible to prevent manipulation of voting rules by making it computationally intractable. To answer this, a key question is how frequently voting rules are manipulable. We [Xia and Conitzer, 2008] recently defined the class of generalized scoring rules (GSRs) and characterized the frequency of manipulability for such rules. We showed, by examples, that most common rules seem to fall into this class. However, no natural axiomatic characterization of the class was given, leaving the possibility that there are natural rules to which these results do not apply. In this paper, we characterize the class of GSRs based on two natural properties: it is equal to the class of rules that are anonymous and finitely locally consistent. Generalized scoring rules also have other uses in computational social choice. For these uses, the order of the GSR (the dimension of its score vector) is important. Our characterization result implies that the order of a GSR is related to the minimum number of locally consistent components of the rule. We proceed to bound the minimum number of locally consistent components for some common rules.

[1]  H. Young.  Social Choice Scoring Functions , 1975 .

[2]  Martin F. Porter,et al.  An algorithm for suffix stripping , 1997, Program.

[3]  Vincent Conitzer,et al.  When are elections with few candidates hard to manipulate? , 2007, J. ACM.

[4]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[5]  Tim Leek,et al.  Information Extraction Using Hidden Markov Models , 1997 .

[6]  Vincent Conitzer,et al.  Generalized scoring rules and the frequency of coalitional manipulability , 2008, EC '08.

[7]  Piotr Faliszewski,et al.  Copeland voting: ties matter , 2008, AAMAS.

[8]  Edith Elkind,et al.  Hybrid Voting Protocols and Hardness of Manipulation , 2005, ISAAC.

[9]  Ariel D. Procaccia,et al.  Algorithms for the coalitional manipulation problem , 2008, SODA '08.

[10]  Felix Brandt,et al.  Some Remarks on Dodgson's Voting Rule , 2009, Math. Log. Q..

[11]  Inon Zuckerman,et al.  Universal Voting Protocol Tweaks to Make Manipulation Hard , 2003, IJCAI.

[12]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[13]  Ariel D. Procaccia,et al.  Average-case tractability of manipulation in voting via the fraction of manipulators , 2007, AAMAS '07.

[14]  Mark Craven,et al.  Representing Sentence Structure in Hidden Markov Models for Information Extraction , 2001, IJCAI.

[15]  Anders Krogh.  Hidden Markov models for labeled sequences , 1994, Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3 - Conference C: Signal Processing (Cat. No.94CH3440-5).

[16]  Limsoon Wong,et al.  Accomplishments and challenges in literature data mining for biology , 2002, Bioinform..

[17]  Ariel D. Procaccia,et al.  Complexity of unweighted coalitional manipulation under some common voting rules , 2009, IJCAI 2009.

[18]  Ariel D. Procaccia,et al.  Junta distributions and the average-case complexity of manipulating elections , 2006, AAMAS '06.

[19]  Richard M. Schwartz,et al.  An Algorithm that Learns What's in a Name , 1999, Machine Learning.

[20]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[21]  Andrew McCallum,et al.  Maximum Entropy Markov Models for Information Extraction and Segmentation , 2000, ICML.

[22]  Yoram Singer,et al.  The Hierarchical Hidden Markov Model: Analysis and Applications , 1998, Machine Learning.

[23]  Edith Hemaspaandra,et al.  Dichotomy for voting systems , 2005, J. Comput. Syst. Sci..

[24]  Andrew McCallum,et al.  Information Extraction with HMM Structures Learned by Stochastic Optimization , 2000, AAAI/IAAI.

[25]  toby. walsh.  Where are the really hard manipulation problems ? The manipulation phase transition , 2008 .

[26]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[27]  Ariel D. Procaccia,et al.  Junta Distributions and the Average-Case Complexity of Manipulating Elections , 2007, J. Artif. Intell. Res..

[28]  Kenneth O. May,et al.  A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision , 1952 .

[29]  Yann Chevaleyre,et al.  Compiling the votes of a subelectorate , 2009, IJCAI 2009.

[30]  P. Pattanaik,et al.  Social choice and welfare , 1983 .

[31]  Scott Miller,et al.  A Novel Use of Statistical Parsing to Extract Information from Text , 2000, ANLP.

[32]  Vincent Conitzer,et al.  Nonexistence of Voting Rules That Are Usually Hard to Manipulate , 2006, AAAI.

[33]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[34]  Bojan Cestnik,et al.  Estimating Probabilities: A Crucial Task in Machine Learning , 1990, ECAI.

[35]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .