Decentralized voting with unconditional privacy

The aggregation of conflicting preferences is a key issue in multiagent systems. Due to its universality, voting has a central role among preference aggregation mechanisms. Voting among a set of alternatives can be used for such diverse tasks as choosing a joint plan in a multiagent system, determining a leader in a group of humans or agents, or voting among different resource or task allocations. Maintaining privacy of individuals' votes is crucial in order to guarantee freedom of choice (e.g., lack of vote coercing and reputation effects), and not facilitate strategic voting. We investigate whether unconditional full privacy can be achieved in voting, that is, privacy that relies neither on trusted third parties (or on a certain fraction of the voters being trusted), nor on computational intractability assumptions (such as the hardness of factoring). In particular, we study the existence of distributed protocols that allow voters to jointly determine the outcome of an election without revealing any information but the election outcome. We show the impossibility of reaching unconditional full privacy for a variety of the most common voting schemes ranging from simple veto voting to the single transferable vote scheme. On the positive side, we propose several distributed protocols that privately compute the outcome of common voting schemes while only revealing a limited amount of information.

[1]  Eyal Kushilevitz,et al.  Privacy and communication complexity , 1989, 30th Annual Symposium on Foundations of Computer Science.

[2]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[3]  D.C. Parkes,et al.  Distributed implementations of Vickrey-Clarke-Groves mechanisms , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

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

[5]  Ronald Cramer,et al.  A secure and optimally efficient multi-authority election scheme , 1997, Eur. Trans. Telecommun..

[6]  Birgit Pfitzmann,et al.  Unconditionally Untraceable and Fault-tolerant Broadcast and SecretBallot Election , 1992 .

[7]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[8]  Eyal Kushilevitz,et al.  On the structure of the privacy hierarchy , 2004, Journal of Cryptology.

[9]  Vincent Conitzer,et al.  Vote elicitation: complexity and strategy-proofness , 2002, AAAI/IAAI.

[10]  David Chaum,et al.  Elections with Unconditionally-Secret Ballots and Disruption Equivalent to Breaking RSA , 1988, EUROCRYPT.

[11]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

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

[13]  Eric Horvitz,et al.  Social Choice Theory and Recommender Systems: Analysis of the Axiomatic Foundations of Collaborative Filtering , 2000, AAAI/IAAI.

[14]  Eithan Ephrati,et al.  Deriving Consensus in Multiagent Systems , 1996, Artif. Intell..

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

[16]  David C. Parkes,et al.  Using redundancy to improve robustness of distributed mechanism implementations , 2003, EC '03.

[17]  Oded Goldreich,et al.  Foundations of Cryptography: Basic Tools , 2000 .

[18]  Felix Brandt,et al.  (Im)possibility of unconditionally privacy-preserving auctions , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[19]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[20]  Felix Brandt,et al.  Unconditional privacy in social choice , 2005, TARK.

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

[22]  Donald E. Knuth,et al.  The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm , 1981, ICALP.

[23]  Josh Benaloh,et al.  Secret Sharing Homomorphisms: Keeping Shares of A Secret Sharing , 1986, CRYPTO.

[24]  Aggelos Kiayias,et al.  Self-tallying Elections and Perfect Ballot Secrecy , 2002, Public Key Cryptography.

[25]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[26]  Eyal Kushilevitz,et al.  A zero-one law for Boolean privacy , 1989, STOC '89.

[27]  Vincent Conitzer,et al.  Communication complexity of common voting rules , 2005, EC '05.