We study the problem of designing a distributed voting scheme for electing a candidate that maximizes the preferences of a set of agents. We assume the preference of agent $i$ for candidate $j$ is a real number ${x}_{i,j}$, and we do not make any assumptions on the mechanism generating these preferences. We show simple randomized voting schemes guaranteeing the election of a candidate whose expected total preference is nearly the highest among all candidates. The algorithms we consider are designed so that each agent has to disclose only a few bits of information from his preference table. Finally, in the important special case in which each agent is forced to vote for at most one candidate we show that our voting scheme is essentially optimal.

@article{ITA_2006__40_2_389_0, author = {Auer, Peter and Cesa-Bianchi, Nicol\`o}, title = {A distributed voting scheme to maximize preferences}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {389--403}, publisher = {EDP-Sciences}, volume = {40}, number = {2}, year = {2006}, doi = {10.1051/ita:2006015}, mrnumber = {2252646}, zbl = {1112.68133}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2006015/} }

TY - JOUR AU - Auer, Peter AU - Cesa-Bianchi, Nicolò TI - A distributed voting scheme to maximize preferences JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 389 EP - 403 VL - 40 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2006015/ DO - 10.1051/ita:2006015 LA - en ID - ITA_2006__40_2_389_0 ER -

%0 Journal Article %A Auer, Peter %A Cesa-Bianchi, Nicolò %T A distributed voting scheme to maximize preferences %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 389-403 %V 40 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2006015/ %R 10.1051/ita:2006015 %G en %F ITA_2006__40_2_389_0

Auer, Peter; Cesa-Bianchi, Nicolò. A distributed voting scheme to maximize preferences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 2, pp. 389-403. doi : 10.1051/ita:2006015. http://www.numdam.org/articles/10.1051/ita:2006015/

[1] Tight bounds on the cumulative profit of distributed voters, in Proceedings of the 15th ACM Symposium on Principles of Distributed Computing. ACM Press (1996) 312.

, and ,[2] Distributed voting and maximum satisfiability. Unpublished manuscript (1993).

, and ,[3] Multi-policy iteration with a distributed voting. Math. Methods Oper. Res. 60 (2004) 299-310. | Zbl

,[4] On the probability of correct selection by distributed voting in stochastic optimization. J. Optim. Theory Appl. 125 (2005) 231-240. | Zbl

,[5] Probability Theory. Springer (1988). | MR | Zbl

and ,[6] Distributed decision-making with incomplete information, in Proceedings of the 12ft IFIP Congress. Madrid (1992).

and ,[7] Rank aggregation revisited, in Proceedings of the 10th International World Wide Web Conference (2001) 96-104.

, , and ,[8] Reaching agreement through partial revelation of preferences, in Proceedings of the 10th European Conference on Artificial Intelligence (1992) 229-233.

and ,[9] On the value of information in distributed decision making, in Proceedings of the 10th ACM Symposium on Principles of Distributed Computing. ACM Press (1991) 61-64.

and ,[10] Linear programming without the matrix, in Proceedings of the 25th ACM Symposium on the Theory of Computing. ACM Press (1993) 121-129.

and ,[11] Convergence of Stochastic Processes. Springer (1984). | MR | Zbl

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