Abstract
The Majority game is a two player game with a questioner Q and an answerer A. The answerer holds n elements, each of which can be labeled as 0 or 1. The questioner can ask questions comparing whether two elements have the same or different label. The goal for the questioner is to ask as few questions as possible to be able to identify a single element which has a majority label, or in the case of a tie claim there is none. We denote the minimum number of questions Q needs to make, regardless of A’s answers, as q *. In this paper we consider a variation of the Majority game where A is allowed to lie up to t times, i.e., Q needs to find an error-tolerant strategy. In this paper we will give upper and lower bounds for q * for an adaptive game (where questions are processed one at a time), and will find q * for an oblivious game (where questions are asked in one batch).
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References
Aigner, M.: Variants of the majority problem. Applied Discrete Mathematics 137, 3–25 (2004)
Aigner, M., De Marco, G., Montangero, M.: The plurality problem with three colors and more. Theoretical Computer Science 337, 319–330 (2005)
Alonso, L., Reingold, E., Schott, R.: Determining the majority. Information Processing Letters 47, 253–255 (1993)
Alonso, L., Reingold, E., Schott, R.: Average-case complexity of determining the majority. SIAM J. Computing 26, 1–14 (1997)
Alonso, L., Reingold, E.: Determining plurality. Manuscript (2006)
Chung, F.R.K., Graham, R.L., Mao, J., Yao, A.C.: Finding favorites. ECCC Report TR03-078, Electronic Colloquium on Computational Complexity (2003)
Chung, F.R.K., Graham, R.L., Mao, J., Yao, A.C.: Oblivious and adaptive strategies for the majority and plurality problems. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 329–338. Springer, Heidelberg (2005)
Dvořák, Z., Jelínek, V., Král’, D., Kynčl, J., Saks, M.: Three optimal algorithms for balls of three colors. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 206–217. Springer, Heidelberg (2005)
Fischer, M.J., Salzberg, S.L.: Finding a majority among n votes. J. Algorithms 3, 375–379 (1982)
Kral, D., Sgall, J., Tichỳ, T.: Randomized strategies for the plurality problem. Manuscript (2005)
Moore, J.: Proposed problem 81-5. J. Algorithms 2, 208–210 (1981)
Pelc, A.: Searching games with errors — fifty years of coping with liars. Theoret. Comput. Sci. 270, 71–109 (2002)
Rényi, A.: On a problem in information theory. Magyar Tud. Akad. Mat. Kutató Int. Közl. 6, 505–516 (1961)
Saks, M., Werman, M.: On computing majority by comparisons. Combinatorica 11, 383–387 (1991)
Srivastava, N., Taylor, A.D.: Tight bounds on plurality. Information Processing Letters 96, 93–95 (2005)
Ulam, S.M.: Adventures of a mathematician. Charles Scribner’s Sons, New York (1976)
Wiener, G.: Search for a majority element. J. Statistical Planning and Inference 100, 313–318 (2002)
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Butler, S., Mao, J., Graham, R. (2007). How to Play the Majority Game with Liars. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_21
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DOI: https://doi.org/10.1007/978-3-540-72870-2_21
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