Abstract
Aggregating votes that are preference orders over candidates or alternatives is a fundamental problem of decision theory and social choice. We study this problem in the setting when alternatives are described as tuples of values of attributes. The combinatorial spaces of such alternatives make explicit enumerations of alternatives from the most to the least preferred infeasible. Instead, votes may be specified implicitly in terms of some compact and intuitive preference representation mechanism. In our work, we assume that votes are given as lexicographic preference trees and consider two preference-aggregation problems, the winner problem and the evaluation problem. We study them under the assumption that positional scoring rules are used for aggregation. In particular, we consider k-Approval and b-Borda, a generalized Borda rule, and we discover new computational complexity results for them.
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Notes
- 1.
Given a set \(\varPhi \) of n 2-clauses \(\{ C_1,\ldots ,C_n \}\) over a set of propositional variables \(\{ X_1,\ldots ,X_p \}\), and a positive integer l (\(l \le n\)), decide whether there is a truth assignment that satisfies at most l clauses in \(\varPhi \).
- 2.
We will build \(P_i\) according to what \(C_i\) contains: the two atoms in \(C_i\) are the labels of the top two levels of trees, and whether the atom is negated affects the preference on that atom.
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The work of the second author was supported by the NSF grant IIS-1618783.
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Liu, X., Truszczynski, M. (2019). New Complexity Results on Aggregating Lexicographic Preference Trees Using Positional Scoring Rules. In: Pekeč, S., Venable, K.B. (eds) Algorithmic Decision Theory. ADT 2019. Lecture Notes in Computer Science(), vol 11834. Springer, Cham. https://doi.org/10.1007/978-3-030-31489-7_7
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