Complexity of Sincere-Strategy Preference-Based Approval Control in k-Peaked Elections

Single-peaked elections have been attracting much attention recently. It turned out that many NP-hard voting problems become polynomial-time solvable when restricted to single-peaked elections. A natural generalization of the single-peaked elections is the $k$-peaked elections, where at most $k$ peaks are allowed in each vote in the election. In this paper, we mainly aim at establishing a complexity dichotomy of controlling behaviors of a variant of the sincere-strategy preference-based approval voting under $k$-peaked elections for different values of $k$. It turns out that most NP-hardness results in the general case also hold under $k$-peaked elections, even for $k=2,3$. On the other hand, we derive polynomial-time algorithms for certain sincere-strategy preference-based approval voting control problems for $k=2$. In addition, we also study the sincere-strategy preference-based approval control problems from the viewpoint of parameterized complexity and prove some FPT results.

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