We provide the first polynomial-time algorithm for recognizing if a profile of (possibly weak) preference orders is top-monotonic. Top-monotonicity is a generalization of the notions of single-peakedness and single-crossingness, defined by Barbera and Moreno. Top-monotonic profiles always have weak Condorcet winners and satisfy a variant of the median voter theorem. Our algorithm proceeds by reducing the recognition problem to the SAT-2CNF problem.

We provide the first polynomial-time algorithm for recognizing if a profile of (possibly weak) preference orders is top-monotonic. Top-monotonicity is a generalization of the notions of single-peakedness and single-crossingness, defined by Barbera and Moreno. Top-monotonic profiles always have weak Condorcet winners and satisfy a variant of the median voter theorem. Our algorithm proceeds by reducing the recognition problem to the SAT-2CNF problem.

Election control problems model situations where some entity (traditionally called the election chair) wants to ensure some candidate’s victory by either adding or deleting candidates or voters. The complexity of deciding if such control actions can be successful is well-studied for many typical voting rules and, usually, such control problems are $$\mathrm {NP}$$ -complete. However, Faliszewski et al. (Inf Comput 209(2):89–107, 2011) have shown that many control problems become polynomial-time solvable when we consider single-peaked elections. In this paper we show that a similar phenomenon applies to the case of single-crossing elections. Specifically, we consider the complexity of control by adding/deleting candidates/voters under plurality, Condorcet, and approval voting. For each of these control types and each of the rules, we show that if the control type is $$\mathrm {NP}$$ -complete in general, it becomes polynomial-time solvable for single-crossing elections.

Election control problems model situations where some entity (traditionally called the election chair) wants to ensure some agent's victory by either adding or deleting candidates or voters. The complexity of deciding if such control actions can be successful is well-studied for many typical voting rules and, usually, such control problems are NP-complete. However, Faliszewski et al. [16] have shown that many control problems become polynomial-time solvable when we consider single-peaked elections. In this paper we show that a similar phenomenon applies to the case of single-crossing elections. Specifically, we consider the complexity of control by adding/deleting candidates/voters under Plurality and Condorcet voting. For each of these control types and each of the rules, we show that if the control type is NP-complete in general, it becomes polynomial-time solvable for single-crossing elections.