Modeling Single-Peakedness for Votes with Ties

The model of single-peaked preferences is one of the most important and well-known domain restrictions on preferences. The computational study of single-peaked electorates has been largely restricted to elections with tie-free votes, and recent work that studies the computational complexity of manipulative attacks for single-peaked elections for votes with ties has been restricted to newly defined nonstandard models of single-peaked preferences for top orders. We study the computational complexity of manipulation for the standard social-choice models of single-peaked and single-plateaued preferences for votes with ties. We show that the standard models avoid the anomalous complexity behavior exhibited by the nonstandard models. We also state a surprising result on the relation between the societal axis and the complexity of manipulation for single-peaked preferences.