We derive two hardness results on stable winning coalitions in Gamson’s game. First, it is coNP-complete to decide whether there exists a stable winning coalition that is connected. Secondly, it is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Delta _2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="normal">Δ</mi> <mn>2</mn> </msub> </math> </EquationSource> </InlineEquation>P-complete to decide whether there exists a stable winning coalition...</equationsource></equationsource></inlineequation>

We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient...

Given a tournament T, a Banks winner of T is the top vertex of any maximal (with respect to inclusion) transitive subtournament of T. In this technical note, we show that the problem of deciding whether some fixed vertex v is a Banks winner for T is NP-complete. Copyright Springer-Verlag Berlin...