In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the proportion of profiles, at which a successful attempt to manipulate might take place, is in both cases bounded from above by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$K/\sqrt n$$</EquationSource> </InlineEquation>,...</equationsource></inlineequation>

In this paper, we classify all maximal peak-pit Condorcet domains of maximal width for n È 5 alternatives. To achieve this, we bring together ideas from several branches of combinatorics. The main tool used in the classification is the ideal of a domain. In contrast to the size of maximal...