Ideological reversal occurs in an election when parties choose policy platforms that reverse their ideological order. We study an ordinal spatial voting game in which voter and party preferences are single peaked. When every voter participates in voting, single peakedness alone prevents reversal at equilibrium. However, when voters are allowed to abstain, we show that single peakedness is insufficient to rule out such reversals. We demonstrate an example where parties are ideologically reversed at the unique equilibrium. We then identify a sufficient condition on party preferences which rules out the existence of such reversed equilibria, even under abstention.
Multiple zeta functions typically have singularities at non-positive integer tuples. In particular, their special values are not always well-defined. In this talk, we introduce ordered limits values which correspond to a type of regularization of multiple zeta values at non-positive integer points, and we investigate their vanishing behavior.