Connections and Implications of the Ostrogorski Paradox for Spatial Voting Models

Abstract

In this chapter we connect spatial voting concepts with the troubling Ostrogorski and Anscombe paradoxes (where a majority of the voters can be on the losing side over a majority of the issues). By doing so, answers to longstanding concerns are obtained; e.g., Kelly conjectured that an Ostrogorski paradox ensures that no candidate can be a Condorcet winner; we prove this is true for any number of issues and establish a connection with McKelvey’s spatial “chaos theorem.” Other results include explaining why these paradoxes occur (i.e., “issue-by-issue” voting strips any intended connections a voter might have among the issues) and showing that if an Ostrogorski paradox occurs, then all possible spatial voting representations have an empty core. We firmly establish the long-suspected connection between the Ostrogorski paradox and the lack of a Condorcet winner in paired comparison voting. While providing new supermajority conclusions for the Ostrogorski paradox, we introduce a new class of paradoxes based on when a party can propose issues.