Electing the Pope: Elections by Repeated Ballots

• Authors: Clara Ponsatí and Jan Zápal
• BSE Working Paper: 1553 | January 2026
• Keywords: repeated ballots, conclave, Pope, electable, stable, supermajority
• JEL codes: D71, D72, Z12

A finite group of voters must elect the pope from a finite set of candidates. They repeatedly cast ballots (possibly for ever) until one candidate attains at least Q votes. A candidate is electable—if enough voters prefer him to a continuous disagreement—as well as stable—if no other candidate is preferred to him by a sufficient number of voters. We provide a necessary and sufficient condition for the existence of a candidate that is both electable and stable. When there are three candidates and voters are willing to compromise somewhat, the condition requires choice by two-thirds supermajority, which coincides with the procedure that the Catholic Church has used to appoint the pope for almost a millennium.