When Pope Benedict XVI resigned in February 2013, there was much scrabbling by journalists to establish when last a pope resigned voluntarily. After a bit, they came up with the correct answer. It was in 1294, when the elderly hermit Pietro of Murrone, who had been elected as Celestine V after a two-year deadlock, abruptly resigned after five months and went back to being a hermit, a life he evidently preferred. But Celestine V was remarkable for two things, of which his resignation was but one. The other was his enforcement of the conclave. That distant event has decisively shaped the procedure for electing popes. To see why, we need to understand a lesson from social choice that papal electors learnt the hard way: the trade-off between stability and decisiveness.