SUMMARY: Catholic Popes elected via Approval Voting 1294-1621

Renaissance conclaves were hotbeds of intrigue, the outcome of which was rarely predictable.
   – Eamon Duffy, Saints and Sinners, a history of the popes, Yale University Press 1997, p.148.

This page succinctly summarizes my conclusions about how approval voting worked in the real world when used to elect 41 Catholic Popes (actually more, since several "antipopes" were elected too). Our conclusions are based on our large collection of all the stories of all these elections; see also our attempted collection of the corresponding bare vote data. You can also read this for a description of the pope election rules and the story of

  1. how they came about
  2. the power of the Pope and his role in history.

Finally, there is a critique / frequently-asked-questions page about our Pope-conclusions here.

The Pope at his peak was one of the most, if not the most, powerful person in Europe; the Papacy remains the single longest-lasting elected position on the face of the Earth; and the period during which the pope-elections were conducted via approval voting lasted 326 years, substantially longer than the entire history of, e.g, the USA so far. Because of that and the large number of historians researching Popes, the Popes seem one of the easiest ways for somebody like me to find out how well approval voting performs in the real world.


1. Those pope elections were the most strategic, nasty things imaginable. Every trick you can think of was tried to game the system, plus plenty you wouldn't have been smart enough to think of.

2. The system used was basically repeated approval-voting elections (repeated until somebody got over threshold, which was about 2/3, whereupon the winner won). They had secret ballots, which seems to have been essential because otherwise, there was not inconsiderable risk that the new pope would literally have his opponents tortured and killed. They also had secret everything and the conclave was to be totally isolated from the world, which was intended to prevent corruption, etc – but that latter kind of secrecy usually totally failed – which is how I got all this data (there are many books on this in both English and Italian packed with info about what went on)

3. An oversimplified but still quite-accurate model of what happened was this. The 3-step strategy (A,B,C) all voters used was:

  1. Start out cautious by only approving the candidates you considered really very very good. A decent fraction of the time, that'd work to produce a pope quickly who had high approval – at which point everybody was happy (well, almost everybody) and game over.
  2. Then gradually lower your standards for approving somebody, keeping track of the strategic environment and introducing new candidates as appropriate. (As do this, try to tell lies about candidates, threaten, intimidate, bribe, etc etc). Of course, a faction could try to hold out forever, but that was discouraged by the fact that as time went on, they'd feed the conclavists less food.
  3. Eventually, all sides will have lowered their standards enough that some pope would get over-threshold number of approvals, and then would win.

4. So given the oversimplified strategy I just said, the result was roughly this: if you take everybody's utility function, the pope-candidate whose minimum utility (among his friendliest 2/3 of the voters) was greatest, would be elected. If we were to replace "2/3" with "1/2" in that sentence, this would have been exactly "maximum median utility" i.e. yielding almost exactly the same effect, with the ultra-strategic voters they had, as median-based range voting with honest voters would have yielded. (But it's actually "maximum 66-percentile utility" not "median.")

And that was a pretty good result! All in all, it's looking to me like the system they were using to select popes was actually quite good and did nearly as well as could be expected under the enormous stresses placed upon it by the ultra-conniving corrupt and colluding voters that were present.

The repeatedness of the approval voting, combined with the 2/3 supermajority threshold termination condition, probably significantly enhanced its quality.

5. What if they'd had range instead of approval voting? Well, due to the immensity of the strategicness, I think they'd have all voted in approval-style for all the perceived favorites, so in that sense it would have made no difference whatever.

However, for nonfavorites it might have made a difference, especially in early rounds, and probably for the better since good candidates would have been brought to the fore, and more quickly.

On the other hand, I think there is good reason to believe (discussed more in the critique and stories pages) that Borda, plain plurality, or instant runoff voting (IRV) all would have done worse.

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