Here's an idea for an SPE method that should be pretty hard to manipulate. It can only be done interactively. First, the moderator chooses two candidates at random. The group votes pairwise between the two. Like in SPE, the winner of the two is retained. Then the moderator repeatedly chooses an unevaluated candidate at random, pairs the current champion with the challenger, and whoever wins pairwise goes on to the next round. The last candidate standing is the winner So basically it's SPE with a random candidate order, except that the order is not fixed in advance. That it's not should make it harder still to manipulate because it's far from obvious who a candidate should be buried under in order for the burial to succeed. For instance, suppose A and C are called. B>A voters know that A has good support so they would like to bury A to create a cycle where B wins. But they don't know if the future agenda order is set up so that burying under C will make some loathed candidate D win. Since it's interactive, it could also be combined with a candidate withdrawal option. James Green-Armytage has suggested that this could further limit strategy in Condorcet methods. In this version, after the winner has been decided in a round, the moderator asks if any of the candidates would like to withdraw, before continuing to the next round's random selection. It's not cloneproof since it uses Random Candidate instead of Random Ballot. A better version would use Random Ballot, but it would be harder to do so interactively - to pick a random voter and ask for that voter's favorite among the unevaluated candidates. And obviously there should be great security around the entropy source so that the moderator can't control the agenda. -km

On Sat, Jan 29, 2022 at 7:35 AM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > Here's an idea for an SPE method that should be pretty hard to > manipulate. It can only be done interactively. > > First, the moderator chooses two candidates at random. The group votes > pairwise between the two. Like in SPE, the winner of the two is > retained. Then the moderator repeatedly chooses an unevaluated candidate > at random, pairs the current champion with the challenger, and whoever > wins pairwise goes on to the next round. The last candidate standing is > the winner > > So basically it's SPE with a random candidate order, except that the > order is not fixed in advance. That it's not should make it harder still > to manipulate because it's far from obvious who a candidate should be > buried under in order for the burial to succeed. > > For instance, suppose A and C are called. B>A voters know that A has > good support so they would like to bury A to create a cycle where B > wins. But they don't know if the future agenda order is set up so that > burying under C will make some loathed candidate D win. > Up to this point, would the system work the same way if the order was set by a pseudo-random number generator? You could use properties of the ballots cast as a source of entropy. It's not cloneproof since it uses Random Candidate instead of Random > Ballot. A better version would use Random Ballot, but it would be harder > to do so interactively - to pick a random voter and ask for that voter's > favorite among the unevaluated candidates. > > And obviously there should be great security around the entropy source > so that the moderator can't control the agenda. > In the interactive version, I wonder what would happen if the losing candidate gets to pick the next candidate. I'm hoping that that could make the strategy complex enough to be impractical. Cheers, -- Dr. Daniel Carrera Postdoctoral Research Associate Iowa State University