Has there been any consideration of a random ballot / Smith combo method? That is, select a random ballot, and chose its highest-ranked Smith-set candidate. It's very simple, and it also looks both monotonic* and clone-proof. Granted, we lose the strategy-proofness of random ballot, but maybe even then it's not too bad? Consider the burial problem. A faction with a particular Favorite tries to force a cycle between the Honest Condorcet Winner (HCW) and a Bus candidate to throw HCW under, even though Bus is truly their least preferred of the three. Under typical methods, the ideal outcome for this strategic faction is to have the resulting three-way cycle break in favor of Favorite, so the final outcome shifts from 100% HCW to 100% Favorite. Under random ballot / Smith, though, the best case is a lottery between HCW, Favorite, and Bus. (If the faction could make Favorite a Condorcet winner outright, they wouldn't need to try this trick.) Maybe that lottery is still preferable to 100% HCW, but then again maybe not. At the same time, as with any Condorcet method, if it blows up in their face they end up making Bus the Condorcet winner instead. Less upside for the same downside. * when raising a candidate X, if that makes X join the Smith set that clearly doesn't hurt X (might not actually help if X wouldn't have any first preferences among the Smith-set candidates); likewise, if raising X knocks one or more non-X candidates out of the Smith set that also doesn't hurt X. Raising X can cause a non-X candidate to enter the Smith set, but only if it also causes X to enter too, in which case X had zero probability to begin with and nothing to lose. At the random ballot step, raising X similarly can never hurt X.

On 2025-09-15 23:33, Joshua Boehme via Election-Methods wrote: > > Has there been any consideration of a random ballot / Smith combo > method? That is, select a random ballot, and chose its highest-ranked > Smith-set candidate. It's very simple, and it also looks both monotonic* > and clone-proof. > > Granted, we lose the strategy-proofness of random ballot, but maybe even > then it's not too bad? Consider the burial problem. A faction with a > particular Favorite tries to force a cycle between the Honest Condorcet > Winner (HCW) and a Bus candidate to throw HCW under, even though Bus is > truly their least preferred of the three. Under typical methods, the > ideal outcome for this strategic faction is to have the resulting > three-way cycle break in favor of Favorite, so the final outcome shifts > from 100% HCW to 100% Favorite. Under random ballot / Smith, though, the > best case is a lottery between HCW, Favorite, and Bus. (If the faction > could make Favorite a Condorcet winner outright, they wouldn't need to > try this trick.) Maybe that lottery is still preferable to 100% HCW, but > then again maybe not. At the same time, as with any Condorcet method, if > it blows up in their face they end up making Bus the Condorcet winner > instead. Less upside for the same downside. I think that this property is balanced by that it also goes random if an innocent cycle occurs or if the buriers' attempts would otherwise fail. A deterministic method sometimes gets it right (and elects either the honest winner or the bus) and sometimes is fooled (and elects the burier's candidate); Smith/RB gets it partially right all the time instead of fully right or not right at all. I'm not sure what the expectation of getting it right over, say, all impartial or spatial elections of a particular candidate would be (in the limit of number of voters going to infinity), so I can't say for sure if it would be worth it. Maybe it is - maybe even risk aversion would keep people from trying to engineer a cycle at all. But without testing, I wouldn't know :-) It does open the possibility to other "nonconventional" methods, though. For instance, you could have a second round if there's a cycle (runoff style), or you could draw an assembly at random and have them decide after deliberation, using some kind of supermajority requirement or Heitzig-type consensus mechanism. If the burier's favorite is easy to spot, these should both make burial impractical. Armytage also suggested a candidate withdrawal option, where the bus withdraws and thus makes the burial fail. -km

On 9/20/25 7:13 AM, Kristofer Munsterhjelm wrote: > I think that this property is balanced by that it also goes random if an > innocent cycle occurs or if the buriers' attempts would otherwise fail. A > deterministic method sometimes gets it right (and elects either the honest > winner or the bus) and sometimes is fooled (and elects the burier's > candidate); Smith/RB gets it partially right all the time instead of fully > right or not right at all. > > I'm not sure what the expectation of getting it right over, say, all > impartial or spatial elections of a particular candidate would be (in the > limit of number of voters going to infinity), so I can't say for sure if it > would be worth it. Maybe it is - maybe even risk aversion would keep people > from trying to engineer a cycle at all. But without testing, I wouldn't > know :-) > > It does open the possibility to other "nonconventional" methods, though. For > instance, you could have a second round if there's a cycle (runoff style), > or you could draw an assembly at random and have them decide after > deliberation, using some kind of supermajority requirement or Heitzig-type > consensus mechanism. If the burier's favorite is easy to spot, these should > both make burial impractical. Armytage also suggested a candidate withdrawal > option, where the bus withdraws and thus makes the burial fail. > > -km Where I would quibble is with the characterization of the "right" solution for a cycle. Sure, if you absolutely cannot implement any stochastic solution at all, then yes break the weakest link in a 3-cycle. Then again, what happens if two or three links are tied for weakest? Avoiding stochastic solutions entirely is very challenging. I'd argue it's also unnecessary. Everyone's comfortable with a random tiebreaker for plurality elections. Cycles are just a more general form of tie. (It's also worth mentioning that avoiding impacts from clones in tiebreakers generally requires a little more care than in the plurality case -- since plurality isn't cloneproof anyway -- but in at least some voting systems it's still straightforward; picking a random ballot as the basis for breaking the tie typically suffices.)

On 2025-09-21 13:33, Joshua Boehme via Election-Methods wrote: > > > On 9/20/25 7:13 AM, Kristofer Munsterhjelm wrote: > >> I think that this property is balanced by that it also goes random if >> an innocent cycle occurs or if the buriers' attempts would otherwise >> fail. A deterministic method sometimes gets it right (and elects >> either the honest winner or the bus) and sometimes is fooled (and >> elects the burier's candidate); Smith/RB gets it partially right all >> the time instead of fully right or not right at all. >> >> I'm not sure what the expectation of getting it right over, say, all >> impartial or spatial elections of a particular candidate would be (in >> the limit of number of voters going to infinity), so I can't say for >> sure if it would be worth it. Maybe it is - maybe even risk aversion >> would keep people from trying to engineer a cycle at all. But without >> testing, I wouldn't know :-) >> >> It does open the possibility to other "nonconventional" methods, >> though. For instance, you could have a second round if there's a cycle >> (runoff style), or you could draw an assembly at random and have them >> decide after deliberation, using some kind of supermajority >> requirement or Heitzig-type consensus mechanism. If the burier's >> favorite is easy to spot, these should both make burial impractical. >> Armytage also suggested a candidate withdrawal option, where the bus >> withdraws and thus makes the burial fail. >> >> -km > > > Where I would quibble is with the characterization of the "right" > solution for a cycle. Sure, if you absolutely cannot implement any > stochastic solution at all, then yes break the weakest link in a > 3-cycle. Then again, what happens if two or three links are tied for > weakest? Avoiding stochastic solutions entirely is very challenging. I meant "right" as in "a way that doesn't reward the buriers" by electing the pre-burial winner or punishing the buriers by electing the bus (under which the honest candidate is thrown). I guess I could have made that clearer before I used the term. Breaking at the weakest pairwise victory may not be "right" in this sense; e.g. fpA-fpC and Smith//IRV resist burial more effectively than minmax does. So my point was more that if you want to ignore or punish buriers who set up a cycle, then deterministic methods discourage strategy by making burial only work some of the time, and be detrimental to the buriers the rest of the time. In contrast, Smith,RB makes burial work partly all of the time (as long as the buriers can engineer a cycle), because the burier's candidate has a nonzero chance of being elected. The appeal (as I read it) is that even if burial succeeds, there's a chance that the pre-burial honest winner or the bus gets elected instead, which makes it risky to bury in the first place. But it's still possible that there exist deterministic methods where the expected probability of burial succeeding is lower than the same expectation for Smith,RB. > I'd argue it's also unnecessary. Everyone's comfortable with a random > tiebreaker for plurality elections. Cycles are just a more general form > of tie. The few large-scale political Condorcet cycles (Minneapolis and Oakland IIRC) seem to be noise, and a random tiebreaker would be okay in that case, I think. But adopting Condorcet could lead to more candidates running and more issues being considered at once, which in turn could lead to "true" Condorcet cycles. Warren Smith used an example like: Candidate Domestic Foreign Corruption A Improve Wage war Some dirty public services dealings B Maintain status quo Peace Clear mob with disinterest connections C Drain maintenance Vague Clean and budgets mumbling transparent Suppose the voters who mainly care about services vote A>B>C, the ones who care about foreign policy vote B>C>A, and the ones who care about corruption vote C>A>B. Then you could get a Condorcet cycle if they're mainly focused on their own issue. If such situations would be common, then just breaking things by a tie may not be good enough, because the presence of a cycle indicates a society with conflicted opinions rather than one that's indifferent. > (It's also worth mentioning that avoiding impacts from clones in > tiebreakers generally requires a little more care than in the plurality > case -- since plurality isn't cloneproof anyway -- but in at least some > voting systems it's still straightforward; picking a random ballot as > the basis for breaking the tie typically suffices.) Random ballot is cloneproof, so that should work. Random plurality - picking proportional to first preference counts after eliminiating non-Smith members - would also work, since the sum of clones' first preferences is the same as the first preference count of the cloned candidate. -km