[EM] Random Ballot / Smith

[Kristofer Munsterhjelm]

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