[EM] Random Ballot / Smith

[Joshua Boehme]

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.)