[EM] Random Ballot / Smith

[Joshua Boehme]

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.