[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 15.01.2022 15:04, Colin Champion wrote:
> This seems very interesting. If I understand it correctly, Daniel is
> saying that when a voting method can be subverted by tactical voting in
> such a way that candidate c is elected in place of the rightful winner
> w, the subversion can nearly always be accomplished if all voters who
> prefer c to w simultaneously compromise on c and bury w.

Yes, that's correct.

>    I'm surprised that "false cycles" don't come into it. Should I
> conclude that artificially placing a candidate second hardly ever
> achieves anything not achieved by compromising and burial?

The setting may be a bit misleading: in the game that the strategy's
being calculated on, there's first an "honest" round, and then factions
who prefer someone else to the winner get to try to make that someone win.

In particular, there's no hidden information. In a real election, voters
who prefer some Y to X might not know that Y is the candidate they
should be compromising for, and that e.g. trying to compromise for Z
instead would backfire. So adjusting lower ranks may still be useful in
such a situation, or when the voters are aiming for destructive strategy
("anyone but T") rather than constructive.

Since the simulator tests the compromise+burial strategy first, it also
doesn't determine whether a less stark strategy would also have worked.
In a real setting, the candidates may not enjoy total loyalty from Y>X
voters.

As an argument in favor of Range, Warren sketches a scenario where the
frontrunners are X and Y and everybody either votes X>...>Y or Y>...>X.
As a consequence of the majority criterion, either X or Y wins; and then
he says that this probably will lead to two-party domination because the
strategy is self-stabilizing . The results from the strategy
calculations could be used to back up that argument.

However, it may well be that if everybody but one voter is doing so, and
a third party voter does A>X>...>Y instead of X>...>Y, then X still
wins; and so on up until enough tird party voters put A first, after
which A wins. And if the X>Y voters can't all be relied on to put X
first no matter what, then such weaker strategies may grow until there
are no longer only two frontrunners.

Dynamic strategy (my response to your response to...) is much harder to
model than static. But I would expect that methods that resist static
(one-shot) strategy better would also resist dynamic strategy better.

-km