[EM] Method Y

[Forest Simmons]

On Fri, Aug 4, 2023, 2:41 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 8/4/23 22:54, Forest Simmons wrote:
> > If there is an honest cycle, then there can be no burial of the (non
> > existant sincere CW) the only kind of burial  we should worry about
> > until we have that completely under control, which (almost) no other
> > proposed method claims to do.
>
> In that case, you should be able to use any ordering you'd like for the
> elimination process.


True, except we still have to deal with sincere cycles no matter how rare
they may be. My point is that insincere cycles are much more likely to be
brought about by burial of a CW than some other kind of burial.

The simplest policy (imho) is to treat all cycles as though they were
either subverted CW's or sincere.

Sincere cycles should be resolved by Classical Condorcet. Insincere cycles
should be resolved by some method akin to Method Y.

Here's how to do it when the ballot Smith set has exactly three candidates
X, Y, and Z:

Suppose without loss that X is the candidate whose max pairwise defeat
(among the three Smith members) is minimal.

Then the manual runoff should be between Y and Z unless a majority of
voters prefer X to the Y vs Z runoff.

This ceremony will elect the Sincere CW if there is one ... otherwise it
will elect X.

To see the truth ofthis fact suppose that there is no sincerely unbeaten
candidate among the three. Then there is a sincere cycle XYZX or its
reverse ZYXZ.

In the first case, if X is passed up, then the winner is Y, the runoff
winner between Y and Z. But X is preferred pairwise over Y, so a well
informed electorate would probably not pass up the opportunity to elect X.

The other case is similar ... but this time if X is passed up, Z wins ...
but X (in the sincere ZYXZ cycle) is preferred over Z ...  so it would be a
mistake to pass up the chance to elect X (mod self hating voters).

In sum, when the Smith set is a triple, and X is the MinMax PairwiseDefeat
candidate (according to the actual preference ballot set) of the three,
then a manual runoff between Y and Z if a majority decides to not elect X
... will elect the sincere CW if there is one ... else it will break the
sincere top cycle at the weakest link.

Pretty nifty?

fws


Even a random one disclosed ahead of time should
> work! (And with random, all you'd have to ask the voters is one binary
> question per round.)
>
> I'm curious if there's a backwards induction argument that traditional
> exhaustive runoff should also elect the honest CW. I'm thinking
> something like: every voter who prefers the outcome of continuing the
> process to the current candidate will vote against the current
> candidate, but when the current candidate is the CW, that's not
> feasible. All that the supporters of whatever the result is when
> continuing have to do, is to vote for someone else than the current
> honest Plurality loser.
>
> -km
>
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