[EM] Rethinking Burial Detection Runoff

[Forest Simmons]

Critiques by Kevin Venzke and Chris Benham have caused me to rethink my
approach to detection of a buried CW.

To see the extent of the difficulty, let's reconsider one of Benham's
example profiles:

46 A>B
44 B>C
5 C>A
5 C>B

There are three possible unilateral burial explanations for the ABCA cycle:

1. Sincere 46 A>C --> 46 A>B
2. Sincere 44 B>A --> 44 B>C
3. Sincere 5 C>A --> 5 C>B

If we are to depend on a final sincere binary runoff to determine the
sincere CW, which two candidates should be the finalists?

Instead, I suggest a different kind of ballot that will detect a sincere CW
under the assumption of rational voters in possession of perfect
information about each other's sincere preferences.

For Chris's example profile the new tangled ballot might look like ...

B?(C?A)

There are only four valid ballot submission possibilities:

B>(C>A)
B>(C<A)
B<(C>A)
B<(C<A)

The instructions are (for each question mark), to answer the indicated
question by replacing the question mark with an inequality mark.

It can be shown that if B is the sincere CW, a majority of the rational
voters will replace the first question mark with ">".

Otherwise, the final runoff choice, answering the question C?A, will
determine the winner.

For rational voters the other ballot possibilities, including; A?(B?C) aas
well as C?(A?B), would (theoretically) work just as well to elect the
sincere CW.

What in general is the best psychological policy for setting up the
decision tree?

Is it to set apart the RP winning votes alternative?

Or perhaps the implicit approval chain climbing winner ... or perhaps the
Sequential Pairwise Elimination winner ... with or without "takedown."

fws
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