[EM] DMC Based Burial Resistance

[Forest Simmons]

The DMC candidate is the candidate with the least Implicit Approval that
defeats every candidate with more IA.

The original formulation of DMC was as Benham, IA: eliminate the lowest IA
candidates one-by- one until there remains an undefeated candidate among
the uneliminated.

To base burial resistance on DMC, let X1 be the DMC candidate. Let X2 be
the highest IA candidate to defeat X1, and let X3 be the highest IA
candidate to defeat X2. [Assuming no undefeated candidate exists].

More often than not, X1 will be the candidate of the buriers, X2 will be
the buried candidate, and X3 will be the "bus" candidate under whom the X1
faction buried X2.

To punish the buriers, elect the bus X3.

To fairly and squarely "unbury X2," i.e. restore the (likely) sincere CW to
its rightful status, elect the winner of a sincere runoff between X1 and X2.

To wean ourselves entirely from dependence on the "more often than not"
assumption, do a sincere three candidate runoff of the form ... (X1 vs X2)
vs X3.

The first stage decides between two alternatives a1 and a2, where a1 is to
elect the winner of a runoff between X1 and X2  (thereby rejecting
alternative a2), and a2 is to reject a1 and elect X3.

Optimal runoff strategy is to vote for a2 in the first stage of the runoff
iff you prefer X3 to the projected winner of the a1 runoff.

If a2 wins the first stage, then there is no second stage ... X3 is elected.

If a1 wins the first stage, your optimum strategy in the second stage is to
vote for your sincere preference between X1 and X2.

If the voters are both rational and well informed about the preferences of
the other voters, then they will vote according to the above strategy
recommendations, and the Sincere CW will be elected, if one exists among
the three candidates X1,X2, and X3.

A slightly cleaner version DMC' of DMC can be formulated by replacing
Implicit Approval with MaxPairwiseSupport: The DMC' candidate is lowest
MaxPS candidate that defeats every candidate with greater MaxPS, etc.

Examples ... coming soon!

fws
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