[EM] Majority Approval/Disapproval based aggregate social order

[Forest Simmons]

Approval Sorted Margins is a good way to get an aggregated social ranking
of the candidates ... but here's another one with it's own charms inspired
by the question what to do when more than one or fewer than one candidate
gets majority approval ...

First the manual version ...

For now let's assume an odd number of voters to keep things simple ...

At stage n each voter submits an approval ballot constrained by a
consistency rule explained below.* Each alternative gets a point of plus or
minus 1/2^n depending on whether or not it was approved on more ballots
than not or vice-versa (that is approved on fewer ballots than disapproved
... for the vice-versa part).

At any stage n when the candidates' scores attain complete numerical
distinction, their numerical order gives the finish order.

*If at some previous stage k<n a voter V's approval/disapproval for
candidate X is contradicted by the majority decision, then the voter is
locked in to its approval/disapproval decision for that candidate at all
subsequent stages ... consistency requires this doubling down... think
about it!

A faithful simulation "instant" version of this method is easy to devise on
the basis of Dyadic Approval ballots or "ranked rankings" in general.

...more on this next time ...

FWS
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