[EM] Dyadic Votes

[Martin Harper]

I was considering using a Dyadic Approval vote for this poll, primarily to get a
feel of what it'd be like to vote with it unaided by fancy computer graphics and
the like. Anywho - the following occured to me:

Suppose I want to vote  A > B > C >> D  - such that my approval vote would be
A,B,C, and I believe that B is equidistant in utility between A and C. Or,
equivalently, that I know that A>B>C, but have no info to guide me on whether B
is closer to A or C - whether it is above or below the mean of A,B,C.

This ought to be weighted to be conceptually equivalent to half a vote for
A>B>>C>>>D and half a vote for A>>B>C>>>D. In Universal Approval, Simulated
Approval Runoff, and the like this means that in an {A,B,C} approval election we
give a point to A, no points to C, and half a point to B.

A similar generalisation allows votes like A>B>C>D>>E. This is all very nice,
because increased flexibility for the voter means that the voter doesn't have to
do arbitrary tie-breaking and other nasties - but it makes the interface to
create the votes directly look even more complicated. But hey, that can be dealt
with eventually... :-)