[EM] Converting super-majorities to margins

[Bart Ingles]

Rob Lanphier wrote:
> 
> I think a generally useful definition of "super-majority" in
> multi-candidate race is the pairwise winner with approval of the required
> super-majority.  Approval on a ranked ballot could be expressed as a line,
> all above which are considered approved, and all below which are not
> (methods for doing this were discussed very early on on this, circa 96q1
> or so).
> 
> So, for instance, for a two-thirds super-majority, the candiate would have
> to achieve both of the following:
> *  Simple majority pairwise victories over all opponents
> *  Approval of two-thirds of voters.
> 
> Of course, super majorities could only be required in cases where the
> status quo is an acceptable outcome, since that's what will result short
> of anyone acheiving a super-majority.

The same is true of simple majority approval.  The highest approval
level you can guarantee is 1/K of the vote, where K is the number of
candidates.  Even this assumes a voter always approves of his first
choice, and that you only count ballots with at least one choice.

I view this as an advantage of approval voting, in that it stops at a
meaningful plurality of approval votes, rather than trying to decree a
majority where none exists an any meaningful sense.  Approval Voting
also naturally leans toward any candidate who has the approval of a
super-majority (or the highest super-majority).

 * * *

A hypothetical system in Weber's essay on approval voting suggest a sort
of Borda-Approval hybrid, which could be viewed as a way to draw a line
in a ranked ballot.  The system would be similar to Borda, except there
are (to pick a number) twice as many rank levels as there are
candidates.  All voter rankings would have to start from the top and/or
bottom, so that all vacant levels are grouped together in the middle.

In other words, in a 5-candidate race a typical ballot might contain
votes for "1-2---8-9-10".  The ballots would be tallied the same as
Borda, so that the points going to each choice in this example would be
9, 8, 2, 1, and 0.

The system would likely contain the same strategy weaknesses as Borda,
but much reduced.  Insincere voting would generally occur only within
the approved and disapproved groups, and would tend not to cross between
them.