[EM] Improved Approval?

[Abd ul-Rahman Lomax]

Perhaps there is a name for what I'm going to describe here, and 
someone will kindly inform me.

I have suggested in the past that Approval elections include an extra 
position for each candidate to mark "Preferred," even if this mark is 
not used to determine the winner, because it would answer the major 
objection that seems to be made about approval, that it does not 
allow voters to express a preference. The mark would also be useful 
for the division of, for example, public campaign finance money, and 
would provide a definitive poll on who *was* the most popular 
candidate, so that the public could assess the performance of approval.

However, I was today writing about Approval and pointing out, as I 
often do, that voting for more than one is equivalent to voting for 
each of the marked candidates in every pairwise election with 
unmarked candidates and abstaining from the pairwise elections 
between the marked candidates.

And then it occurred to me that it might be possible to analyze the 
two-position approval ballots in this way: consider the election as a 
series of pairwise elections.

When a candidate has been marked "Preferred," the "Approved" vote is 
presumed. In all pairwise elections between any approved candidate 
and any unapproved candidate, the votes are obvious, they come from 
the approved/preferred votes; in these pairwise elections, preference 
is not considered, only approval.

But in the pairwise elections between approved candidates, where the 
voter would have effectively abstained under basic approval, the 
voter will be considered to have voted for the preferred candidate.

Thus preference *would* be considered in those pairwise elections. I 
have not considered all the implications....

Comments?