[EM] Question/Strategic Approval Voting

[Michael A. Rouse]

I've been bouncing back and forth between Range and Approval voting for 
the past couple of days, trying to see how each is affected by strategy. 
I seem to vaguely recall an Approval voting method that tried to use 
complete knowledge of voter preferences to maximize each voter's best 
strategy. As a temporary label, let me call it "Strategic Approval 
Voting," and for a brief description:

1. Rank all candidates (ties are possible).
2. The first candidate on every ballot is "approved" and receives one vote.
3.  If the top-scoring candidate has neither been approved nor is the 
next choice on a ballot, the next candidate is approved.
4. Continue adding approvals until there are only bottom-ranked 
candidates remaining.
5. The one with the most Approval votes is the winner.

One addition that may be desirable (or may not be, if it introduces 
approval cycles that can't easily be resolved) is the following step 
between 3 and 4 above:

3.5 If the candidate with the most votes has been approved on your list 
and there are one or more ranked above him, remove all approvals from 
that candidate on down.

Steps 3  and 3.5 are there because if your top choice is being approved, 
you don't want to add approval votes to less desirable candidates, nor 
is there any need to add to the top candidate's score at the possible 
cost to a candidate you prefer higher.

Any names or links to a site covering this method would be great.

One problem I can see with the above method (especially if step 3.5 is 
included) is that you can have a voting cycle -- Approval votes are 
added, one of your higher choices gets more votes, Approval votes are 
removed, and the cycle starts again. One would have to come up with an 
Approval completion method. Here are some possibilities:

1. The first time a cycle repeats, it is frozen and the winner is 
determined from that cycle.
2. The cycle with the lowest total number of Approval votes is the one 
selected (lowest number of Approval votes should mean there are fewer 
"less approved" candidates).
3. The candidate with the greatest cycle victory, the smallest cycle 
defeat, or the best overall average could be picked.

Well, it's time for me to drive out in the snow. I'll try to think of 
some examples in case my explanation is too confusing (grin). If anyone 
can help, that would be great. Thanks!

Mike Rouse
mrouse1 at mrouse.com