[EM] Re: approval strategy

[Forest Simmons]

>Date: Sat, 08 Jan 2005 07:42:29 -0800
>From: "Michael A. Rouse" <mrouse1 at mrouse.com>
>Subject: [EM] Question/Strategic Approval Voting

Mike wrote:

>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.

Forest replies:

A couple of years ago several ideas along these lines were bandied 
about on the EM list.

Another variant was to initialize by approving the highest ranked 
candidate (or candidates) and disapprove the lowest ranked (or 
truncated) candidate(s).

Then at each successive stage either move the approval line down one 
rank or else move the disapproval line up one rank, until the two lines 
meet.

The interesting part is deciding at each stage which of these two moves 
to make.

One possibility was this: Move the line farthest from the current top 
approval-minus-disapproval getter.  If they are the same distance, then 
on one side of the top approval getter there will (almost surely) be a 
candidate which has more current approval-minus-disapproval votes than 
any candidate on the other side. Move the line of demarcation that is 
closest to this "weather vane candidate."

Kevin and I worked on improving this for awhile, but we never settled 
on anything definite, and we got distracted by other ideas.  He might 
remember where to locate the thread. He even tried out some of our 
ideas with random simulations.

As I remember, what got us started was a search for a better use of 
three slot ballots.  In that case the method always ended in one step, 
and seemed to give reasonable results.  That was pretty nice, so we 
wanted to find a way of generalizing it to any kind of cardinal or 
ordinal ballot.

But work on it yourself so our ideas don't get you moving into our old 
ruts too soon.  There are some advantages in re-inventing the wheel; it 
might have rubber tires on it the second time around.

Forest