Coombs-Davison (was Re: The Davison Run-off)

[Steve Eppley]

Donald D wrote:
>     I would like to announce a change I am thinking about making
>to the Instant Run-off method. The change has to do with the
>candidate that is to be dropped first. As you know, Instant Run-off
>drops the candidate with the lowest vote total on the first set of
>selections. I am going to drop the candidate first that has the most
>selections in the last set of selections.
-snip-

I applaud Donald for developing a method better than MPV.  Davison
Runoff (Coombs, according to Mike O), like the Condorcet tie-breaker,
has the philosophy of counting "votes against" to defeat candidates
opposed by many voters.

All the examples Donald provided are cases where Coombs produces the
same winner as Condorcet and Smith-Condorcet, but in most of them
MPV produces a different winner.  If I'm not misinterpreting his
intent, perhaps he would like to amend his response to the EM
single-winner methods poll to be something like:
   1.   Coombs
   2&3. Condorcet & Smith-Condorcet     (I'm not sure which order 
                                         he'd rank these two)
   4.   MPV
I'd like to be able to report that the EM group has reached
unanimity, among those who expressed an opinion, that Condorcet
or Smith-Condorcet or both are better methods than MPV for 
reformers to advocate.  MPV has a lot of inertia with reformers,
but that method would still deter multiparty democracy.  It would 
be harder for reformers to ignore a unanimous preference.

I'd certainly be willing to re-tally the responses, and even tally 
them using Coombs, and submit an updated report to the ER list.

>Steve's second example: 46 AB    20 B     34 CB
>In this example we must fill in the missing selections.
-snip-
>In the one case in which two selections are left off, we can assume
>that the voters do not care which is second or third. I am going to
>divide the second and third spots between A and C.

An alternative is to count those ballots as being full votes against 
both A and C, rather than splitting them.  It's unclear why Donald 
prefers to split them.  My instinct would be to count them as full 
votes.  (This would not violate the "one person, one vote" principle.)

-snip-
>     Condorcet people have often said that it is not proper for
>Instant Run-off to drop the last candidate. The solution is simple -
>we do not drop the last - we drop the candidate that is the lead
>candidate in the last set of selections.

The problem with elimination methods is that the measurement used to
decide which of the remaining candidates is in last place is usually
fallacious.  Coombs is still dropping what it takes to be the "last" 
candidate, but it measures "lastness" differently than does MPV.

MPV is the one-seat case of the STV proportional representation
method, which emphasizes voters' top ranked choices because the prop
rep principle is that every voter is best represented by his/her
first choice.  People who understand STV know that as the number of
seats decreases, the number of misrepresented voters increases. 
It's nice to see Donald exploring other principles like
"reverse-plurality".

I'm not going to argue in this message that Coombs' measurement of
candidate "lastness" is also fallacious, and that there are important
criteria failed by Coombs, though I believe these two things are
true.

Donald wrote in a subsequent message that he believes in dropping 
candidates iteratively, but I don't believe he has ever explained why 
he finds that so appealing.

>     If this run-off change pans out I will call it the "Davison
>Run-off" and incorporate it into my list of election reforms - and
>Steve can have the name Instant Run-off for Condorcet.

I would prefer Instant Runoffs, not Instant Runoff, for Condorcet or
Smith-Condorcet.  If this wish were granted, I'd also want Instant 
Runoff to no longer be used for MPV since it would create confusion.

I wish Donald had the power to make it so easy to seize the name
Instant Runoffs.  Rob Ritchie wrote that he still wants to use 
Instant Runoff for MPV, so it would probably take the weight of 
many reformers to persuade Rob to acquiesce.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)