[EM] "scored condorcet", etc

[Dave Ketchum]

On Sun, 20 Nov 2005 23:29:16 -0800 rob brown wrote:

> Hi again.
> 
> You might remember me from a good while back when I did a little work on 
> a (web based) UI for a ranked voting system (it is still at 
> http://karmatics.com/voting/ )  Aside from my little question a week 
> ago, I haven't been around much, so let me introduce myself again and 
> tell you where I'm coming from.  Like most here (presumably) I think 
> that the plurality system is seriously broken.  In particular, I think 
> it polarizes people by causing parties to form.  I like systems that 
> tend to elect a middle ground candidate, and that don't provide 
> strategic advantage to forming parties.


An aside - Plurality is not broken - it does EXACTLY what it was designed 
to do.  Problem is that those of us who bother to think about it want 
something else.

BUT, I do not understand your words about parties - Plurality pushes 
toward two strong parties while Condorcet gives parties enough visibility 
that more might thrive.

> 
> While I don't claim to be a math expert, I am confident that most any of 
> the condorcet methods -- if actually put into practice -- would solve 
> this problem, for all practical purposes.  I can't claim to have a 
> preference of a particular one. To me, however, the biggest problem to 
> be solved is that existing condorcet methods (and IRV, for that matter) 
> don't lend themselves to showing results in a way that is comprehensible 
> to "regular" people. In a certain way, I suppose this could be 
> considered more of a marketing issue than anything, since I think this 
> is standing in the way of people getting comfortable with condorcet methods.

Your mention of IRV makes me wonder what you are thinking of:
.     Condorcet with something else mixed in, such as Approval - too 
complex - leave this as a challenge to those wanting such.
.     IRV - does not produce the array I discus below.
.     Pure Condorcet - produces an array of counts (while variations inspire 
debates as to which variation is better, all produce the same arrays).
> 
> Therefore, my goal is to come up with a way of producing numerical 
> scores from a condorcet election that can be shown, for instance, as a 
> bar graph.  When I suggested this here on the list over a year ago, the 
> general reaction seemed to be that numerical scores and condorcet 
> methods were mutually exclusive.  I didn't agree, obviously, but I did 
> accept that it is not as simple a problem as it might appear.

Condorcet uses an array to count the votes - 5x5 for 5 candidates.  Look 
at one ballot for 6 candidates - A thru F:
A>B=C>D
1 A>B
1 A>C
1 A>D
1 A>E
1 A>F
.5 B>C
.5 C>B  The idea here is that 2 voters voting B=C shall have the same 
effect as 1 B>C plus 1 C>B (but EM members vote this down, doing none of 
this .5 counting).
1 B>D
1 B>E
1 B>F
1 C>D
1 C>E
1 C>F
1 D>E
1 D>F
0 E>F (all seem to agree to not count compares among truncated candidates).

With this formatted as a 6x6 array, comparative candidate strengths are visible.

While complete arrays have to be used to determine winner, could be an 
option to print a smaller array excluding fringe candidates. 
> 
> I keep revisiting this problem, and each time, I seem to get closer and 
> closer to something that I feel would work well.  My general approach 
> has *not* been to find a way to take existing methods (beatpath or 
> ranked pairs or what-have-you) and then work backwards to produce 
> scores, but instead to come up with a brand new method that produces 
> scores first, with the top scoring candidate being considered the 
> winner.  Meanwhile the system must still meet the condorcet 
> criterion...so if there is a condorcet winner, that candidate must have 
> the highest score.  Of course it must do a reasonable job of selecting a 
> winner when there is a condorcet tie.  Also it is important that the 
> scores do a good job of showing how the other candidates did 
> comparatively.  For instance, if the #2 candidate's score is very close 
> to the #1 candidate, that would indicate that a relatively small number 
> of additional ballots could cause #2 to surpass #1 and win instead.  Of 
> course, the more stable the scores, the better.

If there is a Condorcet winner, the evidence WILL BE that that candidate 
will have the highest score vs each other candidate.

Worth commenting when there is a cycle - which has to be resolved whether 
or not doing pretty displays.

And, of course, the numbers WILL BE close on near ties.

You mention bar graphs - not clear how this could be done neatly, 
considering that each pair of candidates is of possible interest.
> 
> So before I start talking about the specific approaches I am looking at 
> and getting into the math and algorithms and such, I figured I'd first 
> kind of reintroduce myself (and my goals) to the list, and see if there 
> is a receptive audience to what I'm working towards.
> 
> Does this seem interesting (and valuable) to anyone?

I am responding because many do not realize that these arrays are a NORMAL 
production of counting Condorcet ballots - and SHOULD be accessible to 
the voters as part of the election report.
> 
> -rob

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
                  If you want peace, work for justice.