[EM] Looking for a little voting insight...

[Dave Ketchum]

On Tue, 2 May 2006 22:31:33 -0700 Matthew Welland wrote:

> Thanks Markus,
> 
> I don't follow the logic perfectly but looking at the example it seems that 
> intuitively "A" is the choice that would leave the least number of people 
> unhappy and since no-one has contradicted you I will go with that.


Thanks to Markus for clarifying a bit - though NOT completely.

You could be useful by setting up your Condorcet program to let the user 
select from a variety of variations of Condorcet (and providing accessible 
definitions of each).  Thinking, from what Markus wrote:
      He offered a contorted example - 3 cycles if I count right.  One 
cycle of three candidates seems EASILY doable with real live voters - more 
complexity should be RARE in real life, though we can imagine much.
      He offered one tailored example - think what other collections of 
voters might vote.
      i am getting rusty as to details, but noting strength of defeats 
needs more thought - here he looks only at strength of victor, not at 
magnitude of difference.  25>5 is stronger than 26>24.

Discussion here has mentioned having multiple winners:
      Single winner is always needed - mayors, governors, etc.
      I have seen little thought about multiple winners - worth thinking 
what can be done here ala Condorcet - but please keep such separate from 
single winner.

Discussion has mentioned having a zillion candidates.  I had thought of 
handling write-ins when their existence is not known until a write-in 
candidate turns up as the ballots are being stored in the Condorcet array. 
  That is doable if the program expects such may happen.  The zillion 
candidates could be handled the same way - keep the array to include only 
the candidates that ballots read so far have actually voted for.

Single precinct districts vs multiple precinct districts.  Your program 
may only handle single precincts, but multiple precincts need at least a 
mention - methods should be required to be workable for both cases 
(results from each precinct can be stored in a Condorcet array, and the 
district's arrays then be added together).
      This also applies to the zillion candidates problem.  each 
precinct's array need only include candidates voted for, while the 
district program understands summing.

The infinite numbers associated with zillions brings up another thought. 
      When scanning the array for winner it is NOT necessary to look at 
all the details a zillion times:
      First, assume no cycles.  Pick any candidate.
      See if any candidate beats or ties this one.
           On any beat, check for cycling with those we have scanned.  If 
no cycle yet, start over from this new candidate.
           Just remember ties.
      If no beats and no ties there is no cycle and we have the winner.
      We have a candidate to list as in a cycle.  Whoever beats or ties 
those we list gets added to the list for cycle analysis.

> 
> I think it would be interesting in a range of polls to have people rank the 
> comparative results of plurality vs approval vs condorcet etc.. Maybe it has 
> been done before. If anyone has pointers to such an experiment I'd be 
> interested. If it hasn't been done perhaps I can build it into my site. Of 
> course that begs the question - which voting system to use to measure the 
> quality of the voting system!


More local would be voting among Condorcet methods.  As to bigger issues:
      Plurality ONLY permits approving a single candidate.
      Approval permits approving one or more candidates at the same level, 
but NOT to show any preference among those approved.
      Condorcet permits approving one or more candidates at the same 
preference level, but ALSO to show different levels of preference if the 
voter chooses.  Note:  equal ranking should be permitted; voters should 
not be required to rank more candidates than they choose to approve.
      For all of the above, data of the utility of Condorcet arrays is 
publishable and understandable with little special education.
      Method X - there are a zillion, often beyond documenting 
or understanding results.

While many voters may be satisfied with Plurality or Approval, those who 
understand that more is possible should appreciate Condorcet's offer of 
making more available while not taking away the simpler ability to vote.

IRV needs mention.  While it uses a different way of counting:
      IRV usually agrees with Condorcet as to winner.
      IRV does NOT look at all that the ballots say.  This can result in 
the best-liked candidate losing (in a 3-candidate race A can win with 35 
votes while 65 voters vote that they like B better - but 33 confuse IRV by 
voting that, while they like B better than A, they like C even more).

> 
> Matt

-- 
  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.