[EM] (Possibly) new method/request for voting paradoxes. :)

[robert bristow-johnson]

hi,

this is my first post to this list.  i subscribed to it a while ago  
after some internet searching on issues regarding multi-candidate  
elections which i did after our recent mayoral race in Burlington  
Vermont (dunno if you heard about it or not).


On Oct 12, 2009, at 2:22 PM, Dave Ketchum wrote:

> To look for a better sway to resolve cycles is worthy.  However, I  
> still do not see the gain in what you offer, considering the expense.
>
> Each of the members of a cycle would be winner if only one of them  
> ran.
>      When they are close to a tie it matters little which wins.

it's true that the metric of disappointment or even a measure of  
sense of unfairness in the election result would not be *much* affected,

>      When far away the deciding is easy.

sure.  but that only means that it's a good thing to focus on what  
isn't easy.  unless one thinks that there is virtually no  
*likelihood* of the close election.

>      We have many competing methods already - choosing among them  
> needs more effort than has happened,

a simple rule that is meaningful to principles of democracy is the  
most salient.  negative reasoning is perfectly valid in considering  
different methods (it is perfectly valid to choose the lesser of  
evils).  at the most superficial level, i am convinced that a simple  
Condorcet rule works and is solid.  if a Condorcet winner exists,  
what principle of democracy is fulfilled in giving the election to a  
different candidate when a majority of voters have expressed on their  
ballots that the prefer some other specific candidate (the Condorcet  
winner)?

in considering different methods of resolving a Condorcet cycle  
(which, frankly, i doubt has any likelihood in an electorate mostly  
distributed along a single political spectrum (Nader voters in 2000  
would not likely choose Bush as their 2nd choice over Gore), i think  
that choosing between different Condorcet methods has less salience  
or urgency than getting *some* Condorcet method.  but some method  
needs to be enacted along with adopting Condorcet.

supposedly the Schulze beatpath method is supposed to be the most  
optimal for theoretical reasons (i understand what the goal of the  
Schulze method is, but not all of the mathematical steps), but it is  
also important to have a deterministic and monotonic measure of voter  
support that is understandable to the less scholarly.  some advocate  
the Tideman ranked pair method as such.  perhaps a simple elimination  
scheme similar to IRV (but, after elimination, the following round is  
decided by Condorcet rules).  it wouldn't break my heart if the  
candidate (in the Smith set) that is eliminated is the lowest ranking  
among 1st-choice votes or even transferred votes not originally a 1st  
choice for the Smith candidate .  and some even advocate deciding an  
election by the common IRV rules (single transferable vote) if it's a  
Condorcet paradox.  i care less about which of these are used than i  
care about getting Condorcet.  being a resident and voter in  
Burlington VT might hint to y'all for why.

>>>>>>
>>>>>> Step 1: For each ranked ballot, create a matrix for each  
>>>>>> pairwise vote,
>>>>>> based on the distance and direction between each candidate.  
>>>>>> For example,
>>>>>> on the ballot A>B>C, you would get:
>>>>>>
>>>>>>       -2    -1    0    1    2
>>>>>> AB    0     0    0    1    0
>>>>>> BA    0     1    0    0    0
>>>>>> AC    0     0    0    0    1
>>>>>> CA    1     0    0    0    0
>>>>>> BC    0     0    0    1    0
>>>>>> CB    0     1    0    0    0


like Borda, i wonder what eternal principle determines the weightings  
you've assigned.  all we know is this voter likes A better than C and  
B better than C.  but we do not know how much more this voter prefers  
B over C.  maybe this voter thinks that both B and C are two pieces  
of crap, but flipped a coin as to which was worse (which is the main  
reason i see no reason, whether it's Condorcet or IRV, that ties  
shouldn't be allowed, even ties for 1st choice).  or maybe the voter  
only thinks that C is a piece of crap and flipped a coin between A  
and B.  there is no way to know (without range voting which i also  
don't like).

that is the reason i am not excited about this method, nor Borda.  no  
arbitrary thresholds or quantitative weightings (unless they are  
unavoidable) should be required in the method.  if such are used in  
resolving a Condorcet paradox, i'm much less bothered (since i think  
such is so unlikely, far less likely than IRV rejecting the Condorcet  
winner), but i do not see why a simpler method (like either  
elimination or ranked-pairs) would do less well.  Tideman ranked- 
pairs or some simple elimination would have more transparency and  
confidence of the electorate than any complicated scheme, including  
this one or Schulze which might be better from the artificial  
threshold and weighting POV.

also, politically, i think it is unwise to attach to legislation  
adopting Condorcet any ancillary method (for resolving cycles and  
ties) that is complicated and looks funky.  that, to me, includes  
chance methods (drawing lots among the Smith set in case of a cycle  
to select a winner) which qualify as "funky".  if there is absolute  
symmetry in the breakdown of ballots among Smith set candidates  
(after all the recounts and nasty litigation), that is the only time  
that lots should be drawn.

BTW, if anyone is interested, they can go to fairvote blog at http:// 
www.fairvote.org/blog/ and read some back-and-forth between myself  
and some IRV proponents, mostly Rob Ritchie.  i also have an analysis/ 
polemic about what happened in the Burlington mayoral election last  
March on Town Meeting day.  i'll send it to whoever asks.  i think  
the 2009 Burlington election is the perfect case study for what can  
screw up with IRV (as well as what it can be expected to accomplish)  
in terms of the *very* goals that motivated the use of IRV in the  
first place.  please lemme know if you want a pdf of this (it's about  
6 quick pages).

regards to all,

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."