[Election-Methods] IRV-Tournament

[Dave Ketchum]

On Tue, 15 Jul 2008 14:38:32 -0000
Bruce R. Gilson wrote:
> --- In RangeVoting at yahoogroups.com, Dave Ketchum <davek at ...> wrote:
> 
>>On Mon, 14 Jul 2008 20:04:19 -0000 Bruce R. Gilson wrote:
>>
>>>[...]
>>>
>>>
>>>I wish I could be so sure that cycles are going to be rare. That's the 
>>>one thing that scares me about Condorcet methods. A sort 
>>>of "Obama beats Clinton, Clinton beats McCain, McCain beats 
>>>Obama" cycle could really cause a scandal.
>>>
>>
>>Such should not result in a scandal, assuming valid counts of the 
>>ballots.  They simply describe a near tie in power, such as A>B>C>A.
>>
>>Note that while single voters can vote any two of the three 
>>inequalities, it takes multiple voters in about equal strengths to 
>>vote all three together.
> 
> 
> My very point is that last sentence, except for the "about equal strengths." I 
> am not very sure how equal the 6 numbers have to be: those voting ABC, 
> ACB, BAC, BCA, CAB, CBA. Certainly not all 6 need be close, though 
> perhaps some combination does; I have not worked out the arithmetic.
> 
> As soon as you put in some cycle-resolving system, you will downgrade the 
> preferences of some of these 6 groups -- obviously you have to, because 
> that's the only way to break the cycle. And the people in those groups will 
> feel that the election mechanism is disregarding their preferences (or at 
> least weighting them less than others' preferences). And that will be the 
> scandal. 
> 
Saying it more clearly, for A+B+C as the simplest cycle:

Given six equal sized groups of voters:
      A>B, B>C, and C>A can do an A>B>C>A cycle with 2/3 of the 
strength of each group pushing the cycle forward and 1/3 acting as a 
brake.
      A>C, C>B, and B>A can do a similar A>C>B>A cycle.
      Combine the two cycles and you still have a three member cycle, 
again with a tie.

Stray far enough from equality and the weakest candidate has no 
effect, leaving a two candidate race,

In between you have a headache for which the rules BETTER be decided 
on before the election.  This does not require favoring any groups - 
vote counts are the proper basis for the decisions.

"at highest a flaw in the laws of nature"?  No, but could be a flaw in 
our understanding of such.
-- 
  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.