[Election-Methods] rcv ala tournament

[Dave Ketchum]

On Sat, 29 Dec 2007 20:31:13 -0800 CLAY SHENTRUP wrote:
> On Dec 29, 2007 7:03 PM, Dave Ketchum <davek at clarityconnect.com> wrote:
> 
>>Somehow we are not talking the same language.
>>
>>An example that could be executed, with voters each splitting candidates
>>into two groups (as many as they choose into each) and voting via:
>>       Approval, using its full capability of approving vs not approving.
>>       Condorcet, with voters restricting themselves to rank 1 vs not ranked.
>>       Range, with voters restricting themselves to max rating vs not rated.
>>
>>Approval's full capability is used here.
>>
>>Condorcet and Range each have other abilities not used in this demo.
> 
> 
> yes, but condorcet (and many other methods) allow voters to employ
> strategies that can actually diminish the extent to which the election
> satisfies "my" preferences, even if they give "me" more apparent
> expressiveness on my ballot. ("me", meaning "joe blow")
> 
> as for range voting, you are correct, but as i recall, i was promoting
> approval in contrast to rank-order methods.
> 
My point is that, whatever Approval can do, the other methods are also 
capable of doing.

Certainly the other methods have abilities not used in this demo.
> 
>>BUT, Approval has no way to express intensity.
> 
> 
> of course it does.  if you and i both prefer X>Y>Z, but i like Y more
> than the average of X and Z, and you like Y less than the average of X
> and Z, then i'll vote for both X and Y, and you'll just vote for X.
> it's what is called "revealed preference" in ecenomics - we are forced
> to say something about the relative intensity of our support for Y,
> even though we have the same ordered preferences.
> 
That might reveal a bit, though even that not clearly.

BUT, assuming I want to indicate preference of X and Y over Z, Approval 
can show my less liking for Z, but cannot, in the same vote, indicate my 
relative preference as to X vs Y.
> 
>>Where does Approval have a limit on quantity of comparisons?
> 
> 
> if we have n candidates, a ranked method allows n(n-1) head-to-head
> comparisons to be expressed.  approval allows, at most, (n^2)/4
> 
> so with 4 candidates, for example, a ranked method allows the
> expression of 12 comparisons, whereas approval allows a maximum of 4.
> 
I am getting dizzy.  With 4 candidates, how do you come up with more than 
6 pairs to even consider comparing?
> 
>>How does Approval qualify as having ratings vs ranks?  It is too simple to
>>reasonably care.
> 
> 
> this is a non-controversial fact of election theory.  approval voting
> is cardinal. it only allows us to classify each candidate into a
> predefined set of (2) categories, but does not restrict how many
> candidates may go into any of those categories.  if we look at
> plurality, for instance, there are two categories, "voted for" and
> "not voted for", but you may place only one candidate in the "voted
> for" category.  with RCV (with 3 candidates allowed) you have 4
> "categories", first, second, third, and non-ranked.  again, you can
> only place 1 candidate in 3 of those categories.  of course, we might
> then ask if equal rankings would make RCV a cardinal method.  it gets
> fuzzier.  maybe a concrete definition is this.  a voting method is
> cardinal if it complies with iia, as the votes are cast.  i could be
> totally wrong, and maybe there's a simple strict definition.
> 
REALLY dizzy now.

"RCV (with 3 candidates allowed)"?  Is this from some definition I have 
not seen, or something that seemed to make sense in the above statement?
> 
>>Costs deserve more attention than some offer.  Still, voters being able to
>>express their desires, and be understood, is a non-trivial topic.
> 
> 
> that is measured by social utility efficiency, and approval is better
> in that regard than ranked methods.  there are some ranked methods
> that can apparently satisfy expressed preferences better than
> approval, but they have externalities (what rob brown likes to talk
> about) that cause problems - if we're talking about public adoption at
> least.
> 
> 
>> > rank-order voting methods are chaff.
>>How and why?
> 
> 
> utility efficiency and complexity/adoptibility.  to quote from william
> poundstone's forthcoming booking _gaming the vote_
> 
> "The profession dealing with collective choice is just about
> completely dysfunctional," Hillinger said, "from the point of view of
> dealing with the social problem that they are ostensibly dealing
> with."  That "social problem" is of course making our elections
> fairer.  To have any chance of solving the problem it is necessary to
> recognize the gaping chasm between what Arrow's theorem says and what
> people thought it meant.  The impossibility theorem is poised on the
> knife's edge of truth.  Frame the problem exactly the way Arrow did,
> and rational democracy is "impossible".  Drop the obsession with
> ranking, and life becomes a lot easier.
> 
> So what does the impossibility theorem mean?  Smith's and Hillinger's
> answer could hardly be more different from the pessimistic
> interpretations that have prevailed.  The message of the impossibility
> theorem is: don't use ranked voting systems.
> 
> "There is an open door to social choice," Hillinger says, "and another
> one...that is closed.  One would have expected choice theorists to
> pass through the open door; they chose instead to bang their heads
> against the closed one."
-- 
  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.
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