[Election-Methods] rcv ala tournament

[CLAY SHENTRUP]

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.

> 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.

> 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.

> 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.

> 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."