[EM] Cyclic Ambiguities = misinformed voters? (was: The True Majority Ghost)

[Alex Small]

> Donald:  Condorcet is better without the second half.  Cyclic
> ambiguities aka circular ties, are not the fault of Condorcet, they are
> the fault of the voting public.  Usually this happens when the voters
> are so uninformed about the lower choices that the voters make the
> mistake of voting in a circle.

Really?

If all candidates fit on a one-dimensional spectrum then this is certainly
true.  The person whose preference order is Bush>Nader>Buchanan>Gore needs
to start reading some newspapers.  The person whose preference order is
Buchanan>Gore>Nader>Bush probably lives in Florida ;)
But what if we have two dimensional candidates?  Suppose that ideally I
want people who are close to me on all issues, but in the end I care more
about social issues than economic issues.  My preference order might be
Libertarian > Democrat > Republican

Another person might be concerned first and foremost about economic
issues, but disagree with me on social issues.  A plausible preference
order for this person is
Republican > Libertarian > Democrat

Finally, a third voter might decide that the Libertarians go too far for
him, so while his first choice is the Democrat, he'll take the Republican
over the Libertarian, because the Republicans and Democrats are only
interested in small changes to the status quo, while the Libertarian
candidate is interested in drastic reforms.  A plausible preference order
for this voter is
Democrat > Republican > Libertarian

Now assume that there are a lot of other people who agree with one of us
three, and voila!  A significant fraction of the electorate voted in a
circle.  A cyclic ambiguity is entirely possible.
>    We would do well not to continue Condorcet after the first half if
>    the
> condition of a circular tie would arise.  The fact that there is a
> circular tie means that the lower choices are no good, so don't use the
> lower choices.  Only the first choices are good, so use Plurality or
> the next method to use would be IRVing because IRVing uses less lower
> choices than any other method.  Besides, IRVing only uses lower choices
> to replace some first choices, there is no net increase of choices
> being used at the same time.

>    If the election still has three or more candidates after we have
> eliminated the lowest one, we can go back and use the Condorcet method
> again and maybe this time there will be no circular tie, if not, then
> we have a winner, a Condorcet winner - I think.  That is my solution to
> circular ties, which I presented to this list years ago, but I'm
> digressing.

Are you suggesting that if a CW exists we should elect him?  Are you
further suggesting that the best way to resolve a cyclic ambiguity is to
eliminate candidates as we would in IRV, and after each elimination see if
we now have a CW?
If so I think you and I might have some common ground.  At first glance
this method seems reasonable.  The CW is the one who says "Come one, come
all!  None can defeat me!"  It seems quite reasonable to elect him.  If,
however, there is no such champion, it seems plausible (for political
reasons) to say "Well, whoever has the fewest fans can leave now."  Of
course, I will have to think a little about strategic aspects of this
method, but it seems reasonable.
Furthermore, as far as methods for resolving cyclic ambiguities go it
seems relatively straightforward.  Finally, because it uses the same
equipment as IRV, and is very similar to IRV in some aspects, it seems
like a method that could be easily sold to the public if IRV were
implemented.  We could say "Well, modify IRV in such-and-such way to
improve it."
In any case, it's a method worth contemplating.

> Donald:  Why should any method be required to elect the so called
> `Condorcet Wiener Winner'.  Your bogus remark can be turned around.  It
> can also be said that it is true that Condorcet can fail to elect the
> IRVing winner and fail to elect the Approval winner and fail to elect
> the Bucklin winner, etc, etc.

Well, the concept of a CW is directly related to the concept of a cyclic
ambiguity.  From a theoretical perspective the existence of cyclic
ambiguities is interesting.  Saari has done interesting work proving that
if you "subtract out the Condorcet [cyclic] profiles" and also cancel out
all "reversed profiles" Arrow's Theorem can be satisfied (after the
cancellations).  Mike pointed out that if we relax the definition of
"irrelevant" then IIAC (one of Arrow's conditions) can be satisfied by
Condorcet methods, and hence Arrow's impossibility theorem no longer
holds.
So, since the CW is related to academic considerations that are
interesting in their own right, it is a concept that can be said to exist
independent of any election method.  By contrast, I'm not aware of any
academic work where concepts related to the IRV Winner, or Approval
Winner, etc. show up in any context not directly related to that
particular method.
Alex

-- 
The first thing we do, let's kill all the lawyers!

Of course, that's just my opinion.  I could be wrong.


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