[EM] Cycles in sincere individual preferences andapplication to vote-collection

[Paul Kislanko]

"But I do NOT believe that an individual can have such preferences.  Or,
more accurately, an individual may have such preferences, but I do not
consider them logical, and I have absolutely no interest in factoring such
preferences into a social choice algorithm."

 

If you do not believe an individual should be allowed to think, you should
not be worried about voting methods. I gave an example of how an individual
might sincerely have different pariwise rankins that cannot be inferred from
a single ranked ballot.

 

Now PROVE that an individual's pairwise preferences can be inferred from a
ranked ballot. And "I don't understand it" is not a proof. 

 

  _____  

From: election-methods-electorama.com-bounces at electorama.com
[mailto:election-methods-electorama.com-bounces at electorama.com] On Behalf Of
Adam Tarr
Sent: Monday, September 06, 2004 1:06 PM
To: election-methods at electorama.com
Subject: Re: [EM] Cycles in sincere individual preferences andapplication to
vote-collection 

 

Paul Kislanko wrote:




Suppose I were a staunch pro-life believer, so anti-abortion is my most
important criterion. There are 5 candidates in the race, and A & E are both
anti-abortion, but have opposite views on gun control (A for, E against) and
capital punishment (A against, E for). B, C, and D are all pro-choice, and
either pro gun control or anti-capital punishment or both. When asked to
rank all 5 I give A>B>C>D>E.

If you ask me to compare B, C or D to E I d rank E>any.


Then... why on earth would you rank E behind them all?  That runs contrary
to all three pairwise preferences you purport to have.




 If you ask me to compare B, C or D pairwise to each other, the abortion
issue isn t a factor, and my sincere preference might be D>either B or C
because of fiscal policy and a virtual tie on the other pro-life issues.


Then... why do you rank D behind B and C?  Your preferences appear to be
completely transitive as A>E>D>B?C.




To suggest that you can infer my sincere pairwise preference between any two
alternatives who are not my first choice among many is unwarranted. 


Only because you appear to have picked your ranked order arbitrarily, aside
from the first choice.




To prove that construction of a pairwise matrix from ranked ballots is
always possible, I think you d need to show inductively that all orderings
by any voter of N candidates will always be the same for those as those
obtained by asking each voter to order N+1 candidates (with respect to the N
original candidates). 


I agree with all of that, more or less.




I believe a logical consequence of such a proof would be contrary to Arrow s
theorem, and therefore is impossible. (Just substitute issue for individual
and ranked ballot for group and the same logic applies).


(I think you mean, substitute issue AND individual WITH ranked ballot AND
group?)

And therein lies my objection.  I don't think you can simply substitute
individual for group.  A group can have cyclic preferences, and on that fact
rests Condorcet's paradox and Arrow's theorem.

But I do NOT believe that an individual can have such preferences.  Or, more
accurately, an individual may have such preferences, but I do not consider
them logical, and I have absolutely no interest in factoring such
preferences into a social choice algorithm.

I guess this makes me a "transitive preference elitist" of sorts.  I'm
comfortable with that.

-Adam

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