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

[Adam Tarr]

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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