[EM] Utilities?

Jobst Heitzig heitzig-j at web.de
Sun Sep 5 13:57:23 PDT 2004

Dear Adam!

you wrote:
> While they don't create a problem for most methods, allowing cyclic 
> preferences creates significant problems for most _ballots_.  This is
> the key point.  Is the ability to express cyclic preferences requires
> a massive ballot with every pair being voted on; 

I cannot tell why everybody seems to think that the ability to express
pairwise preferences excludes the ability to express a ranking. It is a
trivial task to design a ballot in which the voter can choose to either
(i) mark one candidate as first choice or several as the top set, or (i)
assign ranks or ratings to all or some candidates, or (iii) answer a
pairwise comparison question for every pair. Allowing voters to vote in
a certain way is not requiring others to do the same!

> For the record, I agree with James's criticism of the logic of cyclic
>  preferences.  

Adam, I do too! Personally, I will most probably never feel the need to
express such preferences. But we must not jump to conclusions! Only
because we find something difficult to understand, that doesn't mean
it's not there.

> With enough thought, you can resolve the
> inconsistency and produce a transitive order.

Well, I doubt this and have given several examples some weeks ago.

Anyway, let me repeat that in my opinion the REAL problem with rankings
and ratings is not cyclicity but that they cannot express *incomplete*
preferences like A>B,C>D.


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