[EM] Consistency Criterion

[Forest Simmons]

I like this example much better than your oracle example. Are you going to
replace the oracle one with this one on your website?

Forest

On Sun, 19 Aug 2001, Blake Cretney wrote:

> On Fri, 17 Aug 2001 12:55:04 -0400
> Douglas Greene <douggreene at earthlink.net> wrote:
> 
> > Multiple-districts paradox:
> > ---------------------------
> > also in the literature called the "consistency" problem:
> > if 2 subsets of the voters agree on a winner, to be consistent, the
> > combined election should produce that same winner - but
> > with the IRV, that is not necessarily so.
> 
> Here's an interesting paradox along the same lines.  I'm getting this
> from a book called "The Paradoxicon" by Nicholas Falletta.
> 
> Let's say you have two jars, a tall jar and a fat jar.  You also have
> two kinds of candies, orange and mint.  The jars have the following
> contents.
> 
> Tall:  50 orange 60 mint
> Fat:   30 orange 40 mint
> 
> If you want an orange flavoured candy, and the candies all look the
> same, then you'd want to pick from the tall jar, since it has a higher
> proportion of orange:mint candies.
> 
> Now, imagine a different pair of jars with these proportions.
> 
> Tall:  60 orange 30 mint
> Fat:   90 orange 50 mint
> 
> Once again, you would pick the tall jar for an orange candy.
> 
> OK, now imagine that you dumped the contents of both tall jars into
> one giant tall jar, and both the fat jars into one giant fat jar. 
> Now, the question is, which giant jar do you pick for the best chance
> of an orange candy.
> 
> It would seem sensible that we could rely on a statistical consistency
> criterion to give us an answer, similar to the criterion suggested for
> elections.  That is, if we picked the tall jar both times, it is only
> common sense that we should pick the giant tall jar with their
> combined contents.  Unfortunately, this is wrong.  The giant jars
> contain.
> 
> Tall:  110 orange 90 mint
> Fat:   120 orange 90 mint
> 
> It turns out, the fat jar is the correct choice, in violation of my
> proposed statistical consistency criterion.
> 
> So, I guess it makes sense to be cautious about what criteria one
> adopts.
> 
> ---
> Blake Cretney
> 
>