[EM] Re: Quartiles for CR

[Forest Simmons]

> Date: Fri, 25 Mar 2005 09:25:46 +0100
> From: Jobst Heitzig <heitzig-j at web.de>
> Subject: Re: [EM] Andrew: Sincere methodsd

...

>
> The median is a simpler, more accurate, and more robust measure of
> social utility than the sum! It has the additional advantage that we
> need not assume that utilities possess an additive scale. (Perhaps it
> corresponds to the "median voter theorem" for single-peaked
> one-dimensional preferences in some way?)
>
> I would even go so far and suggest to use an even lower quantile to
> measure social utility, since the goal to get "the most utility for the
> most people" implies that it is more important to give some additional
> utility to the many who possess few instead of giving much additional
> utility to the few who possess much already.
>
> So I suggest to measure social utility by the LOWER QUARTILE of the
> individual utilities (= that utility value where one quarter of the
> voters is below and three quarters of the voters are above).


So this means that perhaps we should look at the set of CR values for each 
candidate, and the candidate who has the highest number q such that the 
number of his CR values that are above q are at least three times the 
number of CR values below q ... that candidate should be the winner 
according to social utility considerations.

[If two candidates have the same q, then the one with the higher ratio 
should win.]

I like this because, it tends to be the lower quartile of the population 
that has the greatest actual need, while the richest quartile can readily 
buy whatever they think they need.

Average utility would make more sense if the benefits actually averaged 
out, i.e. if they actually got spread around, but under modern Bush style 
capitalism the trickle down leaks have been effectively caulked.



On a related note:

I like methods that make use of CR ballots but satisfy the following 
property:

If all of the CR ballots are transformed by different affine 
transformations, the winner of the method will not be changed.

I suppose that we could call this Affine Invariance.

DSV methods that infer approval cutoffs for CR ballots from estimated 
winning probabilities satisfy this affine invariance property.

Note that the above quartile method would not satisfy this invariance, but 
it would satisfy another one:

If the same order preserving transformation is applied to all ballots, 
then the winner is unchanged.

If we use Rob's strategy A, or Joe Weinstein's above median probability 
approval cutoff for a DSV strategy, then both of these invariances are 
satisfied.

Forest