[EM] Compromise allocation of fair share

[Andy Jennings]

On Wed, May 18, 2011 at 5:26 PM, <fsimmons at pcc.edu> wrote:

>
> > Forrest,
> >
> > I'm trying to make sure I understand exactly what the "Ultimate
> > Lottery"methods are.
> >
> > So the "Ultimate Lottery" singlewinner method is:
> >
> > 1. Voters submit homogeneous functions of p1,p2,...,pn
> > 2. Choose the configuration (p1,p2,...,pn) which maximizes the
> > product of
> > all voters' functions
> > 3. Use a lottery that elects candidate i with probability pi.
> > (Ideally we would solve the maximization problem over the space
> > of all
> > possible p1,p2,...,pn which sum to 1. If that's not possible we
> > can allow
> > people to submit possible outcomes and just choose the maximum
> > one out of
> > all the submissions.)
> >
> > And the "Ultimate Lottery" multiwinner method is:
> >
> > 1. Voters submit homogeneous functions of p1,p2,...,pn
> > 2. Choose the configuration (p1,p2,...,pn) which maximizes the
> > product of
> > all voters' functions
> > 3. Entity i gets voting power pi in the parliament.
> > (We can restrict the space we're considering so no more than M
> > entities get
> > seated, or we can just consider the whole space and seat anyone with
> > positive voting power.)
> >
> > Is this correct?
> >
> > Andy
> >
>
> Yes, with the understanding that all of the homogeneous functions are of
> the same degree and non-
> decreasing in each of the arguments.
>


Oh yeah.  I forgot about the non-decreasing-in-each-argument constraint.
 That would translate into a more complicated constraint if voters were
allowed to specify a function on the simplex, then.

Andy
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