On Wed, May 18, 2011 at 5:26 PM, <fsimm...@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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