----- Original Message ----- From: Andy Jennings Date: Wednesday, May 18, 2011 2:02 pm Subject: Re: [EM] Compromise allocation of fair share To: [email protected] Cc: [email protected]
> 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. ---- Election-Methods mailing list - see http://electorama.com/em for list info
