[EM] Compromise allocation of fair share

[fsimmons at pcc.edu]

----- Original Message -----
From: Andy Jennings 
Date: Wednesday, May 18, 2011 2:02 pm
Subject: Re: [EM] Compromise allocation of fair share
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> 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.