[EM] Phragme’n method for a participatory budget election

[Jameson Quinn]

Very interesting. Thanks.

2018-02-11 11:21 GMT-05:00 Ross Hyman <rahyman at sbcglobal.net>:

> Phragme’n method for a participatory budget election.
>
>
> In several wards in Chicago, Alderman allow their constituents to vote
> their spending priorities, on a number of items, each with a different
> cost, in an election.  Sometimes this is done with approval ballots.
> Phragme’n’s method is a natural way to make this process honor proportional
> representation since Phragme’n's method produces a proportional ordered
> list, which is precisely what the Alerman needs to set spending priorities.
> The nth spending item is the item whose election minimizes the Phragme’n
> load (a measure of amount of money that a ballot has successfully voted
> for) of the ballot with the greatest Phragme’n load.
>
> The method:
> Spending items are elected sequentially.  The first elected spending item
> is spending item 1.  The next is spending item 2, etc.  The first item on
> the priority list is the one that minimizes
> s_1 = C_1/V_1
>
>
> and the nth item on the spending priority list is the one that minimizes
>
> s_n = (C_n + sum_m V_m,n * s_m)/V_n
>
> C_n is the monetary cost of the nth spending item. (for electing people to
> a legislature set each C_n to 1.  The only change from the normal Phragme'n
> method is the setting of C_n to the cost of the item).
>
> sum_m is a sum over the elected spending items 1 to n-1.
>
> V_m,n = is the number of approval ballots that approve spending items m
> and  n, and do not approve any of the spending items between m and n.
>
> V_n is the number of approval ballots that approve spending item n.
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