[EM] collective budget setting proposal

[James Green-Armytage]

Dear election methods fans,

	In some cases it may be interesting to engage in a collective budget
setting process, where everyone controls an equal share of a government
budget, and is able to allocate that money to the project of their choice.
	Choices of different projects should probably still be bounded by the
legislature in some way. That is, you wouldn't be able to spend the money
on absolutely anything you want, such as buying yourself a car or
whatever... Rather, there should be a list of approved projects that you
could choose from. Perhaps it would make sense to require something like a
majority of the legislature to approve a project to begin with.
	You wouldn't need to determine an entire budget this way. If you like,
you could determine a certain portion of the budget this way and then have
the legislature fill in the rest on its own.
	It makes sense to use STV as the basic method to translate the individual
allocations into the collective allocation. Projects that are overfunded
could have the surplus money transferred to people's second choices;
projects that are too severely underfunded to be effective might also
transfer funds to people's subsequent choices. If possible it makes sense
to use one of the more sophisticated forms of STV here, such as Meek or
CPO-STV.
	You could also allow people to divide up 'their' allocation money so that
it all doesn't go to the same place. For example, if I have $10,000 in
allocation money, I could say that $6,000 goes to project A, and then if
project A is overfunded, to project B, and then to project C, and so on...
and meanwhile also say that the remaining $4,000 goes to project R, to
project S, to project T, and so on.
	However, this leaves somewhat open the issue of how much money each
project should receive before additional money is transferred elsewhere.
What if someone would like to contribute to project A, but they believe
that the project cap is set too high, and while they'd like to fund A up
to a point, they wouldn't like to fund it all the way to its official cap.
	So what I'm trying to do here is to devise an effective system where
people can decide the level of funding which a given project should reach
before the remainder of their money is transferred elsewhere. At first I
came up with some inferior methods of doing this, but I won’t bore you
with those right now. Here is what I propose... (As always, please inform
me if a similar idea has already been suggested.)

	At each amount of a project's budget, ask how many people are willing to
contribute, taking into account that the amount will be divided by the
number of contributing people. There are a couple factors that determine
whether someone is willing to contribute up to that amount.
	One factor is whether the total amount that I have allocated for the
project is sufficient to pay my share of the total amount. For example,
let's say that there are 20 contributors for project X, including myself.
Let's say that I allocate $500, and everyone else allocates $600. The
total amount for the project would gradually climb from zero upwards,
asking with each increase whether everyone is still willing to contribute
at that level. When the total amount is $2,000, then the share for each of
us is $2,000 / 20 = $200, and yes, we are all willing to contribute $200,
so the amount keeps increasing without interruption. 
	The amount climbs without any change until it reaches $10,000, at which
point our individual share of the cost is each $10,000 / 20 = $500. Now we
have reached the highest point at which I am willing to pay. At $10,001,
my share would be greater than $500, which I did not agree to. So I
contribute my $500, everyone else contributes their $500, making a total
of $10,000. They each still have $100 to spend on this project, but I'm
out, and so now when the amount starts climbing again, I'm not a part of
it, although the rest of them still are. At $10,001 they're all still in,
at $10,002 they're all still in, and so on, up to $11,900, which is the
point at which they've all spent their remaining $100 and have nothing
left to give. So the budget for the project (so far, at least) is $11,900.
	The other factor is whether the amount is greater than the cap I have
indicated for that project. For example, let’s say that I am willing to
allocate $500 to project Y, but only up to a project cap of $5,000,
whereas there are 19 other people who are willing to allocate $500 with a
project cap of $6,000.
	At a total budget of $1 we would all be in, same with $2, $3, and so on
up to $5,000. When we get to a budget of $5,000, we’ve each contributed
$250. So, I contribute my $250, but from that point on I’m no longer
willing to contribute anything. So the remaining $250 that I would have
been willing to allocate to the project under different circumstances
(i.e. less contribution from others) is instead moved along to whatever
project I have indicated as the second priority for that money.
	However, the budget for project Y keeps climbing due to other people’s
contribution. Everyone else is still in at $5,001, at $5,002, and so on up
to $6,000. The extra $1,000 is divided 19 ways, so everyone else pays
another $52.63 (approximately). Added to their prior contribution of $250,
that’s $302.63 for each of them, and $250 for me, with the project budget
now at $6,000.
	So, what happens to the extra $250 of mine that was transferred along to
another project? Does it just get added to the budget of that project
after all the other calculations have been made, and stick there? Well,
no. What you would actually want to do is start a whole new round of
calculations, for all the projects at once, taking into account the new
money that was transferred into them from other projects. That money will
enter into the calculation for its second choice project on an equal basis
with other any other money offered for that project, whether first choice
or second choice or whatever. I may have specified a project cap to go
with it into the second project, or I may not have. The rules are the same
as before.
	At the end of the second round of calculation there may once again be
surplus money from various projects. If so, then a third round will begin,
and so on. Eventually this process will come to rest on its own accord.
	Note: In addition to people’s individual caps for a particular project,
the some projects could also have a total cap of their own. Anyone giving
to that project who doesn’t indicate a cap, or who indicates a cap higher
than the official cap, is treated as if their spending cap is equal to the
official cap.

	Here is a more detailed example. There are 9 people (A, B, C, etc.)
willing to allocate various amounts of money to a given project. (For
example, A allocates 350, B allocates 250, and so on.) The project itself
has no set cap, but the different contributors have indicated various
caps. (For example, A indicates a cap of 1200, G indicates a cap of 1000,
etc.) You can imagine that the figures are in dollars, or whatever
currency you like. Here is the calculation... 
	Note: This table is likely to get mangled in the remailing process, so in
case it does, the link to the same table in html format is
http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting_methods/budget.htm#table


A	B	C	D	E	F	G	H	I	Project
cap		1200	1200	1200	1200	1200	1200	1000	950	1000	none
amount		350	250	150	60	50	40	150	200	500		
9 up to 360	-40	-40	-40	-40	-40	-40	-40	-40	-40	+360
		310	210	110	20	10	0	110	160	460	360
8 up to 440	-10	-10	-10	-10	-10		-10	-10	-10	+80
		300	200	100	10	0		100	150	450	440
7 up to 510	-10	-10	-10	-10			-10	-10	-10	+70
		290	190	90	0			90	140	440	510
6 up to 950	-73.3	-73.3	-73.3				-73.3	-73.3	-73.3	+440
		216.7	116.7	16.7				16.7	66.7	366.7	950
5 up to 1000	-10	-10	-10				-10		-10	+50
		206.7	106.7	6.7				6.7		356.7	1000
3 up to 1020	-6.7	-6.7	-6.7							+20
		200	100	0							1020
2 up to 1200	-90	-90								+180
		110	10								1200

contribution	240	240	150	60	50	40	143.3	133.3	143.3
remainder	110	10	0	0	0	0	6.7	66.7	356.7

	Notice that at each stage of the calculation everyone who is still
involved is paying the same amount of money. Some people stop contributing
because they have exhausted the amount of money that they were willing to
contribute (in this example F, E, D, and C). Some people stop contributing
at the point where they feel the project has sufficient funding (in this
example H, G, I, and eventually A and B as well).
	The end result is that the project has a budget of 1200, and each person
contributes the amount shown above. The remainders shown above are passed
along to whatever project those people indicate as the next priority for
that particular gob of money.

	Is collective budget setting a good idea? I don't know. But if it is
done, I recommend this algorithm as being the best way to do it, assuming
that the needed computational resources are available.

best,
James Green-Armytage