[EM] proportional ordering

[James Green-Armytage]

Dear election methods fans,
	Here is a proposal. Please let me know if you have encountered a similar
or identical idea.

	It seems that there may be some situations where it is desirable to
produce an ordering of options such that if you took the first n options
(n>1) in the ordering, you would find it to be proportionally
representative (to some degree at least, and with that degree tending to
increase as n increases). I call this proportional ordering. It is a means
of arranging options into a hierarchy without excluding non-centrist
options from positions close to the top.

	For example, imagine that there are 50 available frequencies for
broadcast television, and we can assign those frequencies to different
companies based on a popular ranked vote. The frequencies are assigned
channel numbers from 1 to 50, where channels with lower numbers will get
more traffic and are therefore more desirable. What is the best way to
decide which companies get assigned which channels, and which companies
have to stick to other distribution media (cable, internet, etc.)?

	Here's one idea, which I think produces a proportional ordering... 

	Start by doing a ranked pairs tally between all the companies, and assign
channel 1 to the winner, which we will call company A.
	Do a 2-winner CPO-STV tally between all the companies, excluding all
outcomes that do not include company A. The winners of this tally are A
and B. Channel 2 will be assigned to company B.
	Do a 3-winner CPO-STV tally between all the companies, excluding all
outcomes that do not include company A and company B. The winners are A,
B, and C; channel 3 will be assigned to company C.
	... Repeat this process until all 50 channels have been assigned.

	Any comments? Any suggestions for alternative methods for proportional
ordering? Keep in mind that this procedure does not entail the massive
computational cost of an ordinary CPO-STV tally, because the vast majority
of possible outcomes are excluded from consideration.

Sincerely,
James Green-Armytage