[EM] Using PR-STV for districting single member districts

[raphfrk at netscape.net]

 The census information breaks the population into blocks (at the lowest level).

They give lots of information about a block (to say the least), but two important ones they give for districting are

population of the block
long,lat position of the block (I think this is the centre, but is just defined as a point in the block)

So, what about this for a districting method 
(this is based on discussions on the Rangevoting list about a paper by Bottman et al.):

------------------------------------

Possibly convert long,lat to a better projection
(I would rather just leave them and use flat Earth, or whatever system the census uses, as sine and cosine functions cannot be determined exactly using integer maths)

Each block counts as a voter and a candidate.? 

Each block ranks all the blocks in order of distance, giving itself first choice (0 distance)
- there would need to be a clear tie breaking rule

Each block has votes equal to its population.

An N seat PR-STV election is held to select N blocks (fractional transfers (rational numbers), quota = delta + (Population)/(Seats+1) )

The position of each winner becomes the centre of a district.

Each district is assigned an initial distance offset of 0.

Each block is always assigned to the district with smallest ((distance from block to district centre) - (offset)).

A block is considered a pivot block if there is a tie.? The block population is split equally between all tied districts.

The loop is:

1) Set the district group to be the lowest population district

-2) increase the offset of all the district group districts by the same amount.
--- the increase is the lowest amount that will result in them having 
------ an increase in population and 
------ where they have at least 1 external pivot block (pivot between group member and non-member)



 --3) if the sum of the absolute values of the population differences between all district pairs has decreased, goto 1)

-4) reverse the offset changes made in 2)
-5) add the smallest population non-group member district to the group
-6) if the group doesn't contains all the districts, goto 2)

7) Pivot blocks may be manually split in order to balance population (somewhat controversial :) )

--------------------------------------------

This will always end (does it always generate contiguous districts?? I assume so).

For a map distribution when the the algorithm is at 1), it checks N-1 different mobile groups to balance the populations.? If they all fail, it ends.? If it succeeds, the figure of merit will have improved.? There is a limit to how low this figure can go.? It would be possible to check all (2^N)-2 combinations and it would still complete eventually.

Step 2 doesn't transfer population between group members as their offset is increased together.? The only effect is to move population from outside the group to inside the group.? The group increases its members until it eventually draws population from the larger districts.? It then resets and tries again.? This should slowly move population down to the lowest districts.? 

The end occurs when it cannot move population from the largest district to a group containing all the other districts without increasing district inequality.? 

Most of the time, the group would just be the lowest population district increasing in size.

-----------------------------------------------

Another option would be to actually hold the PR-STV step as an election.? The choices would be various possible district centres.? This would give the public some power over the districting process.

Another possible figure of merit would be that the difference between the highest and lowest district is used and if it is a tie, move to the next lowest pairwide comparison (either order by before or after differences).

Also, for step 7) to work, there would have to be a rule for limiting the populations of blocks (or they would end up with a 1 block per State issue).? 

The census would also require rules for defining the centre of blocks and rules for preventing blocks from being decided after the census was held.? I think any reasonable settings for these would be fine as long as they are fixed before the census count actually happens.? (Perhap, the block distribution setting before one census are used for the next census).? This would create at least a 10 year gap between defining the blocks and the census that actually uses those definitions.

The tie break rules for the PR-STV step could just be most Northern and if still tied, most Eastern block.

Also, I think it might be worth reversing the tie break rule for every 2nd tie.? This might make people who live in the Southwest of a State have less of a case that they are being discriminated against (though it would have little actual effect).



Raphfrk
--------------------
Interesting site
"what if anyone could modify the laws"

www.wikocracy.com

________________________________________________________________________
Check Out the new free AIM(R) Mail -- Unlimited storage and industry-leading spam and email virus protection.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20070712/c60401d2/attachment-0002.htm>