Plan B

Well, I got busy at work, and have not had time to keep up-to-date with this, for which I apologize.  However, the time has not been wasted, as I have come up with Plan B for objective redistricting.

This plan does not negate Plan A, but uses a different metric for determining which territories get linked with which other territories.  In Plan A, it’s a matter of simple geometry.  When a territory needs to be linked, it gets linked to the other territory with the largest contiguity (which is basically a simplified measurement of the length of the border).  With Plan B, the question is, which other territory does the majority of the population live closest to?  If more citizens of Wyoming live closest to Colorado and not Montana (to which it is linked in Plan A), then to Colorado will Wyoming be attached.

So, anyway, the plan will be up on the board as soon as I upload it;  I have made it clear in the text of it the differences between Plan B and Plan A.  Let me know what you think.

More equalizations

Having discussed the first three equalizations in an earlier post, we continue….

4.  After three equalizations, the gap is 2.0007.  The fourth  equalization equalizes Western & Middle Europe and Eurasia by bring the four nations of Poland, Slovakia, the Czech Republic, and Hungary from the Eurasian section to the West & Middle Europe section, which now, I suppose, can be called simply Europe.   This drops the gap of highest to lowest to a ratio of 1.9461.

5.  Eurasia, now significantly smaller, needs to be equalized with North China again.  This time we will separate Korea and the Chinese provinces of Heliongjiang and Jilin to Eurasia.  This drops the gap to 1.7889

6.  Eurasia keeps pulling in land from the east and losing it in the west.  This time Southeast Europe, which includes Ukraine, Belarus, and the Balkans, but not the Baltic countries, moves from Eurasia to Europe.    Europe’s population is now 563,737,909, which is close to the median, which means it should not need to be equalized for awhile.  However, for the first time neither of the sections involved were the largest or the smallest, so the gap does not change this time.

More  equalizations as I do them.  It turns out that maps take up a lot of space on this blog, so I will put them up only sparingly.

Redistricting Events

There is a proposal in the Ohio state legislature to amend the Ohio constitution to change the procedure for redistricting, making the committee that does the redistricting more bipartisan.   I’d provide a link to the legislation, but they are currently in the process of throwing amendments back and forth.   As a citizen of the state of Ohio, and possibly the only one with an actual plan for doing redistricting objectively, I need to volunteer my services for this committee when the time comes.  Fortunately I have some time — it does not convene until 2011.  I have until then to refine and produce results with my procedure.

Anybody know of redistricting legislation in your area?  Please, let me know.

After 3 Equalizations

After Bisegmentation, the World was split into 12 sections, described here.

At the starting point, the largest section was West India (Including the provinces West and South of Bihar and Chhattisgarh), Maldives and Sri Lanka, with a population of 835,525,239. The smallest section was West & Middle Europe 20 (Including all European countries west of Germany, Austria, and Italy, inclusive, but not Norway or Sweden), with a popluation 371,390,841. The Gap (largest divided by smallest) is 2.2497. The goal is to reduce the Gap to 1.1.

To do this, you move pieces of territory from one side of an eligible border to another. At the start, the largest difference between two sides of an eligible border are the neighbors West India (aforementioned) and Southwest Asia, which includes nations south of the the former Soviet Union, (and also Armenia, Azerbaijan, and Tajikistan) and West of India. To Equalize these two sections, we moved 10 provinces of Northwest India (Rajasthan, Gujurat, Haryana, Punjab, Jammu & Kashmir, Himachal Pradesh, Delhi, Chandigarrh, Daman & Diu, and Dadra & Nagar Havali) to Southwest Asia. Now, we have South India (Population 633,481,357) and Southwest Asia — Turkey to Northwest India (population 683,028,769)

The Largest section is now Northern China 19 provinces, Korea, and Mongolia (population 806,722,219). The Gap, (between Northern China & Western Europe) is now 2.1721. We are making progress.

The Second Equalization moves a piece of the aforementioned Northern China, Korea, and Mongolia. (China is in two sections. Southern China includes the provinces of Sichuan, Chongqing, Hubei, Jianxi, Zhejiang, Fujian, Guangdong, Hainan, Guangxi, Guizhou, Yunnan, and also Hong Kong, Macau, and Taiwan, while Northern China starts out as the rest of China, but that changes) The piece is to move to East India (which includes Bihar, Chhattisgarh and provinces East of that, as well as Bangladesh, Nepal, and Bhutan). The shape of Northern China is such that the largest piece we can move is the Four Western provinces of Tibet, Xinjiang, Gansu, and Qinghai (total poplulation, 51,769,447). These go to East India (now called East India, Himalayas, and Western China) and North China now consists of 15 provinces, plus Mongolia and Korea.

Although North China has been reduced a bit, it is still the largest section. The GAP is now 2.0328.

At this point, the biggest difference between Eligible Neighbors is between North China and Eurasia 30 (which includes the rest of Europe, most of the former Soviet Union, and Japan). The Chinese Province of Inner Mongolia is a real keystone to the North China section. That is, you can’t move a small enough piece of it without fragmenting it unless you do Provincial Biunication on Inner Mongolia and split that province into smaller chunks.

Which we do. The result is, we move Mongolia, four Eastern Divisions of Inner Mongolia (Bayan Nur, Alxa, Ordos, and Wuhai), and the Chinese province of Ningxia Hui (population 13,699,719) to Eurasia 30, now called Eurasia 31 (population 599,001,050). North China now consists of the rest of Inner Mongolia, Heilongjiang, Jilin, Liaoning, Hebei (with two cities), Shandong, Jiangsu (with Shanghai), Anhui, Henan, Shanxi, and Shaanxi, and also Korea (North and South). Now it’s called North China 13 2/3 and Korea (population 743,051,283). The GAP is now 2.0007.

That’s the story so far.

Testing the Objective Redistricting Procedure

I am going to make public the testing of the objective redistricting procedure as I go. Having gone through phase I (Make a list), Phase II (Biunication), and Phase III, (Bisegmentation), we proceed to Phase IV. Equalization Here is the starting point.

After Bisegmentation, the next step is the Border Analysis Table. While it is too detailed to reproduce here, it reveals that after the initial Bisegmentation, the eligible border with the greatest difference in population is between Western India and Southwest Asia, with a difference of 354,540,343 souls, Western India’s advantage.

Now, in this process, you may read about shifting pieces of territory like chess pieces. Please understand that this is purely hypothetical, and obviously I don’t seriously entertain the idea of, say, breaking off a chunk of India and giving it to Pakistan. But I am using the whole world as the test case because the World is sufficiently complicated, geographically, to be an ideal test case. Can the World be divided into twelve equal parts, using an objective procedure that anybody could do and get the same answer? Let’s find out.

Objective Redistricting: A Procedure

I have posted my Procedure for Objective Redistricting. I’m still testing it, getting bugs out, working through problems, and still have to write up a section about revising after a plan is already in place, but this should be enough to get anyone started.

Let me check it against my criteria previously posted:
1. No criteria other than base population considered. Check.
2. Makes geographic sense. This is what the testing is for, but so far, Check.
3. Administrative units kept in place whenever possible. Administrative units already in place are the backbone of the plan. Check.
4. Reproduceable given the same set of data? Check.
5. As simple as possible but as complicated as necessary? Well, if it can be simplified, I’d be in favor of it. Time will tell.
6. Procedure for modifying based on new data? I have one in my head, but I haven’t written it down yet. No point, I figure, until I’ve tested and gotten feedback on the original plan.
7. Creates a new line only at the lowest level? So far, the lowest level I’ve tested at is the Census Tract level, which, can range in size from a few city blocks to a few square miles. Below that you have the block level, and then then house level, but I think it will be difficult to get data that refined.

The World, Halved and Re-Halved

“What are we going to do tonight, Brain?”

“The same thing we do every night, Pinky: Try to take over the world!”

But what would you do with the world once you’ve conquered it? My answer — start dividing it up again. The second step in the Objective Redistricting process (after step one – make a list of the constituent parts) is to merge everything together into one. The third step is to split the whole into smaller parts, with each split being such that the smaller part is not less than half the poplution of the larger part, until you have the number of segments that you want. Then you go to the fourth step, which is equalization, where, using a controlled process, you take pieces from larger sections and attach them to smaller sections.

Here is the tree of the merging process, which I call “Biunication”. Soon I will be uploading the objective criteria for how one constituency gets attached to another constituency, but for now, here is the tree.

Objective Redistricting: Statement of the Problem

Besides list, the other thing that I have been obsessed with for most of my life is Maps.  One day, in the Summer of 2005, I had an idea.  As time went on, I refined the idea, which I will be explaining on this blog as I work out the bugs (it’s not finished yet).

Anyway, let’s begin with a statement of the problem.

(from a document I wrote in  February, 2007)

Every ten years or so almost every state in the United States encounters the same problem.  The Decennial Census rearranges how many representatives each state gets in the House of Representatives.  Some get more, some get fewer representatives.  Except for those states with only one representative, each representative is elected from a district within the state, and assumed to represent the people of only a specific area within the state.

            How this usually works is, every ten years the governor and the state legislature will draw lines on a map that are most likely to keep the ruling party in power for the next ten years.  Often this leads to rancor from the opposing party, lawsuits and court battles.

            One would think that a objective method of drawing these lines on the map would exist, that legislatures could follow, or city counsels could go by when drawing up school districts, or corporations could use when figuring out where to put the next branch of their franchise.  Well, I’ve looked.  There’s not much out there, and nothing that provides an elegant solution.

            When I went in to vote on Election Day, 2006, I saw an Amendment on the ballot for the Ohio Constitution addressing this problem.  This surprised me, because most such initiatives get a lot of press and advertisements, but I had not heard of this one.  The proposal directed that the lines be drawn in such a way to maximize the Democrat/Republican balance in each district.  Anyone could propose such a map; and the map that maximized this balance would “win” and be the new district map for the next ten years.

            I voted for the amendment[1], because I thought that this contest approach was better than the arbitrary “let’s draw lines so that the [other party] cannot win any seats” approach currently used.   But I saw some flaws in it, which got me thinking – what would be an acceptable solution to this problem?   I wrote a list of criteria:


            1.  No other equalization criterion than Population would be considered.   You want the same number of souls in each district, irrespective of which party affiliation that district happened to be leaning at any given moment.

            2.  Each district must make geographic sense.  I’ve seen district maps where you have two widely divided sections of a city and a long thin corridor in between them.  This does not make geographic sense.  Colorado makes geographic sense.  Michigan, not as much[2].

            3.  Administrative units already in place would be kept unified wherever possible.  Keep as many counties intact as you can.  Keep as many townships intact as you can.  And so on.

            4.  The final answer should be reproducible.  Any two people applying the same rules to the same set of data should get the same boundary lines.

            5.  The process should be as simple as possible but as complicated as necessary.

            6.  The process should include a method for modifying the answer with new data.  If the Decennial Census comes back with a result that Ohio now has two million more people and as such is entitled to another Representative, the process should make allowances for that.   One does not redo the boundaries from scratch, but only tweaks what needs to be adjusted, and the process should follow from that, in a way that is also objective and reproducible, and with results that make geographic sense.

            7.  The process should resort to creating new boundary lines only at the lowest level, i.e., when there needs to be a line where there are no previously defined official boundary lines of any kind.


[1] The amendment did not pass.  After looking at some sample maps, I decided that it was a good thing it failed.  The results made even less geographic sense those produced by the “our party wins” system.

[2] However, I would never dream of breaking up the State of Michigan in the name of geography.   Whatever should have been done back in 1837, the State of Michigan is a Unit according to Criteria 3 (q.v.), now and forevermore.  

What happened was this.  In the Northwest Ordinance northern border of Ohio was to be the parallel of the Southernmost extent of Lake Michigan (a line that is till the Northern border of Indiana).  Toledo was North of this line, but had always thought of itself as part of Ohio, and was surprised.when they resurveyed the lines and found the Toledo was actually in theoretical Michigan territory.  However, the Ohio constitution had a different boundary.  By this time Michigan started pushing for statehood, Toledo had been governed by Ohio laws for some thirty years.  Michigan and Ohio almost came to war over this, until Michigan ceded the claim in an 1836 compromise that gave them the Upper Peninsula.