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1  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: Today at 07:03:58 am
That brings me to the basic score for erosity.

Principle: The quality of the shape of a district is based on how well its areas are connected to each other and to the extent that connected areas are split between different districts. Irregular shapes not due to natural barriers and political boundaries at the borders suggest a poor quality district shape. Unrelated areas connected through unusual means suggest a poor quality district shape. A small district in a densely populated area should be measured in a way that is comparable to a large district in a sparsely populated area.

Definition: Cut link. A cut link is a connection between nodes in different districts.

Definition: Erosity. The erosity of a district is the number of cut links to nodes in that district. (nb. Cut links indicate that areas that share transporation interests are in different districts. This reflects on the external quality of a district and correlates to the geographic shape of the district.)

Item: The erosity of a plan is the number of cut links in the plan. Mathematically the number of cut links in a plan will equal one half of the sum of the number of cut links for all the districts. This is because each cut link for a district shows up in the count of two districts.

Example 1:



In this example there is a state with nine counties labeled A through I with regional roads shown as heavy black lines. Counties A through D form one district and the rest form a second district.

The equivalent graph replaces roads with links between nodes. The nodes are colored to show which district they are in. Blue links are internal to a district. Red links are cut links between districts.

There are seven cut links in the plan so the erosity is 7. Each district also has an erosity of 7 which is the number of cut links associated with nodes in the district.



Example 2:



This example uses the same underlying map as in the previous example. One district now consists of whole counties B through D plus a fragment of E, shown with an outlined node. The remaining counties and fragment form the other district.

The rules for links to fragments changes the graph in county E. The new graph has only five cut links for an erosity of 5. The chop of E created a more compact shape that was reflected in the lower score. The trade off between chops and erosity is the key element in scoring.

2  Forum Community / Off-topic Board / Re: Chicago vs. Philadelphia vs. Pittsburgh on: May 23, 2016, 06:56:25 am
One category where Chicago is unquestionably first is in initial growth. In the first 30 years since its incorporation in 1837 it grew by a factor of about 100 (from 1840 to 1870 it grew from 4.5K to 300K - a factor of 66 and was growing even faster before 1840). By contrast Shenzhen China only grew about a factor of 30 in its first 30 years after being created as a special economic zone.

Chicago also moved up more than out. It pioneered the steel-frame skyscraper and has one of the tallest skylines in the world. Its 10 tallest buildings have an average height that exceeds NYC.
3  Other Elections - Analysis and Discussion / Gubernatorial/Statewide Elections / Re: DIRECT DEMOCRACY WATCH 2016 edition on: May 23, 2016, 06:14:04 am
The IL legislature passed an amendment proposal to create a "lock-box" for transportation funds.

Quote
Provides that no moneys derived from taxes, fees, excises, or license taxes, relating to registration, titles, operation, or use of vehicles or public highways, roads, streets, bridges, mass transit, intercity passenger rail, ports, or airports, or motor fuels, including bond proceeds, shall be expended for other than costs of administering laws related to vehicles and transportation, costs for construction, reconstruction, maintenance, repair, and betterment of public highways, roads, streets, bridges, mass transit, intercity passenger rail, ports, airports, or other forms of transportation, and other statutory highway purposes.

The IL House and Senate passed competing versions of a redistricting amendment, but neither was called by the other chamber. However, the citizen redistricting initiative was filed with nearly twice the number of needed signatures. Shortly after it was filed a group connected to the Cook county Dem machine filed a lawsuit to block the citizen initiative. That case is pending.
4  Forum Community / Off-topic Board / Re: anyone ever heard the pre-disco beegees before? on: May 22, 2016, 03:14:01 pm
As a kid I heard those original Bee Gees on AM pop radio stations. The surprise for me was hearing them in college when they reinvented themselves as a disco group.
5  Presidential Elections - Analysis and Discussion / 2016 U.S. Presidential Election / Re: Trump turns "dangerous donald" around on Hillary on: May 22, 2016, 07:34:30 am
I don't know that "dangerous" is a moniker that will dissuade voters. In 1980 Reagan was portrayed as dangerous to the point of being called a "mad bomber" who would get us into WW3. There was no question that Reagan spoke in very strong, black and white terms on some questions of foreign policy during the campaign. The media liked the diplomatic language of John Anderson, but the voters liked what Reagan said.
6  Forum Community / Off-topic Board / Re: A small map of American colleges I created (in progress) on: May 22, 2016, 06:50:50 am
Very nice work.

I see you have the Southern Illinois University branch campus at Edwardsville. Similarly there is a branch of Western Illinois University - Quad Cities in Moline. Northern Illinois University has a number of satellite campuses in Rockford, Hoffman Estates, Naperville, Oregon, and Chicago.
7  Presidential Elections - Analysis and Discussion / Presidential Election Process / Re: If you were in charge of a State GOP, what sort of primary system is best? on: May 21, 2016, 07:54:59 pm

5) what date?  same day as everyone else in the United States.  Preferably not more than about a month before the general election.


This would really complicate absentee and military voting. It takes about 3 weeks to certify the results of an election and if one uses the typical 5-6 week period for absentees, then It usually takes 8-10 weeks between a primary and general. If clerks really push I've seen the turnaround down to 6 weeks, but I don't know how to get to a month.
8  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 20, 2016, 09:16:17 am
Any road connection at all between the two ends of my district?

Only a dirt road through the mountains between Valley and Custer counties. Boise county has the first paved road that connects coming south from the Panhandle.
Interesting.
Of course the smaller seat is Boise MSA+Twin Falls MSA+Gooding County. That leaves that dirt road as the only road connection. I haven't gave much thought to the question of a dirt road counting as a road connection, which I usually have in my maps.

We have a long history of discussion on what counts as a connection going back to 2012. You can see some of that in my post on ID from that period. If you read the current local vs regional road thread you will see how that has evolved to the present.
9  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: May 20, 2016, 08:03:29 am
The previous posts defined the rules for local connections which are reuired for all areas within a district. This post defines regional connections and what constitutes a link for erosity.

Principle: Road connections between areas are an indication of a community of interest between those areas. State and federal highways are a stronger indication of a connection than local roads. Large areas at the regional scale of counties should be connected by better roads than small areas at the scale of smaller governmental units.

Definition: Regional connection. There is regional connection if there is a continuous path of all season numbered state or federal highways or regularly scheduled ferries that allow one to travel between the nodes of two geographic units without entering any other geographic unit. If the node is not on a numbered highway, then the connection is measured from the point of the nearest numbered highway in the geographic unit to the node. Highways along the border of two units are considered to be in either or both of the units as needed to form a connection.

Item: Regional connections are treated like local connections for shared units, isolated units, fragments, and isolated fragments.

Item: A link exists between two nodes in the same county if there is a local connection between the nodes. A link exists between two nodes in different counties if there is a regional connection between nodes.

Example:

This example is based on the one for connection. The 5 geographic units are now counties Agnew, Burr, Calhoun, Dawes and Elbridge, labeled A through E. There are are three districts creating three fragments from Agnew, called West Agnew, Central Agnew, and East Agnew. The nodes for the counties are indicated with solid stars and the nodes for the fragments are shown with hollow stars.

Roads that count for regional connections are shown with heavy brown lines. They are in the same configuration as the roads in the example for connections. The fine brown lines are other local roads. There are sufficient local roads so that all contiguous counties and fragments are locally connected.



Since the regional roads are in the same configuration and they follow the same rules as local roads, these are the regional connections:

Burr is regionally connected to Central Agnew. The regional path from Burr to Agnew enters Agnew in the Central Agnew fragment.

Burr is only locally connected to Calhoun. The obvious shortest regional path cuts a corner of Agnew and no other path stays only within those two units.

Burr is regionally connected to Elbridge. The regional path is along the border between Burr and Agnew which counts for staying in Burr.

Calhoun is regionally connected to Central Agnew. The regional path from Calhoun to Agnew enters Agnew in the Central Agnew fragment.

Calhoun is only locally connected to West Agnew. The regional path entered at Central Agnew, and though it passes through West Agnew, that does not count as a connection for a fragment.

Calhoun is regionally connected to Dawes.

Dawes is regionally connected to Central Agnew. The shortest regional path from Dawes to Agnew enters Agnew in the Central Agnew fragment.

Dawes is regionally connected to West Agnew. Neither shortest regional path from Calhoun or Dawes entered at West Agnew, so it is regionally isolated. As an isolated fragment it uses other regional links, and that includes the regional road from Dawes to West Agnew.

Dawes is only locally connected to East Agnew. East Agnew is regionally isolated, but there are no other regional paths to East Agnew.

Dawes is regionally connected to Elbridge.

Elbridge is regionally connected to Central Agnew. The shortest regional path from Elbridge to Agnew enters Agnew in the Central Agnew fragment using the border between Burr and Agnew.

Elbridge is only locally connected to East Agnew. East Agnew is regionally isolated, but there are no other regional paths to East Agnew.

The equivalent graph colors the nodes of the districts in different colors. The solid lines count as links. The dashed lines represent local connections between nodes that do not count as links. The red lines indicate links and local connections between nodes in different districts.

10  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 19, 2016, 05:09:22 pm
Any road connection at all between the two ends of my district?

Only a dirt road through the mountains between Valley and Custer counties. Boise county has the first paved road that connects coming south from the Panhandle.
11  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 19, 2016, 08:36:03 am
So I decided to see what a Boise-centered House seat would look like. Republicans back in 2011 shot down the idea.
I was able to split no counties. The Boise-centered House seat would have 782,407 people, while the other seat would have 785,175 people.

The blue seat is 39% Obama, 58.8% McCain; the other seat is 33.4% Obama, 64.1% McCain.

I posted a couple of ID plans a while ago (if you search you can find plans for just about every state). The first is a particular favorite of mine since it is whole county with a population deviation of only 1 person. The second plan keeps the deviation to only 146 while keeping Boise-Nampa whole.

It would be nice to have a clear statement of what the exact role of regions is, vis a vis county/transportation link splits. How does inserting the concept of regions end up with better maps with a system that would apply to all 50 states?  Is part of it an attempt to respect metro regions even when it ends up with more county splits.  The mathematics of this all is quite daunting. Smiley

The simple answer is that it reflects the number of county splits. If D is the number of districts and R is the number of regions then the minimum number of county splits S = D - R. The links provide a constraint on region formation so that one doesn't have a split like this for ID where one county (Lemhi) has no connection to any other in CD 1 even though the districts are whole county with a population variance of 1.



The intermediate answer is that regions are easy to form and configure. By using the links to measure erosity it provides a another way to judge a plan in addition to both county splits and population equality. Public mappers can easily follow a plan based on regions. Links tend to be more dense in areas joined by communities of interest so such a region-based plan using erosity will tend towards districts that also follow the big-picture communities of interest. For example, it could lead to this plan that is better connected with a deviation of 146 that keeps the Boise metro largely intact.



The complex answer is that the notion of nodes and links can be extended into counties that need to be split. This creates a hierarchy of measures, one by region and one for the plan itself. The measures can be related at both levels and derive from the same methodology, so it remains reasonably accessible to the public. The principles that would guide well-formed regions then can also guide the formation of districts within those regions. Using ID as an example, this would provide a way of judging the merits of a plan that splits Ada county and Boise city but keeps the north and east separate.

Edit: I took a closer look at the ID state highways and found I counted a road across Boise County linking SR 55 and SR 21 as a state highway when it is not. Therefore, by my narrow rule for connections there is no way to divide ID without cutting the Boise metro. It does show the utility of the state creating an altered list of connections. It would permit connections from Gem and Adams to Boise and thus to eastern ID without going through Ada County, or allow the state to forbid that type of district by excluding that alteration. More reason to provide a county split mechanism as well as one for whole county regions.
12  Forum Community / Off-topic Board / Re: In which Charleston would you rather live? on: May 19, 2016, 08:15:03 am
Why not Charleston IL, home of Eastern Illinois University?
13  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 18, 2016, 11:11:02 am
Your imgur images aren't working without copying the link to a separate tab. There's a problem with imgur on this site that was described here.

Also, it would help to not make one of the districts white, since that's the color of the neighboring states.
14  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 17, 2016, 08:18:45 am

Here is my effort a 5-0 Democratic Oregon. Blue voted for obama by about 40k votes in 2012, making it D+2 (estimation).
(Cross-posted from AAD)

A nearly even result in 2012 translates to R+2. Obama got 52% of the two-party vote in 2012. A district that was even in 2012 is two points more Pub than the nation as a whole, hence R+2.
I got that number by taking Obama's margin in 2012 (216k votes) and dividing by 5. I get 43.2k for a district to match state's 2012 PVI (D+3). I decided to be conservative and say D+2 because the 40k figure was on the higher end of my estimated Obama margin in the district.
I'm not using the two-party vote measure here, hence the confusion.

It isn't hard to use the two party vote share. Just take the Obama vote and divide it by the total that went to Obama+Romney. For example in OR '12, Obama got 54.24% and Romney got 42.15%. .5424/(.5424+.4215) = .5627 or 56.27%. Nationally in '12 Obama's fraction was .5101/(.5101+.4715) = .5197 or 51.97%. Third parties took a larger share of the vote in OR than in the US, so the effect is to raise Obama's numbers in OR compared to the US. The result would be a PVI of D+4 for the state in 2012.

Technically the PVI should be the average of 2008 and 2012. Even if you just use one cycle but use the actual two-party vote it will reduce confusion.
15  Presidential Elections - Analysis and Discussion / 2016 U.S. Presidential General Election Polls / Re: Reuters junk poll: Clinton up 4, too many undecideds on: May 17, 2016, 07:33:22 am
Well, a lot of undecided voters may be true since both candidates have poor favorability ratings in the whole electorate.

Fake undecideds maybe. Both parties are guaranteed 45% just for showing up.

The breakdown in the poll is 14% neither/other, 6% don't know, 2% won't vote. That doesn't sound fake at this early stage with high unfavorables for both candidates.
16  Presidential Elections - Analysis and Discussion / 2016 U.S. Presidential General Election Polls / Re: Morning Consult national poll: Clinton 42% Trump 40% on: May 17, 2016, 07:23:29 am
I just started drinking my coffee this morning and I couldn't help but laugh at the title in the URL. Cheesy
17  General Politics / Political Geography & Demographics / Re: DRA stuff on: May 16, 2016, 10:26:31 pm

Here is my effort a 5-0 Democratic Oregon. Blue voted for obama by about 40k votes in 2012, making it D+2 (estimation).
(Cross-posted from AAD)

A nearly even result in 2012 translates to R+2. Obama got 52% of the two-party vote in 2012. A district that was even in 2012 is two points more Pub than the nation as a whole, hence R+2.
18  Presidential Elections - Analysis and Discussion / Presidential Election Process / Re: If you were in charge of a State GOP, what sort of primary system is best? on: May 16, 2016, 10:20:57 pm
I like CA's jungle primary myself.
Top two primaries are unfair, undemocratic, and unconstitutional because they unfairly limit voters' choices and discriminate against political minorities (Republicans in Safe D districts and vice-versa).  I'm surprised nobody has sued under the VRA to overturn it.

Explain how they limit voters' choices and discriminate against political minorities.

In safe districts and states, both general election candidates are from the same party, meaning that minority parties are disenfranchised.  If you live in Los Angeles and San Francisco and you're a Republican, you general election ballot will most likely be all Democrats; there are rural parts of California where the opposite happens and both general election candidates are Republicans.  It basically sends the message that member of minority parties don't deserve to have a candidate that represents them, simply because they're a minority.

The problem is that in safe districts the minority party is far more likely to have no candidate from their party. That's real disenfranchisement. In a top-two system their vote matters and they can select the candidate who better represents them.

Wouldn't open primaries accomplish the same thing, though?

That depends what you mean by open primaries. IL has open primaries in the sense that any voter can show up on primary day and take either partisan ballot. It doesn't work to improve competition in Nov any more than closed primaries do.
19  Presidential Elections - Analysis and Discussion / 2016 U.S. Presidential Election / Re: So the Lichtman Test so far on: May 16, 2016, 10:15:59 pm
Lichtman was on Smerconish this morning following his interview with the Fix last week. He claims that there are 4 against the Dems with two keys unable to call. Here was his assessment:

Key 1: The incumbent party (in this case, Democrats) holds more seats in the U. S. House of Representatives after the midterm election than after the preceding midterm election. FALSE
Key 2: There is no serious contest for the incumbent-party nomination. NO CALL; It depends on whether Bernie takes his battle to the convention.
Key 3: The incumbent-party candidate is the current president. FALSE
Key 4: There is no significant third-party or independent candidacy. TRUE
Key 5: The economy is not in recession during the campaign. TRUE
Key 6: Real (constant-dollar) per capita economic growth during the term equals or exceeds mean growth for the preceding two terms. TRUE
Key 7: The incumbent administration has effected major policy changes during the term. FALSE
Key 8: There has been no major social unrest during the term. TRUE
Key 9: The incumbent administration is untainted by major scandal. TRUE
Key 10: There has been no major military or foreign policy failure during the term. TRUE
Key 11: There has been a major military or foreign policy success during the term. NO CALL. Though Iran could qualify the majority of Americans do not consider it a success. As a Dem he urged Obama to hit the trail, but tout his foreign policy, not attack Trump.
Key 12: The incumbent-party candidate is charismatic or is a national hero. FALSE
Key 13: The challenger is not charismatic and is not a national hero. TRUE. He thinks negatives are not an indication of charisma, but the radio team thought about how they would listen every time he went on TV. They leaned true.
20  Presidential Elections - Analysis and Discussion / Presidential Election Process / Re: If you were in charge of a State GOP, what sort of primary system is best? on: May 16, 2016, 03:32:16 pm
I like CA's jungle primary myself.
Top two primaries are unfair, undemocratic, and unconstitutional because they unfairly limit voters' choices and discriminate against political minorities (Republicans in Safe D districts and vice-versa).  I'm surprised nobody has sued under the VRA to overturn it.

Explain how they limit voters' choices and discriminate against political minorities.

In safe districts and states, both general election candidates are from the same party, meaning that minority parties are disenfranchised.  If you live in Los Angeles and San Francisco and you're a Republican, you general election ballot will most likely be all Democrats; there are rural parts of California where the opposite happens and both general election candidates are Republicans.  It basically sends the message that member of minority parties don't deserve to have a candidate that represents them, simply because they're a minority.

The problem is that in safe districts the minority party is far more likely to have no candidate from their party. That's real disenfranchisement. In a top-two system their vote matters and they can select the candidate who better represents them.
21  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: May 16, 2016, 02:34:02 pm
The third and final special rule for local connections is another one we have looked at earlier in this thread.

Definition: Isolated unit or fragment. An isolated unit has no connections from its node to the nodes of any other units based on the basic connection rule or the special rule for shared units. An isolated fragment has no connections based on the special rule for fragments.

Item: An isolated unit has a local connection to another unit if there is a local connection from its node to the node of any contiguous unit or subunit in that order of priority. Subunits can be further divided until at least one local connection is established. (nb. This is a fall back when the normal rules leave a unit with no local connections. There should always be a way to get to the population from outside the unit, even if it is by way of other parts of units.)

Example 1:



In this example there are 4 geographic units:  Adlai, Bryan, Clay, and Dewey. As before the nodes are indicated with stars and the roads are shown with heavy lines. The thick shaded area running roughly vertical represents a natural barrier such as a river. Think of Dewey as an independent city that has grown along the river annexing land in Adlai.

In the example for the basic rule, Clay is connected to Bryan, but not to Adlai or Dewey. One path from Clay to Adlai initially goes into Adlai but then goes through Dewey before reaching the node of Adlai so it fails the basic connection rule.

In this case a chop follows the river splitting Adlai into east and west fragments. The east fragment has the node for Adlai. The west fragment (shaded) has a node based on its population shown by a hollow star.

There is no road that directly connects the east and west fragments so there is no local connection between the fragments. Since there is no connection from Clay to Adlai the road that cuts through the northern part of the West Adlai fragment also doesn't become a link to West Adlai. That makes West Adlai an isolated fragment.

Under the special rule for isolated fragments the node in West Adlai is used with its roads to determine   connections. West Adlai has a path to both Clay and Dewey, so it becomes connected to both.

The equivalent graph colors the nodes of the two districts in different colors. The blue lines represent links between nodes in the same district. The red lines indicate links between nodes in different districts.



Example 2:

This is an example from the area around Canton OH. The colors represent different subunits of Stark county and the nodes are indicated by stars.
Canton city (white)
Canton township (green)
Plain township (dark blue)
North Canton city (light blue, actual location slightly north of image)
Meyers Lake village (red)



Both Canton and Plain townships are split into discontiguous parts by Canton city. As long as those townships are not chopped they are viewed each as single units. Canton city and the townships have sufficient other connections and do not meet the definition of shared units.

Meyers Lake is only bordered by the two townships, and those are both discontiguous from the parts with the nodes. Meyers Lake has no path to any other node so it is an isolated unit.

Based on the special rule Meyers Lake would consider counties and then townships for connections, but none would exist. The rule allows the subunits to be further divided, in this case to precincts. Meyers Lake has connections to precincts in both townships, so Meyers Lake has local connections to both townships by the isolated unit rule.
22  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: May 16, 2016, 08:40:15 am
Are you abandoning the nick exception that has been discussed? Are you seeking comment, or is that a statement of commandments from Moses? Smiley

I am open to comment. This set of posts is my response to your post.

Just move on. Presumably you find some value in bouncing ideas off of me. In the end, a paper can lay out the options, and where people may disagree. In defending what you prefer, your challenge will be not to lapse into jargon, or abstract grand unified theories, but rather persuade folks that it is common sense, and where it isn't, it is not far off, and not worth the additional complexity. What I am receptive to, is public policy and common sense arguments of course. That is what will change my mind.

The issue we are arguing about as I say is of very marginal importance, and very deep in the weeds.

At this point I have only been addressing local connections. The key item is that all nodes must be locally connected. All the nick situations that you support have a local connection, so they don't violate anything I've posted. We never could agree on a good definition for nicks. I'm quite convinced that absent a ban on using nicks for connections (my initial reaction) the best way to handle them is without definition, but by example. My rationale will emerge as I get into regional connections and scoring erosity.
23  General Discussion / Religion & Philosophy / Re: "Low Church" vs. "Evangelical" within the context of Anglicanism/Episcpalianism on: May 16, 2016, 08:19:14 am
I was raised an Episcopalian in the 60's and 70's, and I was very active as an acolyte in the church. We moved a number of times, so I got to experience both "high church" and "low church" as it was understood at that time.

High churches used services that included all the formal elements. The liturgy always followed the Book of Common Prayer. Masses were held on a daily basis in the AM, even though attendance was small. The activities of the priest and other officiants during the service had a very specific ritual.

Low churches used services that lacked some of the formality. Modern language liturgies could be used. Masses were less frequent, sometimes only once a month. The service itself had less reliance on the ritual though many parts were still there.
24  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: May 16, 2016, 07:59:37 am
The second of the special rules deals with a situation that arises in many circumstances from independent cities in VA to cities embedded in townships in OH. I'm calling these situations shared units. The treatment of shared units mirrors the language for fragments within a unit which should make it easier to apply.

Definition: Shared units. Shared units occur when a unit is surrounded or effectively surrounded by another unit, making both the surrounded and surrounding units shared units. A unit is effectively surrounded when it only has local connections to the surrounding unit or other units surrounded by the same unit. Shared units also exist if the node of a unit is in another unit.

Item: Shared units trace paths to their nodes as if they were a single unit. A connection to the node of a specific unit among the shared units exists if the connecting path from another node enters the shared units in that specific unit. Units within a set of shared units are locally connected if their nodes are locally connected. (nb. Shared units are often a city that formed a separate unit from its surrounding county or township, but the roads are designed to go to and through the city. The city should not act as a barrier for connection in those cases.)

Example 1:



Louisville OH (yellow) is an incorporated city in Nimishillen township (blue). Both are subunits of Stark county. The node for Louisville is shown with a white star, and the node for Nimishillen is shown with a blue star. Nimishillen township is bordered by four townships in each of the cardinal directions, and the city of Canton in the southwest (outlined in pink).

Under the basic rule for connections, every path from the node of Nimishillen to any neighbor would have to go through Louisville since the node is in Louisville. That would leave Nimishillen unconnected to any neighbor.

Louisville is surrounded by Nimishillen and contains the node for Nimishillen. That makes Louisville and Nimishillen shared units both ways under the special rule. Paths to both nodes are considered using the shared units together.

All paths to either node enter the shared unit in Nimishillen. So, Nimishillen is connected to all of the neighboring townships and Canton city. Louisville is only connected to Nimishillen.

nb. It is insufficient to define the shared unit only by considering that Louisville is surrounded. Suppose that Louisville annexed more land to the west and became directly connected to Canton city. It would not be surrounded, but the node of Nimishillen would still be inside of Louisville. The special rule would take care of that situation as well.

Example 2:



East Sparta OH (pink outline) is an incorporated city in Pike township, both shown in green. Both East Sparta city and Pike township are subunits of Stark county. Their nodes are shown by stars.

Tuscarawas county in shown in blue. There are no local roads connecting East Sparta to Tuscarawas, and no path from the node of Pike to Tuscarawas. With just the basic connection rule, neither East Sparta nor Pike have connections to Tuscarawas, despite the presence of OH-800 going from the township to Tuscarawas.

East Sparta is only connected to Pike, so it is effectively surrounded. That makes Pike and East Sparta shared units.

By the special rule for shared units, we look at paths for both East Sparta and Pike as they go through the combined shared unit. OH-800 is the shortest path to the nodes of both East Sparta and Pike. It enters the combined shared unit in Pike. By the special rule Pike is connected to Tuscarawas. East Sparta remains only connected to Pike.
25  General Politics / Political Geography & Demographics / Re: Local vs regional road connections on: May 15, 2016, 11:17:33 pm
The first special rule for connections is for fragments. This follows what was worked out earlier in the thread.

Definition: Fragment. A fragment is the contiguous part of a unit entirely within a district formed by a chop of that unit. Fragments are artifacts of a specific redistricting plan and need not correspond to a recognized political unit. The node of the fragment containing the node of the chopped unit is that same node. For a fragment that does not contain the node of the whole political unit, the node is that of the most populous subunit in the fragment.

Item: Fragments trace paths to their nodes as if they were part of the original unit. A connection to the node of a fragment exists if the connecting path to the unit with the fragment enters the unit in that fragment. Fragments within the same unit are locally connected if their nodes are locally connected.

This example is based on the the previous unchopped one. The 5 geographic units are Agnew, Burr, Calhoun, Dawes and Elbridge, labeled A through E. The nodes are indicated with stars and the roads are shown with heavy lines.



The shaded area represents a district that chops unit Agnew.

The East Agnew fragment has a node from the original whole Agnew. The West Agnew fragment has a newly created node shown as a hollow star that will be used as a placeholder for mapping.

The path from Agnew (before the chop) to Calhoun without a chop enters Agnew in the West Agnew fragment, so there is a link from West Agnew to Calhoun.

The path from Agnew to Elbridge enters Agnew in the East Agnew fragment, so there is a link from East Agnew to Elbridge.

The primary path from Agnew to Dawes enters in East Agnew, so there is a link from East Agnew to Dawes. A secondary path from Agnew to Dawes enters in West Agnew, but does not form a link.

The primary path from Agnew to Burr enters in East Agnew, so there is a link from East Agnew to Burr. A secondary path from Agnew to Burr enters in West Agnew, but does not form a link.

There is a path between West Agnew and East Agnew that forms a local connection, so there is a link between those fragments.

The equivalent graph colors the nodes of the two districts in different colors. The dashed lines represent secondary paths between nodes that do not count as links. The red lines indicate links and secondary paths that link nodes in different districts.



nb. As noted in the example the dashed lines represent real local connections, but not links. Links are based on the shortest connecting path. That's important in cases where a path of local connections is required, but no link is available. This situation will be addressed further in the special rule for isolated fragments and in the definition for components.
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