Non Partisan Redistricting.

[jimrtex]

Thanks for the math catch. I'll fix that in the next edit. I appreciate your concern about contiguous, and it's clear than linked counties are also contiguous, so there would be no violation of any constitutional language to restrict regions to linked counties.

How does this look:

link: Two nodes form a link if there is a continuous path between those two nodes that uses only non-seasonal numbered state and federal highways or non-seasonal regular ferry service that does not pass through any county other than the counties of the two linked nodes. A state may add or remove links to reflect unique geographical circumstances. (were you suggesting to drop this?)

connected: Two counties are connected if there is a link between the population nodes of the counties. Connected counties are by definition contiguous.

region: A single county or group of connected counties. The region population {P} is the sum of the population of the counties in the region.

The following relationships should be established well before the actual redistricting begins, preferably before the census is taken.

contiguous: Two counties are contiguous if they share a land boundary, or if they share a water boundary which can be easily and directly traversed on a daily basis by car, rail, or ferry.   Queens and Richmond are not considered to be contiguous, nor are Westchester and Nassau, because they have no regular ferry service.  Contra Costa and Marin counties would be considered to be contiguous via the Richmond-San Rafael Bridge even if the tip of San Francisco cut the bridge.  In rare instances, counties may be considered contiguous if there is a regular transportation link between the two, and it has been past custom to include the two in the same district (example: New York and Richmond).

Counties that touch at corners are not contiguous.  Counties that have near point connectivity may or may not be considered contiguous.   Consideration should be given to the length of the border relative to (the square root of) the area of the counties, irregularity of the shape of the counties, and the ease by which people can move directly between the counties (tough cases: Solano-Sonoma CA, Franklin-Columbia WA).

Are counties considered self-contiguous?  St. Martin, LA; Norfolk, MA; Arapahoe, CO.

connected: Contiguous counties are considered connected if there is a year-round transportation route (numbered Interstate, US, or state highway; commuter rail; passenger ferry) between the county (population) nodes that does not pass through a population node of another county.   The route may pass through other counties or even States.   Non-connected, contiguous counties indicate that there is an extreme level of impassibility between the counties.

region:  A region is a single county, or a group of counties where each county is connected to at least one other county in the region.  Non-connected counties may be included in a region, if there is an indirect connection through other counties.

linked: Two counties are linked if they are connected, and the fastest, most direct transportation link between the population nodes does not pass through a population node of another county.  Erosity is a measure of the number of links that are severed by district boundaries.   Greater erosity indicates a more convoluted boundary, that may sever more links than are necessary for the creation of relative equipopulous whole-county districts.

[muon2]

Thanks for the math catch. I'll fix that in the next edit. I appreciate your concern about contiguous, and it's clear than linked counties are also contiguous, so there would be no violation of any constitutional language to restrict regions to linked counties.

How does this look:

link: Two nodes form a link if there is a continuous path between those two nodes that uses only non-seasonal numbered state and federal highways or non-seasonal regular ferry service that does not pass through any county other than the counties of the two linked nodes. A state may add or remove links to reflect unique geographical circumstances. (were you suggesting to drop this?)

connected: Two counties are connected if there is a link between the population nodes of the counties. Connected counties are by definition contiguous.

region: A single county or group of connected counties. The region population {P} is the sum of the population of the counties in the region.

The following relationships should be established well before the actual redistricting begins, preferably before the census is taken.

contiguous: Two counties are contiguous if they share a land boundary, or if they share a water boundary which can be easily and directly traversed on a daily basis by car, rail, or ferry.   Queens and Richmond are not considered to be contiguous, nor are Westchester and Nassau, because they have no regular ferry service.  Contra Costa and Marin counties would be considered to be contiguous via the Richmond-San Rafael Bridge even if the tip of San Francisco cut the bridge.  In rare instances, counties may be considered contiguous if there is a regular transportation link between the two, and it has been past custom to include the two in the same district (example: New York and Richmond).

Counties that touch at corners are not contiguous.  Counties that have near point connectivity may or may not be considered contiguous.   Consideration should be given to the length of the border relative to (the square root of) the area of the counties, irregularity of the shape of the counties, and the ease by which people can move directly between the counties (tough cases: Solano-Sonoma CA, Franklin-Columbia WA).

I think the best way to deal with these is a state-specific clause added to a tighter definition. There's already another point of state input for the maximum deviation, so a point that allows modification of the list of links by a state is a better solution than trying to encompass all the geographic variations.

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For some legislative plans contiguity does allow this. The wards in WI are a notable example. They stay within a municipality which can be disconnected. The courts have rules that legislative districts that adhere to the ward lines can be similarly disconnected.

One can also treat these special counties as separate units without harm to the general method. I plan definitions to deal with split counties in a map, and that would accommodate these counties, too.

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I think that linked and connected would be sufficiently similar for most occurrences that it is simpler to use a single definition for both regions and erosity. This also better lends the definition to use by public mappers and possible scoring criteria. the alternative forces users to maintain two slightly different sets of information about how counties can be joined. From a theoretical view it keeps the form of the plan into one that is translatable to a simple planar graph which can be analyzed from that perspective using links and nodes as the elements of the graph.

[jimrtex]

The following relationships should be established well before the actual redistricting begins, preferably before the census is taken.

contiguous: Two counties are contiguous if they share a land boundary, or if they share a water boundary which can be easily and directly traversed on a daily basis by car, rail, or ferry.   Queens and Richmond are not considered to be contiguous, nor are Westchester and Nassau, because they have no regular ferry service.  Contra Costa and Marin counties would be considered to be contiguous via the Richmond-San Rafael Bridge even if the tip of San Francisco cut the bridge.  In rare instances, counties may be considered contiguous if there is a regular transportation link between the two, and it has been past custom to include the two in the same district (example: New York and Richmond).

Counties that touch at corners are not contiguous.  Counties that have near point connectivity may or may not be considered contiguous.   Consideration should be given to the length of the border relative to (the square root of) the area of the counties, irregularity of the shape of the counties, and the ease by which people can move directly between the counties (tough cases: Solano-Sonoma CA, Franklin-Columbia WA).

I think the best way to deal with these is a state-specific clause added to a tighter definition. There's already another point of state input for the maximum deviation, so a point that allows modification of the list of links by a state is a better solution than trying to encompass all the geographic variations.

Some ideal properties of districts are:

Compactness
Convenience
Contiguity
Community of interest.
Relative population equality

Compactness, convenience, community of interest are abstract and subjective.   Contiguity has a concrete definition but which can stretched to permit any sort of gerrymandering.  Population equality has a precise definition, but which can be used to rationalize any sort of gerrymandering.  So what we are trying to do is to define some measurable properties that enhance what we think of as compactness, convenience, and community of interest, and providing additional flexibility as to what relative population equality means so that more of these other qualities may be achieved.

We are first defining contiguity in terms of counties, rather than as a single continuous boundary.   This recognizes counties as a first level of community of interest.  If we were defining "touching" among individuals we might want to include hugging, pats on the back, handshakes, and fist bumps - but exclude assault or superficial contact when passing through a crowded room.

Likewise with counties, we want to define contiguous in a deeper manner than is provided by County Adjacency File

We are discussing a conceptual framework, that States might employ.  But if we are going to test whether it is a workable model, we need to identify and test possible criteria that they might use.

So we can specify the starting point as pure adjacency.   We can require exclusion of point adjacency.  The Census Bureau says that Geauga-Summit and Portage-Cuyahoga are adjacent, but we don't want districts connected only by corners.

The Census Bureau says that Clermont-Clinton are adjacent, but that Brown-Warren.  But is there a meaningful distinction between the two, as far as having a district directly connecting the two?  It violates what I think of community of interest, convenience, or compactness.

But what about Montgomery-Clark.   I don't like the length of the boundary, particularly because it depends on a panhandle.   But on the other hand it is easy to travel between Dayton and Springfield.  And perhaps it is Miami that has the odd shape.

Arguably, Ottawa and Erie are not contiguous,

I would consider Ottawa-Erie to  be contiguous.  If someone traveled from Port Clinton to Sandusky via Fremont in Sandusky County, I would describe them as sightseeing or lost.

So we have eliminated some cases where the adjacency is minimal or superficial, and considered whether bodies of water prevent adjacent counties from being considered meaningfully contiguous.

I am reluctant to define Whatcom and Okanogan as not touching or not being contiguous.  A district crossing that boundary would not be non-compact, which must also take into account population density.   But it is grossly inconvenient.  So I am defining an additional relationship where placing counties that are contiguous in a meaningful away are nonetheless grossly inconvenient for purposes of being placed in the same district.

In my opinion, this is not true for Snohomish and Chelan.  It is not grossly inconvenient to travel from Everett to Wenatchee via Stevens Pass.  It is somewhat distant, but not particularly given the size of the counties, and that the nodes are on opposite ends of the two counties.

The "connection" is the relationship between the counties, not the highway route per se.  The counties are adjacent in more than a superficial way, and it is not grossly inconvenient to travel directly between them.  While it might be convenient to show the highway route for purposes of pictorial representation, it is not necessary.

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I think that linked and connected would be sufficiently similar for most occurrences that it is simpler to use a single definition for both regions and erosity. This also better lends the definition to use by public mappers and possible scoring criteria. the alternative forces users to maintain two slightly different sets of information about how counties can be joined. From a theoretical view it keeps the form of the plan into one that is translatable to a simple planar graph which can be analyzed from that perspective using links and nodes as the elements of the graph.
[/quote]
You may be objecting to my terminology, since you are thinking in terms of graph theory where link and connection are used interchangeably.

Likewise, we probably should not use "node" for major population center.  The nodes of our graph are the counties.  The graph of connected counties represents counties that may be included in the same district without inclusion of any other intermediate counties.

Representing the graph with the nodes in geographically accurate position is useful, and any community of interest between counties, is actually between the people of the counties who are heavily concentrated in urban areas.

We are now defining a community of interest relationship between counties.  We are providing a weighting to the links.  Instead of minimizing the number of links severed by our district boundaries, think of it as maximizing the weight of our unsevered links.

So it is OK to go from Whitman to Garfield, but there is a greater reward for going via Asotin (ignoring for the point of illustration that Asotin is in the corner of the state).

So perhaps we should define it as COI weighting.   Which might also include such items as shared urban areas, current districts, socioeconomic relationships, etc.

[jimrtex]

This is my Washington map/graph showing county connection relationships.  The heavy red links  indicate pairs of counties that may be directly placed in the same district.  The fine red links indicate counties that are adjacent, but nonetheless should not be directly connected within a district.



No Ferry: San Juan-Whatcom, San Juan-Island, San Juan-Jefferson, San Juan-Clallam, Island-
Kitsap.

No Direct Route: Jefferson-Grays Harbor, Lewis-Wahkiakum, Lewis-Skamania, Cowlitz-Skamania, Skamania-Yakima, King-Chelan, Grant-Franklin.

Impassable: Whatcom-Okanogan, Skagit-Okanogan, Skagit-Chelan, Pierce-Yakima.

Point Connectivity: King-Yakima, Pierce-Kittitas.

Near Point Connectivity: Franklin-Columbia, Grant-Okanogan.

[muon2]

This is my Washington map/graph showing county connection relationships.  The heavy red links  indicate pairs of counties that may be directly placed in the same district.  The fine red links indicate counties that are adjacent, but nonetheless should not be directly connected within a district.



No Ferry: San Juan-Whatcom, San Juan-Island, San Juan-Jefferson, San Juan-Clallam, Island-
Kitsap.

No Direct Route: Jefferson-Grays Harbor, Lewis-Wahkiakum, Lewis-Skamania, Cowlitz-Skamania, Skamania-Yakima, King-Chelan, Grant-Franklin.

Impassable: Whatcom-Okanogan, Skagit-Okanogan, Skagit-Chelan, Pierce-Yakima.

Point Connectivity: King-Yakima, Pierce-Kittitas.

Near Point Connectivity: Franklin-Columbia, Grant-Okanogan.

I understand what you've done with this list, but it seems entirely too subjective for the goal of having it generally applicable to the states. I much prefer a hard definition, but a recognition that states can alter it using their local expertise. Let the states make the exceptions on a simple rule.

For example, consider Walla Walla. I contend there is no connection to Benton, since the path through OR is much longer than going through Franklin, but that goes right through the Pasco node so it should be excluded. That leaves Walla Walla connected only to Columbia and Franklin. So if there is a connection from Columbia to Franklin, it's irrelevant since any time it would be used, one must also take Walla Walla in the same region.

On the other hand we agree on the lack of a connection between Grant and Okanogan, but for different reasons. For me it's because the highway goes through Douglas for three blocks. With my simple rule, no exception need be made for the near-point contiguity situations you address. The point connectivity cases disappear as well with my rule, through it probably needs to be explicitly included for some urban areas.

On the subject of nodes, when we get to the districting step, I think it will be clearer as to why I like nodes to be the population centers rather than the counties. The natural extension at that step is to split counties by creating new nodes. It allows other definitions of connectivity and erosity to be more smoothly generalized.

[muon2]

Likewise with counties, we want to define contiguous in a deeper manner than is provided by County Adjacency File

We are discussing a conceptual framework, that States might employ.  But if we are going to test whether it is a workable model, we need to identify and test possible criteria that they might use.

So we can specify the starting point as pure adjacency.   We can require exclusion of point adjacency.  The Census Bureau says that Geauga-Summit and Portage-Cuyahoga are adjacent, but we don't want districts connected only by corners.

We are in agreement here. The place where the highway rule would miss adjacent corners is where two state highways form a 4-way intersection at the county corner.

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My rule works fine here. Rt 133 clips through Warren as is goes from Clermont to Clinton. Generally the short segments you'd want to regulate by an arbitrary choice of length are usually excluded because it doesn't make sense to thread a highway through them. There are a few exceptions like our problem around Walla Walla, but this OH case shows how the rule usually works.

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I think the highway planners recognize what your instinct and my travels observe. This is a built up area and it was sensible to have a link through that small length of county boundary. In this case it's interstate 70 which is about a strong a link as one could get. My rule includes this, and I think objections to the link would be weak.

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I've been on both the highway and passenger train over the bay between these counties. It is a solid link and should be included IMO. Ottawa county does raise some questions about nodes. The urban area from Toledo sends a couple of tentacles into the western edge, but the population in them is less than in the county seat of Port Clinton. Port Clinton is an urban cluster as opposed to an urbanized area, so I wonder if that needs to be included in the definition?

[jimrtex]

This is my Washington map/graph showing county connection relationships.  The heavy red links  indicate pairs of counties that may be directly placed in the same district.  The fine red links indicate counties that are adjacent, but nonetheless should not be directly connected within a district.



No Ferry: San Juan-Whatcom, San Juan-Island, San Juan-Jefferson, San Juan-Clallam, Island-
Kitsap.

No Direct Route: Jefferson-Grays Harbor, Lewis-Wahkiakum, Lewis-Skamania, Cowlitz-Skamania, Skamania-Yakima, King-Chelan, Grant-Franklin.

Impassable: Whatcom-Okanogan, Skagit-Okanogan, Skagit-Chelan, Pierce-Yakima.

Point Connectivity: King-Yakima, Pierce-Kittitas.

Near Point Connectivity: Franklin-Columbia, Grant-Okanogan.

I understand what you've done with this list, but it seems entirely too subjective for the goal of having it generally applicable to the states. I much prefer a hard definition, but a recognition that states can alter it using their local expertise. Let the states make the exceptions on a simple rule.

For example, consider Walla Walla. I contend there is no connection to Benton, since the path through OR is much longer than going through Franklin, but that goes right through the Pasco node so it should be excluded. That leaves Walla Walla connected only to Columbia and Franklin. So if there is a connection from Columbia to Franklin, it's irrelevant since any time it would be used, one must also take Walla Walla in the same region.

On the other hand we agree on the lack of a connection between Grant and Okanogan, but for different reasons. For me it's because the highway goes through Douglas for three blocks. With my simple rule, no exception need be made for the near-point contiguity situations you address. The point connectivity cases disappear as well with my rule, through it probably needs to be explicitly included for some urban areas.

It is less subjective than you think.  I had mentioned before a test for near-point connectivity, where the gap across the boundary is compared to the circumference of a circle that has an area of the smaller county:

ratio = gap_length / (2 * sqrt (pi * smaller_area)).

I suggested 5%, unless there was good connectivity, and perhaps also local sentiment.  The Columbia-Franklin and Grant-Okanogan borders are far below that.  The Benton-Walla Walla was far above (which one is not like the others, which one does not belong?  Points at blue one).   The southern route between Kennewick is not that circuitous, and at about 7 or 8 miles south of Kennewick, you reach the cross-over point time-wise.

The Whitman-Lincoln and Lincoln-Okanogan links have direct transportation links.  It is irrelevant whether then Onak-Davenport route skips across the corner of another county.

The Whitman-Douglas is slightly circuitous, but is an alternative route on Google Maps.  I am willing to make concessions for crossings of a major river that has a series of dams.

I rejected the Benton-Grant connection, even though it is close to 5.0%.  When traveling from Pasco to Moses Lake, while avoiding Kennewick and Othello, you have to go east of Othello, which is on the wrong side, in effect forcing an edge crossing in the graph.

I did not include a picture of Yakima-Grant which is at 4.7%.  The transportation link that avoids going past Ellensburg is only slightly longer (16%) and given the problem of finding a river crossing and getting through the two segments of the Hanford Site, it is a reasonable route.  I think that some caution is in order in not becoming too dependent on interstates and their higher speeds defining transportation routes.

Some percentages for western Washington: Skagit-Okanogan 5.8%, Grays Harbor-Lewis 6.0%, King-Chelan 7.5%.

We are attempting to build districts from whole counties.  Clearly, the counties must be adjacent.  But some adjacent counties are barely adjacent, or there is no even marginally direct way to travel between the population centers.   But we should be very careful in excluding links between adjacent counties.   A plan that is dependent on one of the fine red lines for district connectivity is automatically rejected.   It quite likely that districts that depend on one of the more tenuous connections will score badly.

While you have advocated a bright line test, I don't think it is measuring what we want it to (i.e. if the value of the test is false, the two counties shall not be directly connected in a district).

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At that stage, we will either be using townships, virtual townships, or county fragments.  Those will be the nodes.

We are defining relationships between counties.  Where the people in a county are concentrated is an important characteristic of that relationship, particularly when we are defining relationships that help us create equal-population districts.   Ultimately we are determining which people should be placed in the same district.

[jimrtex]

I've been on both the highway and passenger train over the bay between these counties. It is a solid link and should be included IMO. Ottawa county does raise some questions about nodes. The urban area from Toledo sends a couple of tentacles into the western edge, but the population in them is less than in the county seat of Port Clinton. Port Clinton is an urban cluster as opposed to an urbanized area, so I wonder if that needs to be included in the definition?

I intentionally used "urban area".   The census bureau initially defined "urban" as being in a place with a population above 2500, and rural as anything else.   After WW II, they started defining "urbanized areas", which were cities above 50,000 and adjacent densely populated areas, both incorporated and unincorporated.

Beginning in 2000, the Census Bureau began defining urban population based on settlement patterns, irrespective of places.  They started with either census tracts of less than 3 square miles with 1000 people or more per square mile, or census blocks with 1000 people or per square mile, and then augment that with adjacent areas with 500 people or more per square mile.

Any such area with over 2500 persons is classified as an "urban area" and the population as urban.  Any "urban area" with a population above 50,000 is an "urbanized area", and between 2500 and 50,000 an "urban cluster".   This maintains some consistency with past definitions of "urban" and "urbanized area".   "urban area" and "urban cluster" are newly defined concepts.

"Core-based statistical areas" are groups of counties based on urban areas of greater than 10,000 and commuting patterns.  CBSA are classified as "metropolitan statistical areas" or "micropolitan statistical areas" based on whether the largest core population is an urbanized area or an urban cluster.   Micropolitan statistical areas are new for 2000.

Port Clinton Urban Cluster is the largest urban area in Ottawa County.  The portion of the Toledo Urbanized Area that is in Ottawa County, actually ranks 4th in population, behind Port Clinton, Genoa, and Oak Harbor.   So Port Clinton would be the population center for Ottawa County.

The portion of the Toledo Urbanized Area in Wood County is larger than Bowling Green Urban Cluster, so Perrysburg would be the population center for Wood County.   Note: Toledo UA is 42% of the county vs. 24% for Bowling Green UC, so Perrysburg is representing the entire spillover from Lucas County.

Ottawa County is part of the Toledo Metropolitan Statistical Area, which would be based on commuters from Ottawa County into both Lucas and Wood Counties.  This prevents it from being the Port Clinton Micropolitan Area.

A curiosity is that the new definitions lifted Sandusky Ohio (Huron County) to Metropolitan Statistical Area status.  Sandusky city has around 25,000 so was never large enough to have an urbanized area or a metropolitan area.   But the urban area just tops 50,000 so it is classified as an Urbanized Area, and the core of a Metropolitan Statistical Area.

[muon2]

It is less subjective than you think.  I had mentioned before a test for near-point connectivity, where the gap across the boundary is compared to the circumference of a circle that has an area of the smaller county:

ratio = gap_length / (2 * sqrt (pi * smaller_area)).

I suggested 5%, unless there was good connectivity, and perhaps also local sentiment. 

These are the reasons I like the bright line test with an option for local override. This builds soft measures into the rule in a way that defeats the purpose of the constraints.

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The Benton-Walla Walla link is a hard sell. Gerrymandered districts often use crossing of major bodies of water (ie their own census block at times) without the benefit of a bridge, and the IL House has some examples. I really don't want to go there. This also opens up similar impassable mountain borders with a road just beyond the county line (eg Merced-San Benito using Pacheco Pass through Santa Clara). In the discussions on CA it was pretty clear that there had to be a real road link directly between the counties, and even then that was insufficient for some of the natives.

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This is where it seems arbitrary. Lincoln-Okanogan is OK, but it uses the same path that should work for Grant-Okanogan though Coulee Dam. And if either of those is OK, then I still find Columbia-Franklin at least as compelling. I think your method looks too much at the shortest path between centers that are far apart no matter how one draws it. My route from Dayton to Pasco is shorter (1h54 on MapQuest) than either of the aforementioned connections through Coulee Dam (2h9 and 2h38). Convenience by time becomes too subjective at some point for my taste, since the goal is connectivity.

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We agree here, but the path of 24 along the county line shows the type road that needs care. If 260 continued west along the local road and linked up with 24 SW of Othello I'd have a link in my system, but technically it only acts within the two counties on the eastbound side of the road. When I go to connections at the sub-county level I find it useful to allow this as a connecting road, but I'll raise the question as a what if here.

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At that stage, we will either be using townships, virtual townships, or county fragments.  Those will be the nodes.
[/quote]
I think this is a semantic distinction. I'm using the definition of node to identify the representative point within a county used for determining connectivity. It is as you note it is really the county from a graph theoretical perspective, but knowing how rules are constructed I find it handier to define the county's representative member as the node. If you like I can call one the node and the other the vertex as both are used to mean the same thing in the context of graphs.

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We agree here, but my goal is also to put sufficient constraints on the map makers and approving bodies that gaming the system becomes hard, but there is still a degree of flexibility for local choice.

[jimrtex]

These are the reasons I like the bright line test with an option for local override. This builds soft measures into the rule in a way that defeats the purpose of the constraints.

What do you intend to be the purpose of the constraints.

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The concern about Pacheco Pass was likely self-serving.   San Benito is not in the Central Valley, and usually gets lumped in with the Central Coast, particularly the Monterey Bay area, though more the Salinas Valley than the coast itself.   But because of the relative sizes of Santa Clara and San Jose is now part of the SF Bay Metropolitan Area (small population within a long commute of big city makes an exurb).

Because of its size, San Benito may get stuck with a lot of different areas.  It may make the slice-up of the Central Valley a little different, or it may help in creating a Hispanic majority district.  It's being used.

So if you want San Benito to be placed with Monterey and Santa Cruz so that maybe Sam Farr's CD changes as little as possible, you add the rationalization about Pacheco Pass. 

If there were a true principle involved, the commission would not have included San Benito with a Central Valley senate district, where the senator has to cross through a corner of Santa Clara County to get to the two regions of the district.

In practice, two congressional districts fit particularly well on the Central Coast, and even permit use of the Monterey-SLO line, and you can throw in something about Pacheco Pass as additional justification.   But because senate districts are about 1/3 larger, you can only get 1.5 senate districts.   So you center it further south, and distribute the other 350,000 persons on the ends into other districts.   San Benito is probably quite happy not to be included in a senate district that includes a chunk of Santa Clara County that they must traverse to visit the rest of their senatorial district.

[muon2]

These are the reasons I like the bright line test with an option for local override. This builds soft measures into the rule in a way that defeats the purpose of the constraints.

What do you intend to be the purpose of the constraints.

I contend that any commission is inherently biased. The bias may not be overtly biased, but many choices on what constitutes a COI for a commission will correlate to a partisan bias, as my lengthy discussions with Torie on CA followed by analysis of reasonable alternatives can show. As such, I think the public's best defense is to let the biases hang out there, but put reasonably firm constraints such that it's hard to move the partisan needle too far from a "fair map". That drives my view that the rules should be tight, but explicitly identify where local input would be appropriate.

That local input could be though a large representative assembly of counties like you have described or by a typical state commission. However, I would require that those exceptions be established before the actual data is released by the Census. I've watched "rules" crafted after the fact to justify what was in fact a partisan decision. By forcing rules ahead of the data it's much harder to know how a rule would help or hurt a political cause. Yet upfront constraints can embody widely recognized goals for the state, before all their political ramifications are known.

[TJ in Oregon]

I'm a few days late here, but as an Erie County native, Erie and Ottawa Counties should definitely be considered contiguous. Over the Edison Bridge Port Clinton is a mere 15 minute drive and one made fairly often. In the Sandusky area, Ohio Route 2 is a major highway and not a random country road.

Also, Erie and Ottawa Counties share the Lake Erie Islands, which would make it even weirder to say Kelley's Island (in Erie County) and South Bass Island (in Ottawa County) couldn't be in the same district unless it included Fremont.

A curiosity is that the new definitions lifted Sandusky Ohio (Huron County) to Metropolitan Statistical Area status.  Sandusky city has around 25,000 so was never large enough to have an urbanized area or a metropolitan area.   But the urban area just tops 50,000 so it is classified as an Urbanized Area, and the core of a Metropolitan Statistical Area.

Sandusky is in Erie County, not Huron County (or Sandusky County). To make it even more confusing, Huron, Ohio isn't in Huron County either. They certainly didn't make things simple when naming these places

[jimrtex]

Sandusky is in Erie County, not Huron County (or Sandusky County). To make it even more confusing, Huron, Ohio isn't in Huron County either. They certainly didn't make things simple when naming these places

You're right.  I was making such an effort to point out that Sandusky was not in Sandusky County.

Tyler, Houston, Austin, Jefferson, Rusk, Henderson, Sherman, Cameron, Crockett, Bowie, Pecos, Johnson City, and Colorado City, Texas are not in the counties of the same name, and in most cases nowhere each other.

[jimrtex]

The Whitman-Lincoln and Lincoln-Okanogan links have direct transportation links.  It is irrelevant whether then Onak-Davenport route skips across the corner of another county.

The Whitman-Douglas is slightly circuitous, but is an alternative route on Google Maps.  I am willing to make concessions for crossings of a major river that has a series of dams.

This is where it seems arbitrary. Lincoln-Okanogan is OK, but it uses the same path that should work for Grant-Okanogan though Coulee Dam. And if either of those is OK, then I still find Columbia-Franklin at least as compelling. I think your method looks too much at the shortest path between centers that are far apart no matter how one draws it. My route from Dayton to Pasco is shorter (1h54 on MapQuest) than either of the aforementioned connections through Coulee Dam (2h9 and 2h38). Convenience by time becomes too subjective at some point for my taste, since the goal is connectivity.

You have to consider scale.   If we take the square root of the areas of the two counties and add them together, and then add them together, the ratio between the two is 1.85.  This is equivalent to converting the counties to adjacent squares or circles and placing the population centers at the center of the square or circle.  It provides a scaling factor for travel distance.

Omak High School plays league games against schools as far south as Quincy (Grant County), so a journey between Davenport and Omak is not something out of the realm of possibility as being considered a visit to a neighboring county.

The great circling route between Pasco and Dayton is much longer than the direct routes, which are almost entirely in Walla Walla County (the southern alternative goes through city of Walla Walla).   Forcing a route across the corner between Franklin and Columbia gives a route that heads north towards Othello or Spokane, then east toward Pullman, and finally south towards Dayton.

Between Moses Lake and Omak, the Grand Coulee route is not horribly worse than the direct route across Douglas County, and I can see redistricting panel members from Grant County might accept a joining with Okanogan, without use of Douglas or Lincoln counties, especially if they considered the Grand Coulee to "belong to them" based on how the the county line was drawn.   But if the boundary had been drawn down the Grand Coulee, it might be point connectivity.

The route between Omak and Davenport is very straight considering the terrain, it goes nowhere close to Republic or Moses Lake.  That it has a tiny segment through Grant County does not cause it to not to be a direct route.   The length of the border relative to the size of the smaller county is equivalent to a 3.5-mile border for a 30x30  mile square county.  Somewhat more than a jog.

What we are seeking is whether two counties have the property of join-ability: whether they can be joined in the same district without inclusion of intermediate counties.  At a minimum the counties must be adjacent.

But in some cases, adjacency is not sufficient.  Clearly, point adjacency is not.  And use of near point adjacency may result in decidedly non-compact, and convoluted districts.

There should also be some interaction between the people of the two counties.  Under the American ideal of representative government, legislators are representative of their district.  If the district is comprised of isolated populations, no one can be said to be representative of the whole.  In addition, legislators can not represent the interests of the two counties if they have nothing in common.

If two apartments share an interior wall, but have exterior exits on opposite sides of the building, there may be no interaction between the tenants.   They aren't neighbors in any meaningful sense.  

If there is no direct, regular way for people to go between two counties, particularly areas where the population is concentrated there may be little interaction between the people of the counties.  

Definition: Join-ability requires non-trivial adjacency and a direct passenger transportation route between the counties.

Point-connectivity is considered trivial, as may be near-point connectivity.  A heuristic for near-point connectivity would be if it was not immediately obvious from a state county-outline map whether two counties shared a boundary (examples Okanogan-Grant or Columbia-Franklin).   Tougher to judge are cases like Douglas-Kittitas, Grant-Franklin, or Lincoln-Okonagan.

A measure of relative adjacency is the ratio of the distance between the end-points of the two-county border and two times the square root of pi times the area of the smaller county.   This is equivalent to comparing the length of the border gap, to the circumference of a circle with the same area.  A square county which abutted another county along one whole side would have an adjacency of 28.2%.

A square county that was 30x30 miles square with an adjacency of 5%, would share 5.3 miles along its northern border with a county that was offset 5.3 miles or almost a township.  Such a county might well be considered a neighbor.  An adjacency of 1% would mean a border less than 1 mile, with only the county surveyor aware of the other county.  When the adjacency is less than 5%, there should be clear evidence of other connections with the other county.

A direct transportation route permits the people of the county to easily move back and forth, either for commuting or commerce, and indicates that the border is not a barrier, or of trivial adjacency.   The route can be either by highway, or a bridge or ferry connecting counties across bodies of water.  When the route is by ferry, the relative adjacency may be of negligible importance.  Water boundaries may be quite arbitrary and don't reflect where people live.  In a sense, it is the ferry route that creates the point of contact, and unlike point adjacency on land, does not indicate the intersection of 4 or more counties.

A direct transportation route should be non-seasonal (ruling out use of mountain passes that are seasonally closed in winter, or seasonal ferries that are more likely used by tourists).   The transportation link should be between the population centers of the counties, which better reflect where people actually live.  These population centers will necessarily be served by the transportation network.

A direct route should be straightforward, and not be significantly dependent on intervening counties.   The route need not necessarily cross the border between the counties, but should be fairly close.   The direct route is not defining the precise path of the district, but rather indicating a relationship between the people who live in the counties and would share a representative if placed in the same district.

A direct route may cross other counties, particularly near the corner or along an edge (if a river is a border, it is not unusual to have a highway along one side or the other, and perhaps crossing back and forth).    A direct route may travel through adjacent states.  But a direct route should not travel for long distances across other counties, nor pass through or near the population centers of other counties.  These would indicate that the route is indirect.

A direct route should not be circuitous.  It should be relatively short, but need not be the shortest in either distance or time.  In some cases an indirect route utilizing interstate highways can be faster, due to their straighter alignment, higher speed limits, and absence of traffic lights.  Consideration should be given to reasonable alternatives that are of similar distance that utilize US and state highways, or similar designations (Farmer Market roads in Texas for example).  A direct route need not be "the best route", but should be a reasonable alternative.

Direct route would permit a representative to travel about a district to meet his constituents without encountering an excessive number of persons who were not.

A better sense of what a direct route is may be given by what it means for there not to be a direct route.  If you ask a local how to get from A to B, and he tells you, "you can't get there from here" or "you go to C and they'll tell you how to get to B", there is not a direct route.

There may well be subjective judgement in determining whether there is a direct route.  Join-ability should be defined before the redistricting process begins, preferably by persons not intimately interested in that process.  Otherwise, the real meaning of "It is hard to go to County B" is "The only reason I'd go to County B is to spit on Representative Bloggs".

That two counties are join-able does not mean that there is a preference to do so.  Absence of join-ability does not mean two counties might not be placed in the same district.  It merely means that intermediate counties must be included.  Some "mistakes" in determining join-ability will likely have little effect on the quality of the final map.

Join-ability may be represented as a graph, with counties (abstract, as opposed to physical limits) serving as the nodes or vertices, and join-ability relationship serving as the links, connections, or edges.

[jimrtex]

Rather than placing hard restrictions on which counties are joined or not joined, we can provide weights to the connections of our graph which indicate policy preferences that we wish to reward.   Rather than measuring erosity, the number of links that are severed by district boundaries; we would measure connectivity, the weighted number of links that are included within districts.

For example, the following weights certain connections both positively, to encourage their use, and negatively, to discourage their use.



Routes that are somewhat circuitous:

Benton-Walla Walla.  The route south via I-82 quickly gets one to Umatilla, Oregon, but then there is still a significant distance to Walla Walla by US highway.  There are portions of the Benton County where the southern route is direct, but they are far from the population which is highly concentrated in the Kennewick-Richland area.   It would not be horrible to include Benton and Walla Walla in a district without Franklin, but it would be better to include it.

Benton-Grant.  The route between Kennewick and Moses Lake via Washington 240 and I-90, does cross a significant boundary between the two counties, it is quite a bit longer (38%) than the route straight north through Pasco and Othello.  Again it would not be horrible to link Benton with its neighbor to the north, but this is to some extent bypassing other population centers, which are on the same side of the Columbia as Grant.

Yakima- Grant.  Both routes are somewhat circuitous.  The southern route which crosses the Columbia just east if the Yakima-Benton line, is 38% slower, and 16% longer and has stretches that are heading south and west, when the object is to go northeast.  The northern route via I-82 and I-90 basically goes north and then east, rather than northeast, and is not direct because of the substantial dependence on Kittitas, thought it narrowly misses Ellenburg.   If there were a relationship between Yakima and Grant, a highway would have been developed to connect the two; alternatively if there were a convenient route, a stronger relationship would have developed.  In a sense, the two are corner connected, without a true diagonal route.

Lewis-Pierce.  There is a 36-mile boundary between the two, but it is quite remote from the population centers.  The route between Centralia and Tacoma via Washington 508 and Washington 7 is 103% longer, and 170% more time consuming than the route up I-5 through Olympia and Thurston County.

The four connections in green show counties where the largest urban area in the linked counties crosses the county boundary.   Urban areas are based on continuous dense population (greater than 500 persons per square mile).   This level of development blurs the county lines, and indicates a strong community of interest, with significant inter-county interaction on a daily basis.

Snohomish-King-Pierce.   The Seattle Urbanized Area stretches along the east side of Puget Sound from Everett through Seattle and King County, past Tacoma, and barely into Kitsap County.  Bremerton Urbanized Area is by far the largest Urban Area in Kitsap County, so the links to Kitsap County are not enhanced.

Chelan-Douglas.  The Wenatchee Urbaniized Area contains 73% of the Douglas population and 54% of the Chelan population.

Benton-Franklin.  The Kennewick-Pasco Urbanized Area contains 83% of the Benton population and 81% of the Franklin population.   A tiny portion extends into Walla Walla County, but is 1/27 the population of the Walla Walla urbanized area that is in the county (it extends into Oregon).

Another possibility would be to deprecate longer transportation routes.  If routes greater than 2 hours were deprecated, the Stevens Pass and White Pass routes would be devalued, encouraging use of Snoqualmie Pass and the Columbia Gorge for linking east and west.  This standard would also reduce the value of the Klickitat-Benton route between White Salmon and Kennewick, and the Franklin-Whitman route between Pasco and Pullman.  In the latter case you have two panhandles end-to-end, and a route that is circular as it tries to avoid getting too close to the Snake River.

It might be reasonable to deprecate links where the adjacency is relatively low.  Rather than forbidding use of such pairs of counties, their use would be discouraged.

[muon2]

Direct route would permit a representative to travel about a district to meet his constituents without encountering an excessive number of persons who were not.

A better sense of what a direct route is may be given by what it means for there not to be a direct route.  If you ask a local how to get from A to B, and he tells you, "you can't get there from here" or "you go to C and they'll tell you how to get to B", there is not a direct route.

There may well be subjective judgement in determining whether there is a direct route.  Join-ability should be defined before the redistricting process begins, preferably by persons not intimately interested in that process.  Otherwise, the real meaning of "It is hard to go to County B" is "The only reason I'd go to County B is to spit on Representative Bloggs".

That two counties are join-able does not mean that there is a preference to do so.  Absence of join-ability does not mean two counties might not be placed in the same district.  It merely means that intermediate counties must be included.  Some "mistakes" in determining join-ability will likely have little effect on the quality of the final map.

Join-ability may be represented as a graph, with counties (abstract, as opposed to physical limits) serving as the nodes or vertices, and join-ability relationship serving as the links, connections, or edges.

This statement, the preceding numerical basis, and the detailed analysis of specific links that follows is exactly what I had in mind for a state commission to do. It takes a fair amount of detailed local knowledge beyond what many mappers would have. You've made a set of reasonable choices based on a sound principle, but another reasonable panel might have some slight differences in conclusion. My goal is to constrain the mappers away from gerrymandered districts based on personal bias, and if a local determination of what makes them more representative is available then I see that as a plus.

This is why I would advocate my definition as a starting point. It is simple and any mapper working from any platform can apply it without local knowledge. If a state wants to adopt a system based on this approach then they should make a determination if a set of local changes based on a rational principle should supersede the simpler definition in specific instances. The determination should be made in advance of the release of any data used for the map so that all mappers are aware of the special rules for that state. The mappers would get a simple list of exceptions along with the basic rule.

Rather than placing hard restrictions on which counties are joined or not joined, we can provide weights to the connections of our graph which indicate policy preferences that we wish to reward.   Rather than measuring erosity, the number of links that are severed by district boundaries; we would measure connectivity, the weighted number of links that are included within districts.

I would avoid consideration of different types of links for the same reason that I would avoid one set of links for connectivity and another for erosity. If there is a public submission of maps, which I think is desirable whether as a contest or not, the distinction of link types is the type of information that is likely to confuse, cause errors with the well-meaning, and be gamed by those with expertise. I base this on my years of teaching science which often involves precise and subtle differences between physical concepts.

Your idea about measuring connectivity rather than erosity is one that I have also thought of and am still considering. Connectivity has the advantage of being a quantity where a larger number is better. The main weakness I'm trying to overcome involves comparing to regional plans that differ in the number of regions. At the level of regions, the mean erosity can stay fairly independent of the number of regions, but the mean connectivity always decreases as the regions increase. There's a secondary issue with split counties as one moves to the district plan, but its resolution depends on the regional determination.

[jimrtex]

Direct route would permit a representative to travel about a district to meet his constituents without encountering an excessive number of persons who were not.

A better sense of what a direct route is may be given by what it means for there not to be a direct route.  If you ask a local how to get from A to B, and he tells you, "you can't get there from here" or "you go to C and they'll tell you how to get to B", there is not a direct route.

There may well be subjective judgement in determining whether there is a direct route.  Join-ability should be defined before the redistricting process begins, preferably by persons not intimately interested in that process.  Otherwise, the real meaning of "It is hard to go to County B" is "The only reason I'd go to County B is to spit on Representative Bloggs".

That two counties are join-able does not mean that there is a preference to do so.  Absence of join-ability does not mean two counties might not be placed in the same district.  It merely means that intermediate counties must be included.  Some "mistakes" in determining join-ability will likely have little effect on the quality of the final map.

Join-ability may be represented as a graph, with counties (abstract, as opposed to physical limits) serving as the nodes or vertices, and join-ability relationship serving as the links, connections, or edges.

This statement, the preceding numerical basis, and the detailed analysis of specific links that follows is exactly what I had in mind for a state commission to do. It takes a fair amount of detailed local knowledge beyond what many mappers would have. You've made a set of reasonable choices based on a sound principle, but another reasonable panel might have some slight differences in conclusion. My goal is to constrain the mappers away from gerrymandered districts based on personal bias, and if a local determination of what makes them more representative is available then I see that as a plus.

This is why I would advocate my definition as a starting point. It is simple and any mapper working from any platform can apply it without local knowledge. If a state wants to adopt a system based on this approach then they should make a determination if a set of local changes based on a rational principle should supersede the simpler definition in specific instances. The determination should be made in advance of the release of any data used for the map so that all mappers are aware of the special rules for that state. The mappers would get a simple list of exceptions along with the basic rule.

I am not suggesting that those submitting maps would define the join-ability relationship for a  state.   Here define simply means "King Joins Kittitas = TRUE" and "King Joins Chelan = FALSE".

I am playing multiple roles: (1) defining the redistricting process; (2) the role of some central authority in defining the constraints on maps; (3) the role of local authorities and interested individuals commenting on the proposed constraints; (4) submitting a plan for consideration; etc.

If a state were to adopt our redistricting process, the initial stage is to join counties together into regions that form a statewide plan.  There are restrictions on which counties may be joined together, which must be complied with before we begin to even examine the other characteristics of the regions in the proposed plans - such as population equity.

But there is a pre-initial stage where some central authority defines the join-ability relationship for the state.   What I am trying to do is present the considerations that this central authority might consider, and trying to explain join-ability in conceptual terms.   If we call join-ability, "connectivity", and overstress the role of the highway connections, there is a risk in misunderstanding the concept and how it is being used.  That is why I don't like your simple rule.  In my opinion, it produces an inaccurate representation of the concept of join-ability, and could place unwarranted constraints on maps.  If a simple rule is used, I'd probably prefer simple adjacency.

Portions of the initial stages of defining join-ability can be automated.  I was using the census bureau adjacency files, as well as their urban area-county relationship files.  The adjacency measure could be calculated using census files.  I used a GIS tool to determine the length of the boundary gap, but that could be automated.   Generation of the initial set of possible transportation routes could be automated.

Rather than placing hard restrictions on which counties are joined or not joined, we can provide weights to the connections of our graph which indicate policy preferences that we wish to reward.   Rather than measuring erosity, the number of links that are severed by district boundaries; we would measure connectivity, the weighted number of links that are included within districts.

I would avoid consideration of different types of links for the same reason that I would avoid one set of links for connectivity and another for erosity. If there is a public submission of maps, which I think is desirable whether as a contest or not, the distinction of link types is the type of information that is likely to confuse, cause errors with the well-meaning, and be gamed by those with expertise. I base this on my years of teaching science which often involves precise and subtle differences between physical concepts.

There are not different types of links.  There are weightings of the links.  In my scheme, the blue (urban area) links might be weighted as 3; the green (ordinary neighboring county) links as 1; and the red (circuitous transportation routes between reasonably adjacent counties) links as 0.  My map may be confusing because it was illustrating how the join-ability relationship was developed.

A final combined map/graph would eliminate the fine red lines for adjacent but non-joinable counties, and use double yellow lines to indicate non-passable borders.  The links would be shown using curves that cross the actual county boundary, and could use thickness to indicate the weighting.

Your idea about measuring connectivity rather than erosity is one that I have also thought of and am still considering. Connectivity has the advantage of being a quantity where a larger number is better. The main weakness I'm trying to overcome involves comparing to regional plans that differ in the number of regions. At the level of regions, the mean erosity can stay fairly independent of the number of regions, but the mean connectivity always decreases as the regions increase. There's a secondary issue with split counties as one moves to the district plan, but its resolution depends on the regional determination.

I would so severely discourage plans with fewer regions that it doesn't matter.

[muon2]

This statement, the preceding numerical basis, and the detailed analysis of specific links that follows is exactly what I had in mind for a state commission to do. It takes a fair amount of detailed local knowledge beyond what many mappers would have. You've made a set of reasonable choices based on a sound principle, but another reasonable panel might have some slight differences in conclusion. My goal is to constrain the mappers away from gerrymandered districts based on personal bias, and if a local determination of what makes them more representative is available then I see that as a plus.

This is why I would advocate my definition as a starting point. It is simple and any mapper working from any platform can apply it without local knowledge. If a state wants to adopt a system based on this approach then they should make a determination if a set of local changes based on a rational principle should supersede the simpler definition in specific instances. The determination should be made in advance of the release of any data used for the map so that all mappers are aware of the special rules for that state. The mappers would get a simple list of exceptions along with the basic rule.

I am playing multiple roles: (1) defining the redistricting process; (2) the role of some central authority in defining the constraints on maps; (3) the role of local authorities and interested individuals commenting on the proposed constraints; (4) submitting a plan for consideration; etc.

This is certainly consistent given the nature of the thread. However, I'm much more interested in item (1). I have two goals in mind for number (1). One is to be generally applicable to all states (1A). The other is to be easily accessible to members of the public who wish to suggest maps (1B).

(1A) The redistricting definitions should be generally applicable to all states. One way to recognize some of the different needs of the states is to make a general framework independent of any specific state, then provide clear hooks on the framework where a state can provide modifications for its needs. I would equate this to the process of municipal zoning. A city will have a set of ordinances that define the regulations for each property based on its classification. there is also a process for determining variances to the regulations, that must be due to circumstances unique to a given property. There is also a process by which a city council can get input from interested parties and make changes to the zoning map or regulations. I would equate my interest to creating a generic zoning ordinance. You also raise many good ideas that would be equivalent to the process for granting variances or changing the ordinance. Just as in most municipal codes, I would have that information in a separate section than the general regulations themselves.

(1B) The redistricting definitions should be easily accessible to members of the public who wish to suggest maps. One problem I observed with public input to redistricting this cycle was that the public wanted to share ideas on a simple basis, but the state had rules that only experts could reasonably follow. In a state like IA, that's fine because only their legislative bureau has to follow the statute to produce maps for the legislature to approve. In Illinois I saw maps produced from all platforms including hand-drawn lines with a table of numbers. I think a minimal level of software use is OK, so that files can be easily shared. However, I think that software much beyond DRA should not be necessary. As we've seen on this site, that software has produced a lot of interesting map ideas. We also saw in the OH competition that relatively few competitors really understood the nuances of the compactness algorithm. County fragments were easy to see and count, but a Roeck test is not without a full GIS program.

[muon2]

Your idea about measuring connectivity rather than erosity is one that I have also thought of and am still considering. Connectivity has the advantage of being a quantity where a larger number is better. The main weakness I'm trying to overcome involves comparing to regional plans that differ in the number of regions. At the level of regions, the mean erosity can stay fairly independent of the number of regions, but the mean connectivity always decreases as the regions increase. There's a secondary issue with split counties as one moves to the district plan, but its resolution depends on the regional determination.

I would so severely discourage plans with fewer regions that it doesn't matter.

Region count translates directly into the number of county splits (districts - regions = splits). Your statement implies that minimizing county splits is superior to all other criteria assuming populations are equal enough. I proposed something like that for CA and it generated a lot of debate. That led to the conclusion that there needed to be other factors that could be weighed against county splits. In a state with 53 CDs and 58 counties there are going to be lots of splits. The increase of one or two additional splits if it can reduce other undesirable qualities like erosity was worth pursuing.

[Torie]

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.

[muon2]

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.

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.

[jimrtex]

(1B) The redistricting definitions should be easily accessible to members of the public who wish to suggest maps. One problem I observed with public input to redistricting this cycle was that the public wanted to share ideas on a simple basis, but the state had rules that only experts could reasonably follow. In a state like IA, that's fine because only their legislative bureau has to follow the statute to produce maps for the legislature to approve. In Illinois I saw maps produced from all platforms including hand-drawn lines with a table of numbers. I think a minimal level of software use is OK, so that files can be easily shared. However, I think that software much beyond DRA should not be necessary. As we've seen on this site, that software has produced a lot of interesting map ideas. We also saw in the OH competition that relatively few competitors really understood the nuances of the compactness algorithm. County fragments were easy to see and count, but a Roeck test is not without a full GIS program.

In Washington, the public (or at least the amateur map drawers) might be presented with a map like this.



In addition, there might be a browser-based computer application that would be used to permit persons to create a plan.  It could have a simple interface that would let the user click on a county to add or remove it from a district.  As they did so, it would show the cumulative population of the district, whether it was within the ideal population range, and the weight of the enclosed connections.  As connections were severed by placing the linked counties in different regions, they could be shown in a dimmed color.  Enclosed connections could be shown in a bright color.

The application would produce a file consisting of district-number, county-ID, pairs:

2,53037    (Kittitas County is in district 2).

This would permit 3rd-party applications to produce a plan that could be submitted to the redistricting commission.  There would be a verification/scoring application as well, which would verify inclusion of all counties, that the counties in each district were legally connected, and contained the proper population.

The map (graph) itself could be represented in a file with records of the following form:

county1-ID,county1-name,county2-ID,county2-name,weight,comment

53047,Okanogan,53073,Whatcom,0,"link is via Skagit and closed in winter"
53007,Chelan,53017,Douglas,5,"Wenatchee Urbanized area spans boundary"

Population and boundary files would also be available so that the census data would not have to be directly accessed.

[muon2]

(1B) The redistricting definitions should be easily accessible to members of the public who wish to suggest maps. One problem I observed with public input to redistricting this cycle was that the public wanted to share ideas on a simple basis, but the state had rules that only experts could reasonably follow. In a state like IA, that's fine because only their legislative bureau has to follow the statute to produce maps for the legislature to approve. In Illinois I saw maps produced from all platforms including hand-drawn lines with a table of numbers. I think a minimal level of software use is OK, so that files can be easily shared. However, I think that software much beyond DRA should not be necessary. As we've seen on this site, that software has produced a lot of interesting map ideas. We also saw in the OH competition that relatively few competitors really understood the nuances of the compactness algorithm. County fragments were easy to see and count, but a Roeck test is not without a full GIS program.

In Washington, the public (or at least the amateur map drawers) might be presented with a map like this.



In addition, there might be a browser-based computer application that would be used to permit persons to create a plan.  It could have a simple interface that would let the user click on a county to add or remove it from a district.  As they did so, it would show the cumulative population of the district, whether it was within the ideal population range, and the weight of the enclosed connections.  As connections were severed by placing the linked counties in different regions, they could be shown in a dimmed color.  Enclosed connections could be shown in a bright color.

The application would produce a file consisting of district-number, county-ID, pairs:

2,53037    (Kittitas County is in district 2).

This would permit 3rd-party applications to produce a plan that could be submitted to the redistricting commission.  There would be a verification/scoring application as well, which would verify inclusion of all counties, that the counties in each district were legally connected, and contained the proper population.

The map (graph) itself could be represented in a file with records of the following form:

county1-ID,county1-name,county2-ID,county2-name,weight,comment

53047,Okanogan,53073,Whatcom,0,"link is via Skagit and closed in winter"
53007,Chelan,53017,Douglas,5,"Wenatchee Urbanized area spans boundary"

Population and boundary files would also be available so that the census data would not have to be directly accessed.

The browser-based approach is very much what I was thinking. There are a number of software choices that could be used for implementation. It's not unlike the electoral college calculator in that respect.

[jimrtex]

In Washington, the public (or at least the amateur map drawers) might be presented with a map like this.

This is one possible entry.



I believe this is best possible east/west split, that creates two eastern whole county districts, and avoids splitting any eastern counties.   A second map will illustrate an alternative split of the eastern part of the state.

Other combinations are possible - for example Okanogan and Kittitas are triviably swappable.  There is also an extremely convoluted map that ends up Adams County, but has extremely good equality.

I tried splitting along the Snohomish-King line, but could not find a nice region in the northwest.  The district containing Clark County must include a split county.  My ordinary preference would be to split a more populous county (eg Clark) but that would result in two districts extending east of the Cascades in a very significant fashion, with only one wholly eastern district.

Thus the large central region includes the trio of must-split counties: Snohomish, King, and Pierce, and extends south to Vancouver.  The region has an implied split of Thurston.

Scoring:

Paciific: 99.93% of ideal.  10 counties.  9 enclosed links.  Weight 27.  A strung out district, but actually fairly concentrated in the outer Puget Sound area.

Southeast: 99.80% of ideal.  8 counties.  10 enclosed links.  Weight 26.  A strong core of Tri-Cities and Yakima.  The inclusion of Grant is slightly tenuous.

Northeast: 99.95% of ideal.  9 counties.  14 enclosed links.  Weight 42.  7/10 of the district is in Spokane.

Central: 700.32% of ideal (100.05% per district).  6 enclosed links.  Weight 20.  I defined an enclosed link as one in which both counties could be included within a single district.  This excludes all links involving Snohomish, King, Pierce, and Thurston, which in turn cuts off Kitsap.  The 6 links are: Chelan-Douglas-Kittitas-Chelan; and Lewis-Cowlitz-Clark-Skamania.

One possible division into districts would be:
(1) Most of Snohomish
(2) Remnant of Snohomish + Northern King.
(3) Chelan-Kittitas-Douglas + "Eastern" King
(4) Seattle
(5) Remnant of King + Eastern Pierce
(6) Kitsap+Western Pierce + most of Thurston.
(7) Clark-Cowlitz-Lewis-Skamania + remnant of Thurston.

Total: 39 enclosed links, weight 115.

Region score: 7, 4 regions plus 3 single-district regions.

[jimrtex]

In Washington, the public (or at least the amateur map drawers) might be presented with a map like this.

The rules for map-drawers might state:

Washington has 10 congressional districts.   Since Washington has a population of 6,724,540, each district must ideally have a population of approximately  672,454.   Under federal law a deviation of plus or minus 1% (6,724) is permitted.  Thus, each congressional district must have a population between 665,730 and 679,178.  Variation from the ideal is only permitted if necessary for district lines to coincide with county or municipal boundaries.

Proposed plans should provide for congressional districts that are comprised of whole counties.  Ideally, 10 such districts should be drawn.  But this is impossible in Washington, since 3 counties, King, Pierce, and Snohomish, each have a population greater than that needed for one district and must be split among two or more districts.

So in Washington, proposed plans should include regions comprised of whole counties, with a population equivalent to a whole number of districts (1, 2, 3, etc.).  Regions that have a population equivalent to two or more districts will be divided into districts in subsequent stages of the process.

Counties within a region must be contiguous - that is, each county in a region must be connected to at least one other county in the region, that pair of counties connected to another county in the region, and so on, until all counties are connected.

A county is considered to be connected with another county if they are adjacent (share a boundary) and it is reasonably easy to travel directly between the two counties.  

Most adjacent counties are connected.  But others are not.  For example, Skagit and Okanogan are not considered to be connected, since the North Cascades Highway (SR 20) is closed in winter.  Clallam and San Juan are not considered to be connected since there is not regular, year-round ferry service between the two counties.  Jefferson and Grays Harbor are not considered to be connected because there is not a direct route between the population centers for the two counties (Port Townsend and Aberdeen).  The most direct route passes through Mason County in a substantial and significant manner.  On the other hand, Snohomish and Chelan are considered to be connected since the Stevens Pass route (US 2) is a direct route between Everett and Wenatchee - even though it passes through a corner of King County in the Skykomish area.  This cutting across the corner is considered incidental.

On the attached map, red areas mark county boundaries where the two counties are not considered to be connected, while the green links between the population centers of the counties indicate a connection.  The definition of county connections was developed with the assistance of local officials during 2020.  Counties on opposite sides of a red area may be included in the same district, if other counties are included.  For example, Jefferson and Grays Harbor could be placed in the same region if Mason was also included.

The links between counties are weighted.  Most links are ordinary links, and have a weight of three.  

Links between counties spanned by urban areas (continuous areas of dense settlement defined by the Census Bureau) have a weight of five.   This is to provide an incentive to keeping these areas within the same district.   There are three such county-spanning spanning urban areas in Washington: Seattle urbanized area: Snohomish-King-Pierce; Wenatchee urbanized: Chelan-Douglas; and Kennewick-Pasco urbanized area: Benton-Franklin  

A few links have a weight of one.  These indicate connections which are somewhat circuitous.  For example, Pierce and Lewis have a quite lengthy boundary but it is remote from their population centers of Tacoma and Centralia.  While it is possible to drive between the two counties, most persons would use I-5 through Olympia and Thurston County, and only use the more circuitous route when visiting Mount Rainier.  The lower weighting provides a disincentive to bypass intermediate counties.

Scoring of plans.  A plan must include all counties in a region, and a county may only be in one region.  A regional score is based on the sum of (a) number of regions; (b) number of single-district regions; and (c_ number of single-county regions,

A connectivity score is based on the number of county links enclosed within a region (not severed by its boundaries).  A weighted connectivity score is based on the weight of county links within a region.  More compact regions (more squarish) will tend to have higher connectivity scores, while long snakelike regions will score poorly.

Higher scoring plans will be voted on by a panel of your fellow Washingtonians who will select the plan that is used for the next decade.  That is, the "best" plan is not necessarily the highest scoring plan, but rather a high scoring plan that is most preferred by the citizens of Washington.