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Author Topic: Iowa-style Redistricting: Measuring Erosity  (Read 2840 times)
muon2
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« on: July 05, 2012, 03:00:24 pm »

Compactness is a requirement of many redistricting plans, and generally either bases a measure on squareness or on boundary length. IA uses one of each type of measure, one to minimize the difference between the north-south and east-west dimensions of the districts, and one to minimize the total perimeter of the districts. These measure compactness, but they can fail to address erosity, that is how ragged the edges are.

In describing various standards for assembling counties into a district I suggested that counties should be contiguous only if one could drive between county seats on numbered state or federal roads (or regular ferry service) without going into any other county. Highways along a border count in both counties. This would eliminate counties connected over mountain ranges, largely unpopulated forests, or unbridged rivers, and also eliminate many occurrences where the border of contact was small.

If one counts the number of contiguous county borders that make up a district border then one has a simple measure of erosity of a district. This measure only counts the borders with the state. For a state the sum of those borders divided by two become the measure of the erosity of a plan. The plan measure divides by two since every border appears on two districts.





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« Reply #1 on: July 05, 2012, 03:01:46 pm »

As an example I'm going to use WI. I took a county map and drew lines to show all the connections between counties using my rule above. Edit: There should also be a link from Racine to Waukesha.



Now to apply it, here was a map version that minimized all the district deviations by using a single three-way split of Milwaukee. It's not very pretty and the county erosity is 67. In addition Florence county in the northeast is not connected to the rest of CD 8.

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« Reply #2 on: July 06, 2012, 11:32:46 am »

Now by comparison here is the map put together by traininthedistance. It has an erosity of only 51 compared to 67 for the map above.



I previously posted a modified version of his map to reduce the population deviation and improve the shape of CD 5 and 6. The changes reduced the erosity to 49. So by both population deviation and erosity it is a better plan.



Now to compare to the map in the previous post. That map in the previous post can be characterized by a population range of 673, an average deviation of 195.25, 74 county pieces (72 counties plus 2 extra in Milwaukee), and an erosity of 67. The map immediately above can be characterized by a range of 4623, average deviation of 1035.25, 73 county pieces, and an erosity of 49. It has one fewer fragment but much less erosity in exchange for a wider population range and deviation, though still within the 1% range limitation and 0.5% deviation for microchops.
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« Reply #3 on: July 06, 2012, 07:33:09 pm »
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That seems to work well with reasonably shaped counties, but maybe not so well with erose counties. An example would be Inyo County, and then appending counties to the north and south, which creates a CD which looks erose, and is erose, but might not be erose by your standard. It also does not measure erosity within counties, which obtains for LA County, Cook County, and NYC in particular (do the boroughs in NYC count as counties?).
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« Reply #4 on: July 07, 2012, 10:38:10 am »

That seems to work well with reasonably shaped counties, but maybe not so well with erose counties. An example would be Inyo County, and then appending counties to the north and south, which creates a CD which looks erose, and is erose, but might not be erose by your standard. It also does not measure erosity within counties, which obtains for LA County, Cook County, and NYC in particular (do the boroughs in NYC count as counties?).

If the county is erose, it will still be fine. I'll see if I can get some examples from southern states to show, since they tend to have quite a few strange shaped counties. CA shouldn't be worse than any southern state in that regard. What this can't measure is when a state highway connection shouldn't be used such as in a mountain pass. I haven't worked out a way to discriminate those.

For in-county splits, I am leaning toward the MI rule for township splits. It would provide that the split should not increase the bounding circle size around the district, and if it must it should do so minimally. For microchops into a county I'm content that the microchop be connected by any local road to the other county and not unduly create more municipal splits.
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« Reply #5 on: July 07, 2012, 03:14:13 pm »
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That seems to work well with reasonably shaped counties, but maybe not so well with erose counties. An example would be Inyo County, and then appending counties to the north and south, which creates a CD which looks erose, and is erose, but might not be erose by your standard. It also does not measure erosity within counties, which obtains for LA County, Cook County, and NYC in particular (do the boroughs in NYC count as counties?).

If the county is erose, it will still be fine. I'll see if I can get some examples from southern states to show, since they tend to have quite a few strange shaped counties. CA shouldn't be worse than any southern state in that regard. What this can't measure is when a state highway connection shouldn't be used such as in a mountain pass. I haven't worked out a way to discriminate those.

For in-county splits, I am leaning toward the MI rule for township splits. It would provide that the split should not increase the bounding circle size around the district, and if it must it should do so minimally. For microchops into a county I'm content that the microchop be connected by any local road to the other county and not unduly create more municipal splits.

Well one can create an erose CD within a County, or part of a county, without city or township splits, so some rule may be needed for that, if there is a viable one. Do you remember my action in Oakland County, MI, where CD's wrapped around three sides of Pontiac to pick up the Pubs and keep out the Dems except via a chop of one of the Dem townships?  You also still need a rule for splits within cities, in particular Chicago, LA, and NYC. We are osculating here between erosity and splits, which are not the same thing. I still wonder how this rule would work with the Owens Valley and Inyo county, with an erose county and topographic issues.
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« Reply #6 on: July 07, 2012, 04:20:57 pm »

That seems to work well with reasonably shaped counties, but maybe not so well with erose counties. An example would be Inyo County, and then appending counties to the north and south, which creates a CD which looks erose, and is erose, but might not be erose by your standard. It also does not measure erosity within counties, which obtains for LA County, Cook County, and NYC in particular (do the boroughs in NYC count as counties?).

If the county is erose, it will still be fine. I'll see if I can get some examples from southern states to show, since they tend to have quite a few strange shaped counties. CA shouldn't be worse than any southern state in that regard. What this can't measure is when a state highway connection shouldn't be used such as in a mountain pass. I haven't worked out a way to discriminate those.

For in-county splits, I am leaning toward the MI rule for township splits. It would provide that the split should not increase the bounding circle size around the district, and if it must it should do so minimally. For microchops into a county I'm content that the microchop be connected by any local road to the other county and not unduly create more municipal splits.

Well one can create an erose CD within a County, or part of a county, without city or township splits, so some rule may be needed for that, if there is a viable one. Do you remember my action in Oakland County, MI, where CD's wrapped around three sides of Pontiac to pick up the Pubs and keep out the Dems except via a chop of one of the Dem townships?  You also still need a rule for splits within cities, in particular Chicago, LA, and NYC. We are osculating here between erosity and splits, which are not the same thing. I still wonder how this rule would work with the Owens Valley and Inyo county, with an erose county and topographic issues.

In-county erosity will need its own set of rules, but they are complicated by the different types of county subdivisions that exist. Half the states have well defined subdivision and half don't. Of those that do some have overlapping layers, eg municipalities vs townships in IL.

Since the model I'm working towards is a multiphase process, and the first phase concentrates on whole counties, I need an erosity measure for that step. IA counties look very different than ID counties. Even within a state like OH there's quite a difference in the shape of the northern and southern counties. I observed that standard compactness measures were not working well in the OH competitions since some types favored the straightline counties of the north and others were forgiving of the erose river boundaries of the south.

My model here frees the measure from the type of shapes that are prevalent in the counties. It also allows double duty as a stricter requirement for contiguity than the usual legal definition.
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« Reply #7 on: July 07, 2012, 04:42:29 pm »
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Anyway, for the boring county states, I think your rule is most excellent Muon2. Well done. I of course want it all, and want it now, so thus my comments. 
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« Reply #8 on: July 25, 2012, 12:04:04 am »
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Compactness is a requirement of many redistricting plans, and generally either bases a measure on squareness or on boundary length. IA uses one of each type of measure, one to minimize the difference between the north-south and east-west dimensions of the districts, and one to minimize the total perimeter of the districts. These measure compactness, but they can fail to address erosity, that is how ragged the edges are.

In describing various standards for assembling counties into a district I suggested that counties should be contiguous only if one could drive between county seats on numbered state or federal roads (or regular ferry service) without going into any other county. Highways along a border count in both counties. This would eliminate counties connected over mountain ranges, largely unpopulated forests, or unbridged rivers, and also eliminate many occurrences where the border of contact was small.

If one counts the number of contiguous county borders that make up a district border then one has a simple measure of erosity of a district. This measure only counts the borders with the state. For a state the sum of those borders divided by two become the measure of the erosity of a plan. The plan measure divides by two since every border appears on two districts.

My inclination would be to take the smaller county's area divide by pi, take the square root, and multiply by two times pi (circumference of a circle with equivalent area, and then multiply by some factor, say 5%.   If the distance between the two end points of the boundary is greater than that, they are connected.   And possibly consider local opinion.  I suspect Florence County may consider Marinette County more of a neighbor, even though you have to go through Michigan and Norway to get there.
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« Reply #9 on: November 23, 2012, 11:44:57 am »

WV is an interesting state to test this erosity measurement. There is a wealth of whole county plans submitted to the court during the challenge to the WV maps, and the acknowledgement in SCOTUS's decision that larger population variances are permissible. The state also has plenty of interesting geography to please Torie.

This is the map showing connected counties using the rule that connections exist when one can travel between two county seats only on numbered state or federal highways without entering any other county.



As before, the erosity of a district is measured by the number of connections that are severed by its border to other counties in the state. The total plan erosity adds all the districts and divides by two to avoid double counting.

This is the approved plan:

The plan has a population range of 0.79%. The district erosities are 14, 27, and 13, or a statewide total of 27. However, note that the plan is not contiguous by this measure since there is no state highway connection between Hardy and Pendleton in CD 2.
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« Reply #10 on: November 23, 2012, 12:00:59 pm »

Lewis had a WV plan with a population range of 0.09%.

The erosity is lower than the approved plan with districts at 17, 16 and 13, for a statewide total of 23. However, it also used the Hardy-Pendleton connection which violates contiguity by this measure.

The best plan submitted for population deviation was Cooper 3 with a 0.04% range.

The district erosity is 17, 16 and 23, for a statewide total of 28. This is worse than the Lewis plan or the approved plan, but it doesn't violate contiguity.

Next, I'll post some of the other public submissions with their erosity analysis.
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« Reply #11 on: November 23, 2012, 04:16:28 pm »



The above diagram includes 4 plans referenced in the federal redistricting suit. Cooper was the plaintiff in that suit and filed three plans, initially before the redistricting committee then to the court. The federal case also referenced the Facemire-Snyder plan which is a whole county version of an exact plan filed by Sen. Snyder early in the redistricting process.

Cooper 3: Range 0.04%, Erosity 28 (17, 16, 23).
Cooper 2: Range 0.06%, Erosity 32 (17, 32, 15). CD 2 is discontiguous by this method.
Cooper 1: Range 0.09%, Erosity 28 (22, 19, 15).
Facemire: Range 0.42%, Erosity 21 (17, 12, 13).

Using the Facemire plan as a starting point I reduced the erosity to 20 (19, 9, 12) while the range rose to 0.93%. That plan is the large one in the image above.

One way to use this form of erosity with the range is to look at a Pareto optimal plan. To be Pareto optimal the plan should not be able to be improved in one measure without getting worse in another. By that criteria, both Cooper 1 and 2 fall to Cooper 3 since it has a lower range without making the erosity worse. However, both the Facemire and my reduced erosity plan would be equally valid as Pareto optimal choices within a 1% maximum range limitation.
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« Reply #12 on: November 25, 2012, 10:42:31 am »
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Muon2, how do you get to a count of 9 for your WV-2 CD in your "perfect" map?  I count 6 internal border counties myself. I read this entire thread and your explanation of your method, and my mind came up short. I just could not parse how you got your numbers. I feel like an idiot! Sad

It does seem like the 1% variance rule is alive and well assuming that it is justified to avoid splitting stuff. You must be very happy.  Smiley
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« Reply #13 on: November 25, 2012, 12:42:17 pm »

Muon2, how do you get to a count of 9 for your WV-2 CD in your "perfect" map?  I count 6 internal border counties myself. I read this entire thread and your explanation of your method, and my mind came up short. I just could not parse how you got your numbers. I feel like an idiot! Sad

It does seem like the 1% variance rule is alive and well assuming that it is justified to avoid splitting stuff. You must be very happy.  Smiley

It's not the number of border counties but the number of connecting segments that must be broken to partition the district from the rest of the state. That's why I posted the connectivity map first. CD 2 in the low erosity plan cuts nine of those links. One feature I like in this method of counting is that there is no penalty for separating contiguous counties over a mountain that don't have a highway link, for example between Webster and Pocahontas.

The other interesting feature is that it naturally sets up a Pareto choice between erosity and population range. This can be extended to add a choice related to the number of county splits in state with more larger counties.

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« Reply #14 on: November 25, 2012, 06:07:43 pm »
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Oh, it is driven by where the roads are eh?  How creative. Is that your personal little invention? And if you don't like the result, why just build or remove an inter-county road!  Or upgrade/degrade it from a state highway/county road or something. Tongue

I might add that this is not so much an erosity test, as a communities of interest test, no?
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« Reply #15 on: November 25, 2012, 09:18:12 pm »

Oh, it is driven by where the roads are eh?  How creative. Is that your personal little invention? And if you don't like the result, why just build or remove an inter-county road!  Or upgrade/degrade it from a state highway/county road or something. Tongue

I might add that this is not so much an erosity test, as a communities of interest test, no?

The concept arises from network theory. The counties can be viewed as a network with connections between any two that share borders. One network technique is to prune connections before working with the network as a whole. In graph theory the size of a cut set (eg. the number of broken links) is a relevant parameter that points to the internal compactness of partition compared to the graph as a whole.

In our CA maps, many frequently noted weak connections between counties that really weren't as valid as others. These typically fell into two types: counties with small lengths of near point-contact and others that had a significant natural barrier that should discourage linking. I could try to prune these on a case-by-case basis, but I noticed that in most cases there was no more than a local road providing a link. By restricting links to state and federal highways, the map was generally pruned of those two types of weak connections using a neutral standard that could be uniformly applied.

Communities of interest are generally a squishy subject that are hard to establish in a uniform way. If I've accomplished that in part with my pruning algorithm, then I'll take that as a success. Smiley
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« Reply #16 on: November 25, 2012, 09:57:22 pm »
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I find nothing in the content or your post with which I disagree or question. Well done! Yes, all that "hard science/the maths thing" jargon about links theory that I had already penned in the prose poetry of a lawyer more suitable to the noisomeness of the public square, was noted but ignored with mens rea.  Smiley
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« Reply #17 on: November 28, 2012, 09:21:20 pm »
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Oh, it is driven by where the roads are eh?  How creative. Is that your personal little invention? And if you don't like the result, why just build or remove an inter-county road!  Or upgrade/degrade it from a state highway/county road or something. Tongue

I might add that this is not so much an erosity test, as a communities of interest test, no?
Erosity is a measure of compactness.   Non-compact districts are disfavored because they tend to divide communities of interest, or link distant communities of interest, typically for reasons of political, racial, or incumbent-protection gerrymandering.

Traditional measurements of compactness based on perimeter length tend to disfavor use of boundaries that are coincident with rivers and mountain ranges, even though they often create transportation and communication barriers.  They also have scaling problems, and problems determining aggregate compactness (i.e. we can measure how compact a district is, but how compact is a map?)

1992-1996 congressional map

The districts in west Texas don't look too bad, until you start noticing all the chopped up cities (zoom in on Lubbock).   But that little excursion to pick out the minority parts of Lubbock adds very little to the perimeter or area of TX-13, and a mathematical formula based on the ratio of perimeter to area is fooled, just as much as the eye is.   By requiring whole counties, Muon avoids that problem.  When you consider the amount of population, put all of Lubbock County in one district or the other would require substantial additional changes to re-equalize population.

On the other hand, his method would not notice that Amarillo was sliced down the middle.  Amarillo has grown southward so about half is now in Randall County, with the downtown and minority in Potter County.  The map is attempting to make TX-19 about 95% Republican, and make TX-13 winnable by a Blue Dog Democrat (Bill Sarpalius).

In the first Ohio redistricting contest it made sense to draw a district along the Ohio River which had a low compactness score because of the meanders of the river, but it in effect plastered off that area of the state, permitting "smoother" boundaries.

What Muon in effect has done is defined a unit of area, "typical county area" and a unit of perimeter length "typical county-county boundary length" and uses the ratio of the the length of inter-district boundaries defined by the total area.

By using road-connectivity to determine whether a county-county boundary is counted, it eliminates a lot of corner or near corner boundaries.  A boundary that follows jogs in county boundaries is not erose.   It is just maintaining whole counties.   A district that wraps around a whole county on three sides is probably erose.

It also recognizes real transportation and communication barriers.

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« Reply #18 on: November 29, 2012, 10:21:18 am »




The ferry connections in WA probably need some special rules. For example, the Whatcom-SanJuan connection goes through the waters of Skagit. Should that disqualify it much like a road that briefly goes through a part of another county even if there is no population along that stretch? That's the case with the Snohomish-Chelan link which goes through King.

OTOH there is similar ferry service from Jefferson (Pt Townsend) to San Juan that appears to stay in the waters of those two counties, except when boats might choose to take a more easterly line.
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« Reply #19 on: November 29, 2012, 09:33:35 pm »
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The ferry connections in WA probably need some special rules. For example, the Whatcom-SanJuan connection goes through the waters of Skagit. Should that disqualify it much like a road that briefly goes through a part of another county even if there is no population along that stretch? That's the case with the Snohomish-Chelan link which goes through King.

OTOH there is similar ferry service from Jefferson (Pt Townsend) to San Juan that appears to stay in the waters of those two counties, except when boats might choose to take a more easterly line.
I added the outline map which shows boundary relationships as a triangular mesh.  The links are county seat to county seat and don't necessarily cross the boundaries.  I also fused Benton and Franklin (Tri Cities), Chelan and Douglas (Wenatchee-East Wenatchee) and King and Pierce (Seattle-Tacoma).   I don't recall my reasoning on the last pair.  It could have been something like Everett and Bremerton being separated somewhat from Seattle, even though the suburbs run across the Snohomish-King line just as much as they do King-Pierce.

Stevens Pass links Everett and Wenatchee.  I don't think the NE corner of King is accessible from the rest of the county by any sort of ordinary road.  I'll bet if they need a sheriff, that Snohomish County will send someone up.

The Bellingham to San Juans ferry service by the Washington State Ferry is discontinued.  There is whale watching tour from Bellingham that has a two hour stop in Friday Harbor.  I would thus cut the Whatcom-San Juan link.  I think the only regular service to San Juan is now from Anacortes (which continues across to Victoria, BC.  I don't think there is service from Port Townsend.
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« Reply #20 on: November 30, 2012, 12:22:02 am »




The ferry connections in WA probably need some special rules. For example, the Whatcom-SanJuan connection goes through the waters of Skagit. Should that disqualify it much like a road that briefly goes through a part of another county even if there is no population along that stretch? That's the case with the Snohomish-Chelan link which goes through King.

OTOH there is similar ferry service from Jefferson (Pt Townsend) to San Juan that appears to stay in the waters of those two counties, except when boats might choose to take a more easterly line.
I added the outline map which shows boundary relationships as a triangular mesh.  The links are county seat to county seat and don't necessarily cross the boundaries.  I also fused Benton and Franklin (Tri Cities), Chelan and Douglas (Wenatchee-East Wenatchee) and King and Pierce (Seattle-Tacoma).   I don't recall my reasoning on the last pair.  It could have been something like Everett and Bremerton being separated somewhat from Seattle, even though the suburbs run across the Snohomish-King line just as much as they do King-Pierce.

Stevens Pass links Everett and Wenatchee.  I don't think the NE corner of King is accessible from the rest of the county by any sort of ordinary road.  I'll bet if they need a sheriff, that Snohomish County will send someone up.

The Bellingham to San Juans ferry service by the Washington State Ferry is discontinued.  There is whale watching tour from Bellingham that has a two hour stop in Friday Harbor.  I would thus cut the Whatcom-San Juan link.  I think the only regular service to San Juan is now from Anacortes (which continues across to Victoria, BC.  I don't think there is service from Port Townsend.


The Stevens Pass issue is tricky. I recognize that the 627 people in King along US 2 can't get to any other part of King without leaving the county, but I'm hesitant to split the county unnecessarily if that is needed to link Snohomish and Chelan. Once King is to be split as part of a grouping that includes either of the other two counties then I would insist that it stay attached by road. The problem is that there are lots of instances like this in other states, including flat midwestern ones.

I looked at the WA ferry schedule and it appears that the Bellingham-Friday Harbor boat only does tours. However, the Port Townsend-Friday Harbor does offer one-way passenger fares as part of its regular service. It's not year-round, but many of the mountain passes aren't either. That seems like a connection that should exist unless ferries are restricted to those that can carry vehicles as well as people.

One other connection should be added between Franklin and Columbia. WA 261 crosses the river between the two counties. I doubt it would matter for any whole county map.
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« Reply #21 on: November 30, 2012, 12:07:19 pm »
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What is the definition of a "micro-chop" again?
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« Reply #22 on: November 30, 2012, 03:50:43 pm »

What is the definition of a "micro-chop" again?

I used a micro-chop as a portion of a county whose population was less than 0.5% of the ideal district size. If for example the court ruled against a whole or minimal county split plan based on a 1% maximum range, then use of microchops would bring the plan into exact equality with a minimum of population shifts.
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« Reply #23 on: November 30, 2012, 07:03:16 pm »
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The ferry connections in WA probably need some special rules. For example, the Whatcom-SanJuan connection goes through the waters of Skagit. Should that disqualify it much like a road that briefly goes through a part of another county even if there is no population along that stretch? That's the case with the Snohomish-Chelan link which goes through King.

OTOH there is similar ferry service from Jefferson (Pt Townsend) to San Juan that appears to stay in the waters of those two counties, except when boats might choose to take a more easterly line.
I added the outline map which shows boundary relationships as a triangular mesh.  The links are county seat to county seat and don't necessarily cross the boundaries.  I also fused Benton and Franklin (Tri Cities), Chelan and Douglas (Wenatchee-East Wenatchee) and King and Pierce (Seattle-Tacoma).   I don't recall my reasoning on the last pair.  It could have been something like Everett and Bremerton being separated somewhat from Seattle, even though the suburbs run across the Snohomish-King line just as much as they do King-Pierce.

Stevens Pass links Everett and Wenatchee.  I don't think the NE corner of King is accessible from the rest of the county by any sort of ordinary road.  I'll bet if they need a sheriff, that Snohomish County will send someone up.

The Bellingham to San Juans ferry service by the Washington State Ferry is discontinued.  There is whale watching tour from Bellingham that has a two hour stop in Friday Harbor.  I would thus cut the Whatcom-San Juan link.  I think the only regular service to San Juan is now from Anacortes (which continues across to Victoria, BC.  I don't think there is service from Port Townsend.


The Stevens Pass issue is tricky. I recognize that the 627 people in King along US 2 can't get to any other part of King without leaving the county, but I'm hesitant to split the county unnecessarily if that is needed to link Snohomish and Chelan. Once King is to be split as part of a grouping that includes either of the other two counties then I would insist that it stay attached by road. The problem is that there are lots of instances like this in other states, including flat midwestern ones.

I looked at the WA ferry schedule and it appears that the Bellingham-Friday Harbor boat only does tours. However, the Port Townsend-Friday Harbor does offer one-way passenger fares as part of its regular service. It's not year-round, but many of the mountain passes aren't either. That seems like a connection that should exist unless ferries are restricted to those that can carry vehicles as well as people.

One other connection should be added between Franklin and Columbia. WA 261 crosses the river between the two counties. I doubt it would matter for any whole county map.
The Port Townsend-Friday Harbor whale watching tour has ended for 2012.  I think that if you need anything on the mainland, you take the ferry to Anacortes.   You can drive from Bellingham to Anacortes, and you can take a ferry from Port Townsend to Coupeville and drive to Anacortes.

I would disqualify the connection between Franklin and Columbia as a near-corner touching.  I gave a definition upthread for that.   I am also looking for links between the major population centers.   Pasco to Dayton is on 123 up the Touchet river, and not a circuitous route.

My criteria would be:

(1) A minimally significant boundary;
(2) A direct non-seasonal transportation link between population centers.  The link need not cross the boundary between the two counties, and may also pass through other counties even if it does;
(3) Local sentiment.   This could be either to include a link or exclude a link.

I have updated the maps to remove the Whatcom-San Juan link, and to indicate the Columbia-Franklin link as a physical boundary, but not a significant linkage.

I'm quite willing to include/exclude the folks in Skykomish as part of a Snohomish-Chelan district.   The link is between Monroe and Wenatchee.  Skykomish is not a necessary part of the linkage.

By the way, the Skykomish school district is included in a Skagit-Snohomish-King legislative district.  

LD 39 Washington.
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muon2
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« Reply #24 on: November 30, 2012, 10:07:04 pm »


My criteria would be:

(1) A minimally significant boundary;
(2) A direct non-seasonal transportation link between population centers.  The link need not cross the boundary between the two counties, and may also pass through other counties even if it does;
(3) Local sentiment.   This could be either to include a link or exclude a link.


As Torie well knows my goal is to find proxies for communities of interest that avoid the problems that arise when one selects a panel to judge them on a qualitative basis. This prevents me from using (3) as a rule.

On (1) I would want a firm definition of what is significant. Columbia and Franklin are connected by a bridge over the Snake with a state highway. I understand that the boundary isn't very long, but with proxies there are going to be situations one would normally exclude that get in. In reverse Stevens Pass represents a case where one would normally include it but it gets excluded by the neutral proxy.  I'm willing to accept those few instances of each type because they work effectively in far more cases than not.

On (2) I presume that you are excluding all the mountain passes that have regular seasonal closures, but not those that only close for occasional storm events. Seasonally closed roads knock out the connections between Pierce and Yakima and between Skagit and Okanogan (by similarity with Stevens Pass), which you seem to have consistently done. This seems like a sensible rule, consistent with my sense of proxies.
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