Cube Root Rule Legislative Districts

[jimrtex]

New Hampshire would have a 107 member legislature, with each representative having about 11,500 constituents.  This is one less member than Maine, but New Hampshire is likely to surpass Maine in population for the 2010 census, and thus would have a slightly larger legislature.

The following table is based on Census Bureau 2010 projections.


Maine         108 110
New Hampshire 107 111
Vermont        84  86
Massachusetts 185 188
Rhode Island  101 103
Connecticut   150 152


So instead of New Hampshire increasing the size of districts by 12.1% while keeping the legislature size fixed, or increasing the size of the districts the same and expanding the legislature by 12.1%, the number of legislators would increase by 3.7% and the district size by 8.1%.

Coos is just short of 3 members so adds a couple of towns from Carroll, the remnant of which forms its own district.

1. Coos (3.0)
2. Carroll (3.6)

Grafton is entitled to 7.08 members, and is split in two districts, one following I-93 from Plymouth to Littleton, and the other along the Connecticut River from Lebanon to Haverhill.

3. Grafton East (3.4)
4. Grafton West (Lebanon) (3.8)

Belknap and Sullivan are each entitled to their own district.

5. Belknap (Laconia) (4.8)
6. Sullivan (Claremont) (3.6)

Merrimack (districts 7 to 9) is treated with the rest of southeastern New Hampshire.

Strafford is entitled to 9.72 members, and could conceivably be split into 3 districts, but this would require Rochester and Dover to form most of two districts, and the 3rd district everything else.  Instead, the county is split into two districts, with Rochester and Dover forming the core with about 1/2 the population of their respective districts.

10. Strafford West (Rochester) (5.0)
11. Strafford East (Dover, Durham) (4.8)

Cheshire is entitled to 6.39 members, and thus is split into two small districts.  Keene is centrally located, and so the county must be split nearby.

12. Cheshire North (Keene) (3.4)
13. Cheshire South (3.0)



Merrimack is entitled to 11.79 members and thus forms 3 districts.  Concord could form its own district, while also dividing the more rural west from the towns between Concord and Manchester.  Loudon was included with Concord since it has better connectivity, and it also gives a bit better population balance.

7. Merrimack West (4.2)
8. Concord and Loudon (Concord) (4.0)
9. Merrimack East (Hooksett) (3.8)

Hillsborough is entitled to 32.97 members (30.8% of the entire state).  Both Manchester and Nashua are entitled to two districts, leaving the rest of the county with a population of 16.21 which is formed into 4 districts.  A small district must be formed in the southeast corner to avoid splitting Merrimack town.  This results in two other districts formed from Manchester and Nashua suburbs.  The more rural western district includes Milford for population balance.

14. Hillsborough West (Milford) (4.4)
15. Hillsborough North (Bedford, Goffstown) (4.0)
16. Hillsborough South (Merrimack) (4.2)
17. Hillsborough East (Hudson) (3.6)

Manchester city is entitled to 9.72 members and two districts.  One district is formed from the central part of the city east of the Merrimack River.  About half of the other district is west of the river, and half to the south.

18. Manchester Central (4.6)
19. Manchester West and South (4.8)

Nashua city is entitled to 7.50 members and two districts.  The districts are roughly divided by US 3 (F E Everett Turnpike) with the core of the city in the eastern district along the Merrimack River.

20. Nashua East (3.6)
21. Nashua West (4.0)

Rockingham is entitled to 24.02 members, or from 5 to 7 districts.  Derry and Londonderry can form a large district along the western edge.  If the two were split, Londonderry would have to be part of a district wrapping around Derry.  5 other districts were created, one centered on Portsmouth and the coast, two along the Massachusetts border, and two further north.

22. Rockingham West (3.4)
23. Derry and Londonderry (5.0)
24. Rockingham Southwest (Salem) (3.8)
25. Rockingham South (3.8)
26. Rockingham North (Exeter) (3.6)
27. Rockingham East (Portsmouth, Hampton) (4.4)

[minionofmidas]

What's the Edit?

[Kevinstat]

I probably wouldn't support your idea of fractional representatives in practice, but it's interesting to think about.  I assume you used the 2000 census data at least in Maine because you don't show the town of Centerville in Washington County (which deorganzed sometime after the 2000 census) as part of North Washington UT.  When the 2010 census data comes out I am going to make a 35 Senate district-140 House District plan with each Senate district divided into 4 House Districts.  A constitutional amendment establishing such a size of each chamber in the Legislature hasn't been attempted as far as I can tell, while other more drastic ones (33-99, 35-105, 33-132 and even {27,29,31}-115 (amended to {31,33,35}-131 in committee), plus Unicamerals of 99, 101 and 105 (amended to 151 in committee)) have been (under the present language of Maine's constitution the size of the Senate can be any odd number between 31 and 35 inclusive, while the size of the House is established at 151 and has been since the 1850s I believe).

[Edited to correct the proposed set of Constitutional sizes of the Maine Senate in the original version of a failed Constitutional Resolution to reduce the size of the legislature from {31,33,35} to {27,29,31}, although, from a conversation I had with the bill's lead sponsor who had the bill drafted, I think he meant in his orignal bill for the size of the Senate to be 31 members.]

[jimrtex]

What's the Edit?

I had an extraneous parenthesis.

[jimrtex]

I probably wouldn't support your idea of fractional representatives in practice, but it's interesting to think about.  I assume you used the 2000 census data at least in Maine because you don't show the town of Centerville in Washington County (which deorganzed sometime after the 2000 census) as part of North Washington UT.  When the 2010 census data comes out I am going to make a 35 Senate district-140 House District plan with each Senate district divided into 4 House Districts.  A constitutional amendment establishing such a size of each chamber in the Legislature hasn't been attempted as far as I can tell, while other more drastic ones (33-99, 35-105, 33-132 and even {31, 33, 35}-115 (House size amended to 131 in committee), plus Unicamerals of 99, 101 and 105 (amended to 151 in committee)) have been (under the present language of Maine's constitution the size of the Senate can be any odd number between 31 and 35 inclusive, while the size of the House is established at 151 and has been since the 1850s I believe).

The proposal for a unicameral legislature got further than would be expected given that most legislators were going to measure its impact on them.  So that would explain why the proposed size was increased - and the senators are going to want to think of themselves as something special.  Perhaps the use of joint subject matter committees in Maine would make legislators more amenable since senators sit with representatives in hearings on bills.  It is redundant to have two sets of legislators elected on the same basis to serially consider a bill.

I used 2000 census data.  In states without organized townships, the estimate data is limited.  In another couple of years with 5 years of ACS data, it may be practical to do continuous redistricting.

One advantage of using fractional representation is that districts need not be modified in redistricting.  If a district increases in population of 4.4 to 4.6 representatives, or from 4.6 to 4.4 representatives no adjustment in the districts need be made.  In Maine in those cases where a district had to be extended outside a smaller county, they might need to shift a town or two to keep the size up to a minimum of 3 - though 3 and 5 were also somewhat arbitrary limits.

I was getting ready to work out the draw procedures.  Would it be better to use school children or let the lottery do it?

I was thinking about using the 2008 census estimates to make sure that the districts were still viable, even though a couple of representatives had been added.

[Kevinstat]

While Frankfurt has 93 for a population of 650,000.

That's actually pretty close to the number of member's Frankfurt's (Germany I presume) city county would have under the cube root rule (86.62, which rounds to 87).  Frankfurt would need to grow by 21.76%, though, to have enough people to warrent a 93-member council under the cube root rule, assuming you round the cube root to the nearest integer.

[Kevinstat]

I was getting ready to work out the draw procedures.  Would it be better to use school children or let the lottery do it?

I don't get what you're asking here, and looking at your first post on this thread hasn't cleared it up either.  Or were you making a joke?

[jimrtex]

I was getting ready to work out the draw procedures.  Would it be better to use school children or let the lottery do it?

I don't get what you're asking here, and looking at your first post on this thread hasn't cleared it up either.  Or were you making a joke?

In Maine the 29 districts would be apportioned a total of 108.2 representatives (the extra 0.2 is due to a rounding error).  Let's take a district entitled to 3.6 members.  Over a decade (5 legislative terms) it would have 3 representatives for 2 terms, and 4 representatives for 3 terms, so that it averages out to 3.6 representatives.

The question is how to pick which 3 terms the district elects the 4th member.  Collectively, the 29 districts have 99 whole representatives.  8 districts have a whole number of representatives, while the other 21 had a collective total of 9.2 fractional representatives.  If all 21 elected an extra representative to the same term, there would be 120 representatives, and if none of the 21 elected an extra representative to another term, there would only be 9 representatives.  So in general, we want to choose 9 districts to have an extra representative for each of 4 terms, with 10 districts for the 5th term.

This should also be done on a regional basis.  Cumberland has 5 districts with a total of 22.6 representatives.  So it should have either 22 or 23 representatives for each term, rather than varying between 20 and 25.

We start by grouping  counties in regional groups:

Northeast: Aroostook, Penobscot, Piscataquis 19 representatives (18 whole + 1.0 fraction)
Northwest: Franklin, Oxford, Somerset 11.4 representatives (10 whole + 1.4 fraction)
Southeast: Hancock, Knox, Lincoln, Sagadahoc, Waldo, Washington 19.6 representatives (19 whole + 0.6 fraction)
Southwest: Androscoggin, Cumberland, Kennebec, York 57.2 (51 + 6.2 fraction)

We pair the more rural Northwest and Southeast regions, so that 2 terms there will be 12 NW and 19 SE; and the other 3 terms there will be 11 NW and 20 SE.  There will be 19 from the NE, and 57 from the SW, except one session with 58.

If a district has a fraction of 0.2, the extra representative can be elected in term 1; 2; 3; 4; or 5.

If a district has fraction of 0.4, the extra representative can be elected in terms 1 and 3; 1 and 4; 2 and 4; 2 and 5; or 3 and 5.  These patterns avoid consecutive terms, or a gap of 3 terms.

If a district has a fraction of 0.6, the extra representative can be elected in terms 2, 4 and 5; 2, 3, and 5; 1, 3 and 5; 1, 3, and 4; or 1, 2, and 4.  These are the complementary patterns of those for a fraction of 0.4.

If a district has a fraction of 0.8, the extra representative can elected in all terms but, 1; 2; 3; 4; or 5.  These are the complementary patterms of those for a fraction of 0.2.

The first drawing determines which 2 terms the extra NW representative will serve.  There are 5 possible patterns, and that of 2 and 4 is drawn.  In terms 1, 3, and 5 the extra representative will be from the SE.  There are 3 districts in the SE with a 0.2 fraction so each gets one of these terms: Knox in term 1 (its 4th); Hancock in term 3 (its 5th); and Washington in term 5 (its 4th).  The other 3 districts of Waldo, Lincoln, and Sagadahoc have 3 representatives for all terms.

The extra fractions in the NW are in two districts Oxford 0.6 and Somerset 0.8.  We need to choose patterns of 3 and 4 terms, such that terms 2 and 4 have two extra representatives and the other 3 terms have one extra.  The possible patterns are (1,2,3,4) and (2,4,5); or (2,3,4,5) and (1,2,4).  The drawing selects the second combination, so Oxford will elect a 5th representative in terms 1, 2 and 4; while Somerset will elect a 4th representative in terms 2, 3, 4, and 5.  Franklin & Somerset West has 3 representatives for all terms.

In the NE, Bangor & Brewer has a fraction of 0.6, while Aroostook North and Penobscot East have fractions of 0.2.  We draw one of the 5 3-term patterns for Bangor & Brewer (2,4,5); leaving Aroostook North to have a 4th representative in term 2; and Penobscot East its 4th in term 3.

In the SW we first draw to determine which term will have the extra representative.  It is term 1, so in the 1st term there will be 109 members of the house, and 108 in all other terms.  York, Cumberland, and Androscoggin have collective fractions of 0.8, 0.6, and 0.8, respectively (Kennebec has a fraction of 0.0).  There are 3 ways that the patterns of 4, 3, and 4 extra terms can be arranged so that all 3 counties get an extra representative in the 1st term, and 2 counties get an extra representative in the other terms.  Cumberland draws (1,3,5), while
Androscoggin draws (1,2,4,5) and York draws (1,2,3,4).

The 3 districts in Kennebec have fractions of 0.6, 0.4, and 0.0.  The two patterns must complement each other.  Kennebec North draws (1,4) giving Kennebec South (2,3,5).

The two districts in Androscoggin both have fractions of 0.4, the patterns for the two must complete the countywide pattern of (1,2,4,5).  Androscoggin West & North draws (2,5) leaving (1,4) for Androscoggin East (2,5).

In Cumberland, the two districts that include a portion of Portland have a collective fraction of 1.0.  Cumberland Central draws (2,4,5) leaving Portland (1,3).

The outer 3 districts have fractions of 0.8, 0.6, and 0.2 and must elect 2 extra representative in terms (1,3,5).  We draw first for Cumberland North which will elect a 5th representative in terms (1,2,3,4), this then requires Cumberland East to elect its 5th representative in terms (1,3,5) and Cumberland South its 5th in term 5.

In York the 2 inland districts have a cumulative fraction of 1.0.  York West draws (1,3,4) for its 4th representative, leaving terms (2,5) for the 4th representative for York North.

The two coastal York districts have a cumulative fraction of 0.8.  The 4 extra terms must be in (1,2,3,4).  York East will elect a 4th representative in (1,3,4) leaving term 2 for York South.

[jimrtex]

Edit: I have updated the analyis based on permitting cities or counties with a population equivalent to 5 and 6 members to be placed in a single district, rather than being split, with part combined with adjacent areas.

I took a look at the effect of population change from 2000 to 2008 in Maine.  The map below is the one for 2000.



Overall, the population increased 3.2%, which would result in an increase in the size of the legislature from 108 to 110 members.  In rough terms this is distributed as:

York +1; Cumberland +1/2; Androscoggin-Kennebec-Penobscot (Lewsiton-August-Bangor) +1/2; rest of state, but concentrated in small coastal counties from Sagadahoc to Hancock +1/2; Aroostook and Washington -1/2.  There is some decline in the cities with a shift outward to surrounding towns.

Without any adjustments, the following districts would lose 0.2 representatives:

LD1 Aroostock (to 3.0); LD10 Washington (3.0); LD14 Kennebec (3.4); LD 24 Cumberland (5.2).

While the following would increase by 0.2 or 0.4:

LD5 Penobscot (4.2); LD9 Oxford (4.8); LD12 Waldo (3.2); LD15 Kennebec (3.2); LD21 Cumberland (3.8); LD22 Cumberland (4.8); LD23 Cumberland (5.0); LD25 Cumberland (4.4); LD 26 York (0.4 to 3.8); LD 27 (4.8); LD 28 (3.8); LD 29 (4.4).

The loss in population in Arroostook County means that 2 districts would no longer be possible.  Instead the county would form a single district with 6 representatives, which would likely continue in representation.

LD6, 1/2 of which is Piscataquis and the other 1/2 in Penobscot, will need some augmentation to keep it at 3 members.  This can come from the west end of LD5 which had almost all the growth in Penobscot (concentrated in the immediate ring around Bangor).

LD8 which is based in Franklin, but includes Somerset west of the Kennebec River, may need a very small adjustment to keep it at 3 members, but for 2010 at least is fine.  LD9 which is Oxford will increase from 4.6 to 4.8 members, but that is exaggerated a bit by rounding.  With the new rule, the county could continue as a single district even if the population exceeds that needed for 5 members.

LD10 which is based in Washington but includes two towns in Hancock will need further augmentation.  Since it started above 3.0, it may get by for 2010, but will in the future need added towns from northeastern Hancock to avoid cutting off Bar Harbor from the rest of Hancock.

The small counties along the coast (LD12, LD18, LD19, and L20) are growing slightly.  It may be feasible to make LD19 entirely in Lincoln (it currently includes one town in Knox currently).

Most of the growth in Kennebec is in LD15 in the western part of the county.  It may be possible to shift the boundary west.  The current boundary is fairly tight in both the Waterville and Augusta areas to gather enough population for 3 seats.

LD16 and LD17 in Androscoggin are stable.  There is a small decline in Lewiston and Auburn with compensating growth in outlying towns such as Turner. Poland, Lisbon, and Durham.

Growth in Cumberland is in the suburban areas.  Portland itself is declining and approaching a point where it would not even need the new rule.  LD23 in the suburbs to the north will reach a population equivalent to 5.0 representatives.  While it might be possible for a while to shift towns to keep the district representation below 5, in the long term, it will probably be necessary to create a 6th district in the county.  LD22 would retract toward Brunswick with 3 suburban districts being created to the southeast, northwest, and northeast of Portland.

Chebeague Island town which seceded from Cumberland town may be better off in LD24 with other Casco Bay islands, some of which are part of Portland city.

The growth in York is distributed across all districts, all of which will gain 0.2 members (LD 26 would gain 0.4).  The growth is somewhat heavier inland, where the districts have plenty of room to grow.  Along the coast a split into 3 districts may be feasible now.

[jimrtex]

Vermont would have an 85 member legislature, with 7,163 persons per representative.

Essex and Grand Isle are the only counties with a population equivalent to less than 3 representatives.  In both cases, it actually less than 1.0.  Essex could be combined with either Orleans or Caledonia.  Geographically, Caledonia to the south might be a better fit, but there would be a greater population difference between districts.

Grand Isle could be combined with either Chittenden or Franklin.  If it were placed with Chittenden it would be in a district with Burlington suburbs.  Placing it with Franklin makes it a larger share of the district, and it is ess likely to be dominated by St. Albans.

1. Orleans & Essex (4.6 members)
2. Franklin East (3.6)
3. Franklin West & Grand Isle (St. Albans) (3.6)

Chittenden is entitled to 20.46 representatives, with 5.43 of that in Burlington.  Rather than splitting Burlington, and placing a fragment with a suburban town, I changed the rules so that an area with a population equivalent to between 5 and 6 members can form a single district, rather than being split and combined with other areas.  While this results in a somewhat large district, the district will correspond with a political subdivision.  This new rule was also used with two counties in Vermont.

The rest of the county needs to be split into 4 districts.  The relatively large size of the suburban towns, meant there were not too many options in combining them.  Three suburban districts were created surrounding Burlington, with the eastern part of the county forming a 4th district.

4. Chittenden North (Colchester, Milton) (4.6)
5. Burlington (5.4)
6. Chittenden South (South Burlington) (3.6)
7. Chittenden Central (Essex, Williston) (3.6)
8. Chittenden East (3.0)

Lamoille, Caledonia, Addison, and Orange have enough population for their own district.  That of Addison is slightly over 5.0, and avoids being split under the new rule.   Washington has a population equivalent to 8.10 districts.  Barre and Montpelier could be placed in different districts, but the Barre-based district would include towns next to Montpelier whether it was a east/west split or a north/south split.  So instead, a hemi-doughnut was created with Barre and Montpelier forming a central urban district.

9. Lamoille (3.2)
10. Caledonia (St. Johnsbury) (4.2)
11. Washington Outer (3.6)
12. Barre & Montpelier (4.4)
13. Addison (Middlebury) (5.0)
14. Orange (4.0)

Windsor, Rutland, and Windham each require a split into 2 districts, while Bennington forms a somewhat large single district.  The splits of Windsor and Windham are straightforward north/south splits.  In Rutland, the area immediately around the city of Rutland is enough for the center of the district, but the area to the northeast of the city would be isolated from the areas to the south of the west, so the inside of the doughnut is displaced somewhat to the northeast.

15. Windsor North (Hartford) (4.4)
16. Windsor South (3.6)
17. Rutland Northeast (Rutland city) (4.6)
18. Rutland South & West (4.2)
19. Bennington (Bennington town) (5.2)
20. Windham North (3.2)
21. Windham South (Brattleboro) (3.0)

[jimrtex]

Edit: This is a revised version of the districts for Maine based on permitting a city or county with a population equivalent to between 5 and 6 representatives to be place in a single district, rather than being split with part attached two adjacent areas.

In Maine, this permits Portland to be contained in a single district, and as Aroostook continue to lose population, the two 3-member districts can be combined into a single 6-member district.

Based on the cube root rule, Maine would have a 108 member legislature, with each legislator representing about 11,800 persons.  Each district would nominally elect from 3 to 5 members, who would represent multiple mandates wtih a resolution of 0.2 members.

As in Massachusetts, the districts were drawn to conform to county boundaries as much as possible.  Franklin, Lincoln, and Washington were just short of 3 members, and drew additional population from Somerset, Knox, and Hancock, respectively.  Piscataquis was entitled to about 1.5 members and was included in a district that was about 1/2 in Penobscot County.



Aroostook is entitled to 6.26 members, or 2 districts of just over 3 members each, which required population equality to be the primary concern, with Caribou and Fort Fairfield placed in the north, and Presque Isle in the south.

1. Aroostook North (3.2 members)
2. Aroostook South (3.0)

The northern reaches of Penobscot, Piscataquis, and Somerset are virtually unpopulated and attached to districts further south.



Piscataquis was included with Penobscot, which together are entitled to 13.74 members.  While preference might be to pair Piscataquis with the smaller Somerset county, this would have required splitting Somerset, which already was going to be giving up areas to Franklin.  The area in Penobscot paired with Piscataquis is adjacent to the populated areas and of similar density, and relatively remote from Bangor.

This left the rest of Penobscot to be split into 3 districts, with Bangor and Brewer placed in one, and the Penobscot River dividing the other two districts.

3. Penobscot East and North (3.2)
4. Bangor & Brewer (3.6)
5. Penobscot South (4.0)
6. Piscataquis & Penobscot West (3.0)

Franklin is entitled to 2.50 members.  The extra population could have been taken from Oxford which would have made the districts more balanced, but it would have required including towns right up to Rumford.  The area of Somerset shifted to the Franklin district is west of the Kennebec River.

7. Somerset (3.8)
8. Franklin & Somerset West (3.0)

Oxford forms its own district.

9. Oxford (4.6)



Washington is just short of 3 members, and a small area of Hancock (Gouldsboro and Winter Harbor) are shifted.

10. Washington (3.2)
11. Hancock (4.2)



Waldo has enough for its own district.

12. Waldo (3.0)

Kennebec is entitled to 9.9 members.  It could be split between 2 districts or 3 districts.  The plan selected uses 3 districts, two with Waterville and Augusta as their cores and third formed from the rest of the county.

13. Kennebec North (Waterville) (3.4)
14. Kennebec South (Augusta) (3.6)
15. Kennebec West (3.0)

Androscoggin is entitled to a 8.8 members, which requires two districts.  Lewiston and Auburn could form one district, but this would mean that the other district would have to straddle the two.  So the two cites were split with additional area added to each.

16. Lewiston and Androscoggin East (4.4)
17. Androscoggin West and North (Auburn) (4.4)

Lincoln is just short of enough population for 3 members, so it includes Friendship town from Knox.  Sagadahoc just has enough for its own district, so the added population had to come from Knox.

18. Knox (3.2)
19. Lincoln (3.0)
20. Sagadahoc (3.0)

Cumberland is entitled to 22.50 members, which could be accommodated with 5 to 7 districts.  Portland has a population equivalent to 5.44 representatives and was placed in its own district (along with the small town of Long Island).

The rest of the county was divided into 4 districts, two in the immediate Portland suburbs, one based in Brunswick, but extending towards Portland, and one in the more rural areas to the northwest.

21. Cumberland North (3.6)
22. Cumberland East (Brunswick) (4.6)
23. Cumberland Central (Westbrook, Windham, Gorham) (4.8)
24. Portland (5.4)
25. Cumberland South (South Portland, Scarborough) (4.2)

York is entitled to 15.82 members, which could be accommodated by 4 or 5 districts.  5 districts would have 3 districts along the coast, but with some inland extensions, and the splits were awkward, so instead 4 districts were drawn with larger districts on the coast, though Kennebunk and Kennebunkport are split.

26. York North (3.4)
27. York East (Biddeford, Saco) (4.6)
28. York West (Sanford) (3.6)
29. York South (York) (4.2)

[Kevinstat]

Edit: This is a revised version of the districts for Maine based on permitting a city or county with a population equivalent to between 5 and 6 representatives to be place in a single district, rather than being split with part attached two adjacent areas.

In Maine, this permits Portland to be contained in a single district, ...

Did you make any changes outside moving what was the remainder of Portland and Long Island and 1.0 Representatives from District 23 (Cumberland Central) to District 24 (Portland), and moving Gorham and 1.2 Representatives from District 21 (Cumberland North) to District 23?  (I looked at your post on the draw procedures, which hasn't been updated, to see what the quotas of the old districts in Cumberland County were and from that and looking at 2000 census data I was able to guess which towns were in different districts.)

[minionofmidas]

Ah, I was going to make a "bold changes plz kthanksbye" type post yesterday but forgot. Thanks Kev!

[jimrtex]

Edit: This is a revised version of the districts for Maine based on permitting a city or county with a population equivalent to between 5 and 6 representatives to be place in a single district, rather than being split with part attached two adjacent areas.

In Maine, this permits Portland to be contained in a single district, ...

Did you make any changes outside moving what was the remainder of Portland and Long Island and 1.0 Representatives from District 23 (Cumberland Central) to District 24 (Portland), and moving Gorham and 1.2 Representatives from District 21 (Cumberland North) to District 23?  (I looked at your post on the draw procedures, which hasn't been updated, to see what the quotas of the old districts in Cumberland County were and from that and looking at 2000 census data I was able to guess which towns were in different districts.)

Except Long Island town was in LD24 with about 81% of Portland.  The portion of Portland that was in LD23 was in the north and northwestern part of the city.  Many of the Casco Bay islands are part of the city of Portland and Long Island was part of a Portland voting district tabulated by the Census Bureau.  Long Island has a little over 200 people which correspond to about 0.02 representatives.

The voting districts that the census bureau has for Portland are kind of odd shaped, and vary quite a lot in population.  They possibly correspond to an intersection of the senate and house maps.  But since they would be from before the 2003 redistricting, I couldn't really tell.

Another reason for the change was that the 2008 estimates put LD21 (including Gorham) over 5 members.  Gorham was placed in a different district from Windham because including part of Portland and Gorham would have meant that LD23 was over 5 members.  The total population in Cumberland is approaching what would require 6 districts to be used without splitting towns or forcing contorted combinations of towns.

Another variation of the rules would be to permit a county or town with a population equivalent to between 2.5 and 3.0 members to be placed in a single (small) district.  This might be done in cases where the relative share of population had declined.   Instead of gradually adding areas after each census to keep the district at 3.0 members, you could wait until the population had decline to 2.5 or less and make a more radical change in the configuration of boundaries.  If a district was entitled to 2.6 members, it would elect 3 representatives for most (3) terms, and two for the other two - so it would be a 3-member district most of the time.

In Maine, this would mean that Washington and Lincoln could have their own districts.  Washington is continuing to decline, while Lincoln is increasing and may be over 3.0 by 2010.  Franklin is just barely below 2.5 (2.496 in 2000, and 2.495 in 2008) and Piscataquis is below 1.5, so they would still need to be combined with adjacent counties.

If Portland had been split in two districts within the city in the past, then it might continue with two districts of less than 3.0 magnitude until the population dropped to below 5.0.

The updated maps do not recognize the changes in boundaries between 2000 and 2008 due to the dissolution of Centerville (Washington) and Madrid (Franklin), and the secession of Chebeague Island town from Cumberland town (Cumberland).  The Census Bureau estimates also includes 3 small and largely uninhabited island areas as named unorganized territories rather than as "county subdivisions not defined"

The updated draw procedure for Cumberland County would be the following:

Cumberland would continue to have an excess fractional population of 2.6 members which would mean that it would have 3 terms with 3 extra members and 2 terms with 2 extra members.  The terms with 3 members would continue to be determined by the draw distributing extra terms among York, Cumberland, and Androscoggin.  Neither the 3 3-member terms nor the 2 2-member terms could be consecutive, so Cumberland would end up with one of 5 patterns.

We then split the Cumberland districts between those in the immediate Portland area (LD23, LD24, and LD25) and those more remote (LD22 and LD22), which have respective cumulative fractions of 1.4 and 1.2.  The remote districts will usually have one extra member between them, but for one term will have two.  We don't want the remote districts to take both extra districts in a term when Cumberland only has two extra.  In other words the distribution should be:

3 total: 2 Portland area; 1 remote.
3 total: 2 Portland area; 1 remote.
3 total: 1 Portland area; 2 remote.
1 total: 1 Portland area; 1 remote.
1 total; 1 Portland area; 1 remote.

For each pattern of extra terms for Cumberland, there are 3 combinations of patterns of extra terms for LD21 and LD22 that will produce the above distribution.  But combination would result in the Portland area having its two extra seats in consecutive terms, or go 3 terms with only 1 extra seat.  So a draw would choose between the two viable combinations, and then a second draw would determine which pattern was used by LD21 and which was used by LD22.

This first draw would leave the Portland area with a pattern of two terms with two extra and three terms with one extra.  If we require that either LD23 or LD25 have an extra member in every term, then LD24 (Portland) would get its extra members when the Portland area gets 2 extra.  In effect, we can further refine the above distribution to:

3 total: 1 Portland, 1 Portland suburbs; 1 remote.
3 total: 1 Portland; 1 Portland suburbs; 1 remote.
3 total: 1 Portland suburbs; 2 remote.
1 total: 1 Portland suburbs; 1 remote.
1 total; 1 Portland suburbs; 1 remote.

So the extra terms for LD24 are determined by the draw which determined which term LD23 and LD22 both get an extra member.

The final draw determines which one of the five terms that LD25 gets an extra member.  LD23 gets an extra member the remaining other 4 terms.

[jimrtex]

Rhode Island would have a legislature of 102 members, with each representing 10,278 persons.  This is similar to Maine and New Hampshire, but because Rhode Island's population is more concentrated, each district is at most comprised of only a few towns, and four cities, Providence, Warwick, Cranston, and Pawtucket require multiple districts.  All districts are contained within counties, but because each is comprised of only a few towns, they are all named according to their component towns.



Bristol County, the state's least populous, is entitled to 4.93 members, so the entire county was placed in a single district.

Newport County is entitled to 8.31 members, and is split into two districts, one comprised of areas on the mainland to the east and the northern part of Rhode (Aquidneck) Island and the other southern part of the island in the immediate area of the city of Newport.

1. Bristol, Barrington & Warren (5.0 members)
2. Portsmouth, Tiverton, & Little Compton (3.6)
3. Newport, Middletown, & Jamestown (4.8)

Washington County is entitled to 12.02 members, or 3 districts, which are based around the three largest towns of South Kingston, North Kingston, and Westerly.

4. South Kingstown, Naragansett, & New Shoreham (4.4)
5. Westerly, Hopkinton, Richmond, & Charlestown (4.4)
6. North Kingstown & Exeter (3.2)

Kent County is entitled to 16.36 districts, with slightly over half within Warwick.  The remaining western part of the county is divided into two districts.

7. Coventry & West Greenwich (3.8)
8. West Warwick & East Greenwich (4.2)

The two Warwick districts are treated below with the other larger cities.

Providence County is entitled to 60.48 districts, with 31.70 of that within the cities of Providence, Cranston, and Pawtucket, each of which are entitled to multiple districts.  In addition the population and location of East Providence, North Providence, and Woonsocket cities (or town) are such that they need to be placed in districts of their own.  These three cities have a population equivalent to 12.10 members, leaving the remaining 10 towns north and west of Providence with a population entitled to 16.68 members in 4 or 5 districts.

Because of the relative small number of towns (10) to districts (4), viable combinations are limited.  The key appears to be where Central Falls is placed.  If it placed with Lincoln, then the larger suburban towns of Johnston and South Smithfield may placed together, leaving 5 towns in the west to form a more rural district.  But both of these latter districts would be close to the limit of 5 members, and probably require re-organization later on.  Instead, Central Falls was placed with Cumberland, and 3 more moderate sized districts created in the west.

11. Johnston, Scituate, & Foster (4.2)
12. Burrillville, North Smithfield, & Glocester (3.6)
13. Lincoln & South Smithfield (4.0)
14. Woonsocket (4.2)
15. Cumberland & Central Falls (5.0)
16. North Providence (3.2)
17. East Providence (4.8)



Warwick is entitled to 8.35 representatives and is divided into two districts.  Despite being the 2nd largest city in the state, Warwick does not have a historic commercial or industrial core.  The original industrial area is in what is now West Warwick, which was split off leaving Warwick as mostly farmland, until the Providence airport was built and suburbanization occurred.  The two districts are generally separated by the airport, which is on the southwestern edge of LD 10.

9. Warwick West (4.0)
10. Warwick East (4.4)

Cranston is entitled to 7.71 representatives or two districts.  The eastern district (LD18) includes areas wrapped around the southern tip of Providence (most of South Providence was once part of Cranston, and was transferred to Providence as part of a political gerrymander) and the street grids radiate outward from Providence.  The western district (LD19) is more modern suburban development with some curvilinear streets.

18. Cranston East (3.8)
19. Cranston West (4.0)

Pawtucket is entitled to 7.10 representatives or two districts.  The Seekonk River forms a natural boundary between east and west, but there is insufficient population west of the river for 3 representatives, so the western district includes some areas immediately east of the river.  If Central Falls were included with Pawtucket (in the western district) use of the Seekonk river would be feasible.

20. Pawtucket East (3.8)
21. Pawtucket West (3.4)

Providence is entitled to 16.89 districts in either 4 or 5 districts.  I attempted to compose districts of recognized neighborhoods in the city.  With 4 districts, this required dividing up related neighborhoods to the west of downtown in order to keep districts under 5 members.   5 districts permits a central district comprised of downtown and areas to the west which were originally mixed industrial and residential (before commuting was feasible).  The downside of using 5 districts is that it may required continuing adjustment of boundaries to maintain all the districts with sufficient population.

22. Providence East (3.4)
23. Providence South (3.2)
24. Providence West (3.2)
25. Providence North (3.6)
26. Providence Central (3.4)

[jimrtex]

Draw Procedure For Rhode Island.  The collective representation for Rhode Island is 102.6, meaning that three (of five) terms in a decade will have 103 members.

Valid Patterns for one term:

xoooo oxooo ooxoo oooxo oooox

Valid Patterms for two terms (ensures that they are not consecutive, nor that there are three consecutive terms without an extra representative).

xoxoo oxoxo ooxox xooxo oxoox

Valid Patterns for three terms (ensures that they are not consecutive, nor that there are two consecutive terms without an extra representative)

xxoxo oxxox xoxxo oxoxx xoxox

Valid Patterns for four extra terms.

xxxxo oxxxx xoxxx xxoxx xxxox
LD4, LD5, and LD6 all in Washington County have a cumulative fraction of 1.0, which means that Washington County will have 12 representatives for all terms.  LD 4 and LD5 will have an fifth representative for two terms, while LD6 will have a 4th representative for one term.  The term for LD6 is drawn first.  This will restrict the possible patterns for the other two districts to two patterns.  A second drawing is held to determine which pattern is assigned to LD4, with LD5 taking the remaining pattern.

LD7 and LD8 in western Kent County have a cumulative fraction of 1.0 which means the area will have 8 representatives for all terms.  LD8 will have a 5th representative for one term, while LD7 will have a 4th representative at the other 4 terms.  A draw determines which term LD8 will have the extra term, leaving LD7 with the other 4 terms.

LD11, LD12, and LD14 in western Washington County have a cumulative fraction of 1.0 which means that the area will have 12 representative for all terms.  A draw is held to determine which three terms that LD12 has a 4th representative.  A second draw is determined which of the remaining two terms is assigned to LD11, and which to LD 14 for their 5th representative.

LD17, LD20 and LD21 in Pawtucket and East Providence have a cumulative fraction of 2.0 which means the area will have 12 representatives for all terms.  A draw is held to determine which four terms that LD17 (East Providence) has a 5th representative.  This draw dictates which of two possible patterns that LD20 and LD21 may use.  LD21 will have a 4th representative in the 2 terms that LD17 and LD20 don't have an extra representative.  A second draw determines which of the two patterns is used for LD20 and LD21.

LD16 and LD22-LD26 in Providence and North Providence have a cumulative fraction of 2.0 which means that the area will have 20 representatives in all terms.  Providence will have have 17 representatives, except for the one term that LD16 (North Providence) has its 4th representative).

A first draw determines which term LD16 (North Providence) will have its 4th representative.  Then LD25 (the adjacent district in Providence) will draw to determine which 3 terms it will have a 4th representative, avoiding the term drawn by LD16.  LD26 in west central Providence will take the remaining term of the 5 for one of its terms with a 4th representative.  This ensures that one of the two extra representatives is shared among the districts in the north and west of Providence (or immediately adjacent in North Providence), and the extra representative is share among districts towards the south and east.

LD26 will then draw its 2nd term such that its two terms form a viable pattern.  This leaves 4 terms to be distributed among LD22 (2 terms) and LD 23 and LD24 (one term each).   LD22 draws one of the viable two term patterns.  And then LD23 and LD24 each draw one of the remaining terms.

This leaves LD18, Cranston East with a fraction of 0.8, LD 10 Warwick East with a fraction of 0.4, and the two Newport County districts with fractions of 0.8 and 0.6 for a total fraction of 2.6.  The south suburban districts and the Newport districts together have an extra representative in every term.  In addition, both the southern suburban districts will have an extra representative in one of the terms where the legislature has 103 members, and the Newport districts will both have an extra representative in two of the terms where the legislature has 103 members.

We first draw a pattern for the three terms that the legislature will have 103 members.  We then draw for a pattern of two terms when the extra member will be given to the Newport districts, leaving the 3rd term with 103 members to the south suburban districts.

Both LD10 and LD18 will have an extra representative in that term.  LD10 will draw a 2nd term that will form a viable pattern with that term, and LD18 will take the remaining 3 terms for its 4th representative.

In Newport, both LD2 and LD3 will have an extra member for the two terms determined above.  LD2 will draw a 3rd term which forms a viable pattern with these two for its 3rd term with 4 representatives.  LD3 will have the other 2 terms for its 5th representative.

[jimrtex]

Connecticut would have a 150 member legislature, with each legislator representing 22,704 people.  My initial pass in which the magnitude of each district was rounded to a multiple of 0.2, produced a total of 149.6 members (or 0.4 less than the target total).  In the other states of New England, there had been an excess, and I had simply left the excess apportionment.  Here I decided to adjust the apportionment, using St. Lague to apportion seats (in units of 1/5).  The districts that received the extra 1/5 of a seat were LD11 (Enfield and suburbs northeast of Hartford) and LD37 (Stamford).  In the case of LD11, its raw apportionment had been 3.499, which had rounded down to 3.4.



Windham is entitled to 4.80 members and a single district.

1. Windham (Windham town) 4.8

Tolland is entitled to 6.01 members.  The slight excess over 6 requires a split under a strict interpretation of the rules.  Had this method been used historically, and Tolland gradually risen above that threshold, it might have been maintained as a single district.  Alternatively, towns from adjacent counties might have been included to make for more comfortable districts.

2. Tolland West (Vernon) 3.0
3. Tolland East 3.0

New London is entitled to 11.41 members, or 3 districts.  A nice district centered on New London town could be drawn, but this would have isolated areas further east and west along the coast.  So instead two districts were created along the coast on opposite sides of the Thames, and an inland district with a core of Norwich.

4. New London North (Norwich) 4.0
5. New London East (Groton) 3.4
6. New London West (New London town) 4.0

Middlesex is entitled to 6.83 members, and is split into two districts.

7. Middlesex South (Middletown) 3.2
8. Middlesex North 3.6

Hartford is entitled to 37.76 members. with 5.4 for the city of Hartford.  The area east of the Connecticut River is entitled to just short of 10 members.  Because of the arrangement of population, it is not possible to form either two or three districts, and so a river crossing is needed.  This plan crosses the river south of Hartford and includes the airport which with its access highways obliterates the river as a barrier.

This also permits the creation of three districts north of Hartford, with some distinct identity in towns closer to the Massachusetts border such as Enfield and Windsor, plus a more rural district in the northwest.  New Britain has its own district as well.

Connecticut does not appear to distinguish more urbanized area as "cities", but it seemed awkward to name a district Hartford Town.

9. Glastonbury, Wethersfield, Rocky Hill & Marlborough 3.6
10. Manchester & East Hartford 4.6
11. Enfield, South Windsor, & East Windsor 3.6
12. Windsor, Bloomfield, Suffield, & Windsor Locks 3.2
13. Hartford City 5.4
14. West Hartford & Farmington 3.8
15. New Britain 3.2
16. Southington, Newington, & Berlin 3.8
17. Bristol & Plainville 3.4
18. Hartford Northwest (Simsbury) 3.2

Litchfield is entitled to 8.02 members and is divided between two districts. 

19. Litchfield North (Torrington) 4.0
20. Litchfield South (New Milford) 4.0

New Haven is entitled to 36.29 districts, with the cities of New Haven and Waterbury both entitled to their own districts.  Districts were created in the suburbs to the west, north, and east of New Haven, as well as the suburbs surrounding Waterbury.  The last two districts are in the Meriden area, and an agglomeration of areas along the western boundary of the county.

21. Waterbury 4.8
22. Greater Waterbury (Naugutuck, Cheshire) 4.4
23. Meriden & Wallingford 4.4
24. Hamden, North Haven, & North Branford 4.2
25. Branford, East Haven, Guilford, & Madison 4.2
26. New Haven City 5.4
27. West Haven & Milford 4.6
28. New Haven West 4.2

Fairfield is entitled to 38.87 representatives.  Bridgeport, the largest city in the state, must be split into two districts.  Greenwich was short of enough for its own district, and forced a split of Stamford, its only neighbor. 

Two districts were drawn in the north of the county.  The tip of the county was not placed with Danbury because that would have meant Ridgefield would have had to been placed with towns further south, and forced further rearrangement.  Elsewhere districts were drawn along the coast, with a final district created from the the next inland tier of towns.

Bridgeport was generally split along the Pequonnock River, with areas in the southwest included for sufficient population.  The districts appears to at least somewhat follow the attendance zones for the high schools.

The area of Stamford included with Greenwich is in the northwest corner, away from the center of town.  It also appears that the road networks in this area are non-perpendicular with roads following the coast WSW-ENE or north-south.

29. Fairfield North (Newtown) 4.2
30. Danbury & Ridgefield 4.4
31. Fairfield Central (Trumbull) 4.2
32. Stratford & Shelton 3.8
33. Bridgeport East 3.2
34. Bridgeport West 3.0
35. Fairfield Town & Westport 3.6
36. Norwalk & Darien 4.6
37. Stamford 5.0
38. Greenwich 3.0

[jimrtex]

What is the theory behind the cube root thing?  I am just curious. That is about 330 districts in California by the way. Do we really want that many nebbishes and losers prowling around Sacramento getting into trouble at taxpayer expense?  It is bad enough just having 40 and 80 clowns (and most of them are clowns) up there for the respective chambers.

The following paper has some information on the cube root law beginning on Page 98.

On the Causes and Consequences of and
Remedies for Interstate Malapportionment of the U.S. House of Representatives

The paper argues that the effect of inequality in size of districts between states is measurable, and that the only practical way to remedy this is by increasing the size of the House.  Changing the Constitution so that representatives are not elected on the basis of geography, including State boundaries is impractical, and switching away from Huntington-Hill would have very marginal impact.

The article then proposes changing the size of House to match the cube root law.  Though that would improve equality, and presumably effectiveness of representation, it never explains why that use of the cube root law would produce either a material improvement or sufficient improvement.  That is, would increasing the size of the House make it "fairer" to warrant the increase, or if it did make if "fairer" why would adding 200 representatives make it "fair enough".

Also, the House has been as malapportioned in relative terms about the same ever since the size of the House has been fixed at 435.  If it is unfair to have districts 10% larger, it doesn't matter if they average 200,000 persons or 700,000 persons.

The article also contends that if there had been more representatives, that Al Gore would have had an electoral college victory.  But that is using an apportionment based on the 1990 census.  So in effect they are saying that starting from a malapportionment because of using 10-year old data, that apportioning more representatives would produce an increase in absolute error (if there is a 1% error, apportioning 1000 representatives would make a difference of +10).

If the 2000 election had been based on the 2000 apportionment, Bush would have gained 7 more electoral votes, and increased his victory margin from 4 to 18.  If you remove the "senatorial electors" , 30 States for Bush, 20 States and the District of Columbia for Gore, it would have been a 218 to 218.

In fact, the population of the States and Districts carried by the two candidates is almost identical, with Gore winning areas with 50.0112% of the population.  Even with ridiculously large House sizes (eg 7000 members), this would do almost nothing to reduce the 18 vote margin based on senatorial electors.  And even if the senatorial electors were eliminated, the details of the 23th Amendment would generally give Bush a small margin (in a 7000 member House, Wyoming would have 12 representatives and 14 electoral votes; and the District of Columbia would be limited to the same 12 representative electoral votes, even though its population would warrant 14 representatives).

[jimrtex]

These are updated based on ensuring that the total number of mandates
is a whole number.  In the case of Maine, LD 23, Cumberland Central, drops from 4.8 to 4.6.  Its raw apportionment was 4.701 which rounded independently to 4.8.
















The final map depicts how the fractional representatives would be distributed over a 10-year period of 5 terms.  A district with a fraction of 0.6 would have one extra representative for 3 of the 5 terms.  It could be grouped with a district with a fraction of 0.4, which would have an additional representative for the remaining 2 terms (see the two inland York County districts); or grouped with a pair of districts with a fraction of 0.2 each (see Bangor and the districts to the north), such that an extra representative is elected from a general area over a decade.

The cumulative total of the fractions is 9.0, which means that 9 extra representatives (in addition to the 99 fixed representatives) will be distributed among 9 regions depicted in black on the map.

Only 3 of the regions have exactly 1.0 extra representatives.  The others are grouped into two super-regions, one pairing a northwest rural district with a southeast coastal region, and another combining 4 regions from Androscoggin, Cumberland, and York counties.

The northwestern region has 1.4 extra representatives, while the southeast coastal region has 0.6.  So a preliminary draw would determine the two terms when the northwestern region had two extra representatives, with other 3 terms being given to the southeast coastal region.  The extra representatives would then be doled out among the districts in the respective regions such that each district got its respective share.  Over 5 terms the representatives would be distributed:

2 terms: LD7 (Somerset) and LD9 (Oxford) one each;
2 terms: LD7 (Somerset) and southeast coastal region (LD10, 11, or 18)
1 term: LD8 (Oxford) and southeast coastal region (LD10, 11, or 18)

The actual sequence of terms would be drawn by lot.

The second super-region in the southwest urban areas would distribute two extra seats over the 5 terms in the following manner:

3 terms: Androscoggin (LD16 or 17) and York (LD27 or 29)
1 term: Androscoggin (LD16 or 17) and Cumberland (LD23, 24, or 25)
1 term: York (LD27 or LD29) and Cumberland (LD21 or LD22)

The 5 Cumberland districts will form sub-super regions, such that when an extra representative is not awarded to York, it will be awarded to a nearby districts in the Portland area, and when Androscoggin does not get an extra representative, there will be an extra representative for both of the more northeasterly Cumberland districts.

[jimrtex]

These are updated to ensure that there are the same number of representatives (107) for all sessions.  As a result LD6 Sullivan; LD8 Concord & Loudon; and LD14 Hillsborough West drop to 3.4; 3.8; and 4.2 respectively.  Based on their raw share, they were entiled to 3.503, 3.911, and 4.311 seats respectively.







The final map illustrates the draw procedure for apportioning fractional representatives over the 5 2-year terms of a decade.  95 of the 107 seats are fixed,  with 12 floating.

The Hillsborough districts are collectively entitled to 33 seats, with 3 floating.  2 float between Manchester and Nashua (Manchester will always have at least one of the two), while a 3rd seat floats among the other districts in the county.

The Rockingham districts are collectively entitled to 24 represenatives, with 3 floating.  2 float in the more densely populated areas along the coast and the Massachusetts border, with the other shared among the more rural inland areas.

Merrimack districts are collectively entitled to 11.8 representatives, with 1.8 floating.  In 4 of the 5 terms, there will be 2 floating representatives for a total of 12.  In the fifth term, there will only be one floating representative, with the extra assigned to the counties to the north.

Carroll, Belknap, and Strafford are collectively entitled to 18.2 representatives, with 2.2 floating.  In 4 of five terms, they will have 2 floating representatives for a total of 18.  In the other term they will have a 3rd floating seat.

Coos, Grafton, Sullivan and Cheshire are collectively entitled to 20 seats, with 2 floating.  One of the floating representatives will be always be assigned to one of the Grafton districts, with the other floating between Sullivan and Cheshire for 4 of 5 terms, and as 2nd Grafton floating seat in the remaining term.

[jimrtex]

LD 2 Franklin East and LD 18 Rutland South are given an extra 0.2 district so that there are 85 representative statewide every term.  The two districts now have 3.8 and 4.4 representatives based on raw entitlements of 3.697 and 4.298, respectively.




There are 8 floating seats among the 85 total.  Most can be allocated to groups of counties, but one is allocated to the entire state, with two terms for LD2 and LD3 in Franklin and Grand Isle, giving them a total of 8 seats, one term in Chittenden, giving it 22 total rather than the usual 21, and two terms in the south, split between Bennington and Windham.

[jimrtex]

To make the total number of seats an integer (185), LD38 Bristol Central, which includes Taunton drops to 3.6 seats.













There are only 13 floating seats of the 185 total.  This may be that I was trying to get districts with close to an integer magnitude.  It might also be related to the relative few counties, coupled with the large number of towns and seats, which provided greater flexibility in dividing counties.

Most of the draw procedures would be coordinated to ensure that the number of representatives from any one county does not vary by more than one.

[jimrtex]

Three districts lose 0.2 seats so that the number of legislators is a consistent  102 LD 2 Portsmouth, Tiverton, & Little Compton (to 3.4); LD 18 Cranston East (3.6); and LD 20 Pawtucket East (3.6)






The draw is straightforward, with 9 floating seats (among 102 total).  The one term that LD 17 East Providence has 4 rather than 5 seats, the extra seat is shifted to Newport.

[xuinkrbin.]

The People at www.RangeVoting.com have an explanation for the cube root rule (in addition to an interesting voting method idea):

Suppose some constant fraction of the Constituency probably wants to communicate with the Legislator, which is c·P/L communication with Him where c is a constant, P is the population of the country, and L is the cardinality of the legislature.

Meanwhile, each Legislator needs to communicate with all the Others (or anyhow a constant fraction of them) to get things done (e.g. convince Them to do something He wants). That's about k·L communication for each Legislator per thing He wants to do (where k is another constant).

If We now minimize c·P/L + k·L, by choice of L, We get the square-root law, L = (P · c/k)^(1/2),    i.e.    L ∝ √P which is the "optimum" legislature size which minimizes total communication to make something that Legislator wants, get done.  This formula is "optimum", if We assume each Legislator aims for some constant number of goals per (fixed length) term.

Suppose the communication with the Constituents is by mail or email or telephone; but the communication with fellow Legislators is face-to-face 1-on-1 meetings in random order. Further, all the Legislators are along one long corridor. Then each Legislator typically must walk a distance proportionate to L to reach a random target Legislator. So the difficulty of communication with the L-1 others is then not proportional to L, but rather to its square. In that case, We need instead to optimize by minimizing c·P/L + k·(L²), by choice of L, now getting the cube-root law, L ∝ P^(1/3).

If instead of one corridor, They sit in a 2-dimensional grid, then the typical walk-distance is proportional to √L.  In that case, optimizing is instead to minimize c·P/L + k·L^(1.5), by choice of L, now getting the two-fifths power law, L ∝ P^(2/5).

So it seems as though some power law is the "right answer" – although perhaps it is now not so clear what the correct power is!  (I do not see any good argument for L∝log(P).)

[muon2]

The People at www.RangeVoting.com have an explanation for the cube root rule (in addition to an interesting voting method idea):

Suppose some constant fraction of the Constituency probably wants to communicate with the Legislator, which is c·P/L communication with Him where c is a constant, P is the population of the country, and L is the cardinality of the legislature.

Meanwhile, each Legislator needs to communicate with all the Others (or anyhow a constant fraction of them) to get things done (e.g. convince Them to do something He wants). That's about k·L communication for each Legislator per thing He wants to do (where k is another constant).

If We now minimize c·P/L + k·L, by choice of L, We get the square-root law, L = (P · c/k)^(1/2),    i.e.    L ∝ √P which is the "optimum" legislature size which minimizes total communication to make something that Legislator wants, get done.  This formula is "optimum", if We assume each Legislator aims for some constant number of goals per (fixed length) term.

Suppose the communication with the Constituents is by mail or email or telephone; but the communication with fellow Legislators is face-to-face 1-on-1 meetings in random order. Further, all the Legislators are along one long corridor. Then each Legislator typically must walk a distance proportionate to L to reach a random target Legislator. So the difficulty of communication with the L-1 others is then not proportional to L, but rather to its square. In that case, We need instead to optimize by minimizing c·P/L + k·(L²), by choice of L, now getting the cube-root law, L ∝ P^(1/3).

If instead of one corridor, They sit in a 2-dimensional grid, then the typical walk-distance is proportional to √L.  In that case, optimizing is instead to minimize c·P/L + k·L^(1.5), by choice of L, now getting the two-fifths power law, L ∝ P^(2/5).

So it seems as though some power law is the "right answer" – although perhaps it is now not so clear what the correct power is!  (I do not see any good argument for L∝log(P).)

Interesting theory. Do they try to fit the different power laws to see which best matches existing bodies? I ask, since the link isn't working for me.