Cube Root Rule Legislative Districts

[platypeanArchcow]

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.

Yeah, looks like it's rangevoting.org.

[jimrtex]

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).)

Maybe the optimum number of committees is proportional to the square root of the size of legislature - a legislator has to communicate with a constant fraction of them, and the committee chairmen must communicate with the leadership.

And then a legislator must communicate with a number of committees which is proportional to the square root of the size of the legislature L^(1/2); the number of committee members is also proportional to L^(1/2); the number of bills each committee must consider is also proportional to L^(1/2), which mean sponsors will need to spend that much more effort; and the number of bills that each committee will report and be passed is inversely proportional to L^(1/2).  Combine these 4 factors and you get the same factor of L² that you had when the legislator was walking the linear corridor buttonholing individual legislators, which gets us back to the cube root law.

[xuinkrbin.]

The ACE electoral knowledge network, http://aceproject.org (I made sure to get that right this time, sorry.), in a paper on parliamentary size (http://aceproject.org/ero-en/topics/electoral-systems/par_siz/) found a legislature size, S, equating to (2Pa)^1/3 seems to fit best.  In this equation, Pa = P*L*W, where P is the total Population size, L is the literacy rate, and W is the working-age fraction of the whole Population.

[jimrtex]

New York would have 267 members in its legislature, each representing an average of  71,073 persons.  The proposed map has 66 districts, with an average of 4.05 members per district.  Incidentally, the 2000 population of mainland New York is almost identical to the island areas.



In upstate New York the counties with a population in excess of the equivalent of 4 members were identified (Erie, Monroe, Onondaga, Albany, Orange, Rockland, Westchester) and then multi-county districts were drawn around them.

1. Southern Tier West 3.8

5. Niagara 3.0

6. Western New York 4.4

Orleans could be placed with Niagara for better population balance, by tend to avoid placing a smaller county with a larger county where it might be dominated.

10. Finger Lakes 4.2

11. Southern Tier East 4.0

12. Upper Susquehanna 4.2

13. Oneida-Madison 4.2

Similar reasoning would apply here, except that Madison has too much population to be placed in LD12, and it has awkward connections with other districts such as LD16 or LD18.  

16. Ontario Eastern Shore 3.6

17. North Country 4.0

18. Mohawk Valley 4.4

20. Saratoga-Schenectady 4.8

21. Upper Hudson 4.8

Almost all of the population of Warren is in the Glen Falls area, and it would probably make a better match with Saratoga, but that would require splitting Saratoga and Schenectady apart and and re-arranging LD18.  And the Hudson River does form the boundary between Saratoga and Warren, so all of LD21 is on the same shore.

22. Catskills 4.2

23. Dutchess-Putnam 5.2

This violates a rule that no multi-county or multi-town district have a population magnitude greater than 5.  But Putnam (1.35) doesn't have enough population for its own district, and Dutchess is the smallest neighbor.  Putnam could be included with one of the Westchester districts, but that district would not be much smaller (around 4.8 ).

The larger counties were then subdivided into districts.

Erie has a population equivalent to 13.37 members, and was split into 3 districts, with Buffalo forming its own district, and the surrounding towns divided into two districts.

2. Buffalo 4.2 (Buffalo city)

3. Erie South 4.6 (Alden, Aurora, Boston, Brant, Cattaraugus Reservation, Clarence, Colden, Collins, Concord, Eden, Elma, Evans, Hamburg, Holland, Lackawanna city, Lancaster, Marilla, Newstead, North Collins, Orchard Park, Sardinia, Tonawanda Reservation, Wales, West Seneca)

4. Erie North 4.6 (Amherst, Cheektowaga, Grand Island, Tonawanda city, Tonawanda)

Monroe has a population equivalent to 10.35 members and was divided into 3 districts, with Rochester in its own district, and the remainder of the county split into two districts.  The population is slightly imbalanced, but the Genesee River forms a convenient boundary between east and west.

7. Rochester 3.0 (Rochester city)

8. Monroe West 3.2 (Chili, Clarkson, Gates, Greece, Hamlin, Ogden, Parma, Riga, Sweden, Wheatland)

9. Monroe East 4.0 (Brighton, East Rochester, Henrietta, Irondequoit, Mendon, Penfield, Perinton, Pittsford, Rush, Webster)

Onondaga has a population equivalent to 6.45 members.  Syracuse (2.07) is too small to form its own district, so some of its immediate neighbors are added.

14. Greater Syracuse 3.2 (De Witt, Geddes, Salina, Syracuse city)

15. Onondaga 3.4 (Camillus, Cicero, Clay, Elbridge, Fabius, LaFayette, Lysander, Manlius, Marcellus, Onondaga, Onondaga Reservation, Otisco, Pompey, Skaneateles, Spafford, Tully, Van Buren)

Albany, Orange, and Rockland are large enough to form their own districts.

19. Albany 4.2

24. Orange 4.8

25. Rockland 4.0

Westchester has a population equivalent to 12.99 members and was divided into 3 districts, a northern more rural area, and two southern districts.   I attempted to split these into Hudson Valley and Long Island Sound districts, but the population balance didn't really work, so Greenburgh ended up in the eastern district, and the southern district is Yonkers and other cities immediately north of NYC.

26. Westchester North 3.8 (Bedford, Cortlandt, Lewisboro, Mount Kisco, Mount Pleasant, New Castle, North Castle, North Salem, Ossining, Peekskill city, Pound Ridge, Somers, Yorktown)

27. Westchester South 4.4 (Eastchester, Mount Vernon city, Pelham, Yonkers city)

28. Westchester East 4.8 (Greenburgh, Harrison, Mamaroneck, New Rochelle city, Rye city, Rye, Scarsdale, White Plains city)

Nassau has a population equivalent to 18.78 members, so should be divided into 4 or 5 districts.  The towns of North Hempstead (3.13) and Oyster Bay (4.14) are large enough for their own district; while the cities of Long Beach (0.50) and Glen Cove (0.37) are too small.  The town of Hempstead (10.64) requires three districts.  Since Long Beach is surrounded by Hempstead it is included with Hempstead.  

Glen Cove does not have a land boundary with North Hempstead but does connect at the mouth of Hempstead Bay.  Placing it with North Hempstead provides better population balance, and presumably they have more common interest with the area to the west than the southern part of Oyter Bay, such as Massapequa, Farmingdale, Bethpage, and Hicksville.

Hempstead was divided into 3 strips east to west, mainly because the village and CDP boundaries tended to align.

57. Hempstead West-Long Beach 4.0 (Atlantic Beach, Barnum Island, Bay Park, Bellerose, Bellerose Terrace, Cedarhurst, East Atlantic Beach, East Rockaway, Elmont, Floral Park*, Franklin Square, Harbor Isle, Hewlett, Hewlett Bay Park, Hewlett Harbor, Hewlett Neck, Inwood, Island Park, Lawrence, Lido Beach, Lynbrook, Malverne, Malverne Park Oaks, New Hyde Park*, North Lynbrook, North Valley Stream, Point Lookout, South Floral Park, South Valley Stream, Stewart Manor, Valley Stream, Woodmere, Woodsburgh) and Long Beach town.

58. Hempstead Central 4.0 (Baldwin, Baldwin Harbor, East Garden City, Freeport, Garden City*, Garden City South, Hempstead, Lakeview, Mineola*, Oceanside, Rockville Centre, Roosevelt, South Hempstead, Uniondale, West Hempstead)

59. Hempstead East 3.2 (Bellmore, East Meadow, Levittown*, Merrick, North Bellmore, North Merrick, North Wantagh, Salisbury, Seaford, Wantagh)

60. North Hempstead-Glen Cove 3.6

61. Oyster Bay 4.2

Nassau County has a population equivalent to 19.97 members and would need 5 or 6 districts.   Huntington (2.75) and Smithtown (1.63) are too small for their own district but fit together to form one.  Babylon (2.98) is barely short of having sufficient population, while Islip (4.43) has enough for its own district.   The deficiency of about 1400 persons in a district of 210,000+ could probably be overlooked, but I shifted Baywood into the Babylon district.

The towns on the eastern end of Long Island (East Hampton, Riverhead, Shelter Island,
Southampton, and Southold) along with the Poospatuck and Shinnecock Reservations have a population equivalent to 1.77 members, not enough for a district, while Brookhaven (6.23) is too large for a single district.   So Brookhaven was split to form one district wholly within the town, and the remnant combined with the eastern towns to form the final district.

An east-west split of Brookhaven would barely include Patchogue in the western district making it fairly narrow so instead a north-south split was used, with the population concentrated in the western (Port Jefferson, Stony Brook, etc.) area.  Since Brookhaven CDP is in the southern part, the district that includes about the majority of the town's population was given the directional designation.  A case could be made for including Brookhaven in the name of the other district since it forms a majority (about 4/7) of the district.

62. Huntington-Smithtown 4.4

63. Babylon 3.0 (including Baywood)

64. Islip 4.4 (excluding Baywood)

65. Brookhaven North 4.0 (Belle Terre, Centereach, Coram, East Shoreham, Farmingville, Gordon Heights, Holbrook, Holtsville, Lake Grove, Lake Ronkonkoma, Middle Island, Miller Place, Mount Sinai, Old Field, Poquott, Port Jefferson, Port Jefferson Station, Ridge, Rocky Point, Selden, Setauket-East Setauket, Shoreham, Sound Beach, Stony Brook, Stony Brook University, Terryville)

66. Suffolk East 4.0 (Bellport, Blue Point, Brookhaven, Calverton, Center Moriches, East Moriches, East Patchogue, Eastport, Fire Island, Manorville, Mastic, Mastic Beach, Medford, Moriches, North Bellport, North Patchogue, Patchogue, Shirley, Yaphank in Brookhaven town; and the towns of East Hampton, Riverhead, Shelter Island, Southampton, and Southold; and Poospatuck and Shinnecock Reservations)

[minionofmidas]

Hooray!

[jimrtex]

Hooray!

Added description of Long Island (Nassau and Suffolk) districts.

Demba is an odd name for its setting, no?

[minionofmidas]

Hooray!

Added description of Long Island (Nassau and Suffolk) districts.

Demba is an odd name for its setting, no?

Not really. It's a west slavic name... like approximately half the names in Vienna.

Of course, it's also a West African name, but that's a random coincidence Perutz was probably not aware of.

[jimrtex]

Districts within each New York City borough are based on the Community Districts defined by the city.  Certain common areas such as Central Park and the airports are not a part of any community district, but are largely unpopulated, and were assigned to an adjacent legislative district mainly to improve appearance.   NYC assigns the small part of Manhattan north of the (rerouted) Harlem River to Bronx Community District 8.  I placed it in a Manhattan legislative district.  Similarly NYC assigns Rikers Island to Queens Community District 1 even though it part of Bronx borough.  I assigned it to a Bronx legislative district.

Bronx is entitled to 18.75 members in 4 or 5 districts.

29. Bronx South 4.0

Bronx South is comprised of Bronx Community Districts 1, 2, 3, and 6, plus Rikers Island and Bronx Park.  It is generally between Webster Avenue and the Bronx River with Bronx Park at the northern end.  Neighborhoods include Bathgate, Belmont, Bronx Park South, Claremont, Crotona Park East, East Tremont, Hunts Point, Longwood, Melrose, Morrisania, Mott Haven, Port Morris, Rikers Island, and West Farms.

30. Bronx West 3.8

Bronx West is comprised of Bronx Community Districts 4 and 5, and is between the Harlem River and Webster Avenue.  Neighborhoods include Concourse, Concourse Village, East Concourse, Fordham*, Highbridge, Morris Heights, Mount Eden, Mount Hope, University Heights*, and West Concourse.

31. Bronx Northwest 3.4

Bronx Northwest is comprised of Bronx Community Districts 7 and 8, and Van Cortland Park, but excludes the Marble Hill neighborhood of Manhattan, and is along the Hudson and Harlem rivers at the northern boundary of NYC, south of Yonkers.  Neighborhoods include Bedford Park, Fieldston, Fordham*, Kingsbridge, Kingsbridge Heights, North Riverdale, Norwood, Riverdale, University Heights*, and Spuyten Duyvil

32. Bronx East 4.0

Bronx East is comprised of Bronx Community Districts 9 and 10, and Pelham Bay Park and is along the East River as it opens out into Long Island Sound.  Neighborhoods include Bronx River, Castle Hill, City Island, Clason Point, Co-op City, Country Club, Edgewater Park, Harding Park, Parkchester, Pelham Bay, Schuylerville, Soundview, Soundview-Bruckner, Throgs Neck, Unionport, Village of Baychester, and Westchester Square.

33. Bronx North 3.6

Bronx East is comprised of Bronx Community Districts 11 and 12, and is generally east of the Bronx River Parkway on the northern boundary of NYC south of Mount Vernon.  Neighborhoods include Baychester, Bronxdale, Eastchester, Edenwald, Indian Village, Laconia, Morris Park, Olinville, Pelham Gardens, Pelham Parkway, Van Nest, Wakefield, Williamsbridge, and Woodlawn.

Manhattan is entitled to 21.63 members in 5 or 6 districts.  It would be possible to draw a second cross-island district below Central Park, but this would require the West Side district to extend north of the park.

34. Manhattan South 4.2

Manhattan South is comprised of Manhattan Community Districts 1, 2, and 3, and includes Manhattan south of 14th Street.   Neighborhoods include Battery Park City, Chinatown, Civic Center, East Village, Ellis Island, Financial Center, Governors Island, Greenwich Village, Hudson Square, Liberty Island, Little Italy, Lower East Side, NoHo, SoHo, South Street Seaport, South Village, Tribeca, Two Bridges, Wall Street, and West Village.

35. Manhattan West 4.8

Manhattan West is comprised of Manhattan Community Districts 4, 5, and 7, plus Central Park, and includes Manhattan west and south of the park.  Neighborhoods include Chelsea, Clinton, Flatiron, Gramercy Park*, Herald Square, Hudson Yards, Lincoln Square, Manhattan Valley, Midtown, Midtown South, Murray Hill*, Times Square, Union Square, and Upper West Side.

36. Manhattan East 5.0

Manhattan East is comprised of Manhattan Community Districts 6 and 8, and includes Manhattan east and southeast of the park, plus Roosevelt Island.  Neighborhoods include Beekman Place, Gramercy Park*, Lenox Hill, Mill Rock, Murray Hill*, Peter Cooper, Roosevelt Island, Stuyvesant Town, Sutton Place, Tudor City, Turtle Bay, Upper East Side, and Yorkville.

37. Manhattan Northeast 3.2

Manhattan Northeast is comprised of Manhattan Community Districts 10 and 11, and includes Harlem.  Neighborhoods include Central Harlem, East Harlem, Randalls Island, and Wards Island.

38. Manhattan North 4.6

Manhattan North is comprised of Manhattan Community Districts 9 and 12, plus the Marble Hill neighborhood in Bronx Community District 8 on the mainland north of the re-channelled Harlem River, and is the northern tip of Manhattan along the Hudson River.  Neighborhoods include Hamilton Heights, Inwood, Manhattanville, Marble Hill, Morningside Heights, Sherman Creek, Washington Heights, and West Harlem.

Staten Island (Richmond County) is entitled to 6.24 members, which requires splitting into 2 districts.  There are 3 community districts on the island, so the middle community district has to be split.

39. Staten Island North 3.2

Staten Island North is comprised of Staten Island Community District 1 and that portion of District 2 east of Richmond Road.  Neighborhoods include Arlington, Castleton Corners, Clifton, Dongan Hills, Fox Hills, Graniteville, Grant City, Grymes Hill, Howland Hook, Mariner's Harbor, Midland Beach, New Brighton, New Dorp, New Dorp Beach, Old Place, Port Richmond, Rosebank, Shore Acres, Silver Lake, South Beach, Stapleton, St. George, Ward Hill, West New Brighton, and Westerleigh.

40. Staten Island South 3.2

Staten Island South is comprised of Staten Island Community District 3 and that portion of District 2 west of Richmond Road.  Neighborhoods include Annadale, Arden Heights, Bay Terrace, Bloomfield, Bulls Head, Charleston, Dongan Hills, Eltingville, Emerson Hill, Great Kills, Huguenot, New Springville, Oakwood, Pleasant Plains, Prince's Bay, Richmond Valley, Rossville, Tottenville, Travis, Todt Hill, Willowbrook, and Woodrow.

Brooklyn (Kings County) is entitled to 34.69 members and is divided into 8 districts.

41. Brooklyn Northeast 3.8

Brooklyn Northeast is comprised of Brooklyn Community Districts 1 and 4 in the northern part of the borough along the Queens line, generally north of Flushing Avenue and Broadway.  Neighborhoods include Bushwick, East Williamsburg, Greenpoint, Northside, Southside, and Williamsburg.

42. Brooklyn Northwest 4.6

Brooklyn Northwest is comprised of Brooklyn Community Districts 2, 6 and 7, plus Prospect Park, southeast of Manhattan across the East River.  Neighborhoods include Boerum Hill, Brooklyn Heights, Carroll Gardens, Clinton Hill, Cobble Hill, Downtown Brooklyn, DUMBO, Farragut, Fort Greene, Fulton Ferry, Gowanus, Industry City, Navy Yard, Park Slope, Red Hook, Sunset Park, Windsor Terrace, abd Vinegar Hill.

43. Brooklyn North 4.8

Brooklyn North is comprised of Brooklyn Community Districts 3, 8 and 9, in the north central part of the borough.  Neighborhoods include Bedford-Stuyvesant, Crown Heights, Crown Heights South, Prospect Heights, Prospect Lefferts Gardens, Stuyvesant Heights, Tompkins Park North, Weeksville, and Wingate.

44. Brooklyn East 3.8

Brooklyn East is comprised of Brooklyn Community Districts 16, 17 and about 25,000 persons from the northwest corner of Community District 5, in the east central part of the borough.  Neighborhoods include Broadway Junction, Brownsville, East Flatbush, East New York*, Farragut, Flatbush*, Highland Park*, Northeast Flatbush, Ocean Hill, Remsen Village, and Rugby.

45. Brooklyn West 5.0

Brooklyn West is comprised of Brooklyn Community Districts 12 and 14, in the west central part of the borough.  Neighborhoods include Borough Park, Ditmas Park, Flatbush*, Kensington, Manhattan Terrace, Midwood, Ocean Parkway, and Prospect Park South.

46. Brooklyn Southwest 4.2

Brooklyn Southwest is comprised of Brooklyn Community Districts 10 and 11, in the southwestern part of the borough facing the Verrazano Narrows.  Neighborhoods include Bath Beach, Bay Ridge, Bensonhurst, Dyker Heights, Fort Hamilton, Gravesend*, and Mapleton.

47. Brooklyn South 3.8

Brooklyn South is comprised of Brooklyn Community Districts 13 and 15, along the southern shore of the borough.  Neighborhoods include Brighton Beach, Coney Island, Gerritsen Beach, Gravesend, Homecrest, Kings Highway, Manhattan Beach, Plumb Beach, Sea Gate, Sheepshead Bay, and West Brighton.

48. Brooklyn Southeast 4.8

Brooklyn Southeast is comprised of Brooklyn Community Districts 18 and 5, excluding a small part in the northwest corner removed to get the district under 5 members.  Neighborhoods include Bergen Beach, Canarsie, Cypress Hills, East New York*, Flatlands, Georgetown, Highland Park*, Marine Park, Mill Basin, Mill Island, New Lots, Paerdegat Basin, Spring Creek, and Starrett City.

[Antonio the Sixth]

This method gives France 402 Deputies and Canada 323 MPs. Not bad.

Not bad ? 402 deputies would be awful...

Though for USA, it would give 672 reps, which would still be a progress.

[Antonio the Sixth]

Just for the fun, I used Dave's application to make a map of RI's legislative districts (it would have 102). Obviosuly I chose RI because it's the smallest State available, the others would have been horrible to do...
Except in particular cases, districts don't exceeed +/-500 inh. of difference with the average.

[Хahar 🤔]

This method gives France 402 Deputies and Canada 323 MPs. Not bad.

Not bad ? 402 deputies would be awful...

Though for USA, it would give 672 reps, which would still be a progress.

Why would it be awful?

[jimrtex]

Just for the fun, I used Dave's application to make a map of RI's legislative districts (it would have 102). Obviosuly I chose RI because it's the smallest State available, the others would have been horrible to do...
Except in particular cases, districts don't exceeed +/-500 inh. of difference with the average.

An advantage of using multi-member districts and fractional representatives is that you only have to split the largest cities (Providence, Cranston, Warwick, and Pawtucket) in the case of Rhode Island, and still have a maximum error of about 3%.

3%.

[Antonio the Sixth]

Multi-seats districts are great if you use PR to elect reps, and horrible if you use FPP.
Fractional representatives seem quite scary to me, don't know what it would result in.

[Antonio the Sixth]

This method gives France 402 Deputies and Canada 323 MPs. Not bad.

Not bad ? 402 deputies would be awful...

Though for USA, it would give 672 reps, which would still be a progress.

Why would it be awful?

Because the less representatives we have, the less an Assembly is representative.

[Hash]

This method gives France 402 Deputies and Canada 323 MPs. Not bad.

Not bad ? 402 deputies would be awful...

Though for USA, it would give 672 reps, which would still be a progress.

Why would it be awful?

Because the less representatives we have, the less an Assembly is representative.

If you mean representative of social classes, it isn't already and an assembly which pays attention to representation of social classes is corporatist.

[Antonio the Sixth]

This method gives France 402 Deputies and Canada 323 MPs. Not bad.

Not bad ? 402 deputies would be awful...

Though for USA, it would give 672 reps, which would still be a progress.

Why would it be awful?

Because the less representatives we have, the less an Assembly is representative.

If you mean representative of social classes, it isn't already and an assembly which pays attention to representation of social classes is corporatist.

I'm speaking in general : of political views, socio-demographic factors (I don't believe in social classes), etc. The more representative we have, the smaller is the number of voters it represents, so the closer we are to direct democracy (which, though being now senseless with the current political structure, doesn't deserve to be entirely forgotten).

[jimrtex]

Multi-seats districts are great if you use PR to elect reps, and horrible if you use FPP.
Fractional representatives seem quite scary to me, don't know what it would result in.

The representatives would be elected using STV, for 2-year terms.

In a decade (one reapportionment cycle), there would be 5 terms.   A district with 3.4 representatives (ie  3²/₅) would have 3 representatives for all terms, and 4 representatives in 2 of the 5 terms.  The terms with the extra representatives would be selected (drawn) so that there were not 2 terms in a row with 4 representatives, nor 3 in a row with two representative.  And the district would be matched up with neighboring districts so that if one district had an extra representative in one term, its neighboring districts would not have an extra representative, so that the representation for a larger multi-district area would remain constant over the decade.

In Rhode Island, 93 seats (the sum of the whole number of representatives apportioned among the 26 districts) would be assigned to fixed districts through out the decade.  The remaining 9 seats (the sum of the fractions) would float from district to district throughout the decade.



The following map shows the fractional apportionment for each district (multiplied by 10) and the distribution of the fractional seats.

So the 9 floating seats would be assigned as follows:

1) Districts 11-15 in western and northern Providence County (21 total)
2) Districts 7-8 in western Kent County (8 total)
3) Districts 9-10 and 18-19 in Warwick and Cranston (16 total)
4) Districts 4-6 in Washington County (12 total)
5) Districts 20-21 in Pawtucket (7 total).
6) Districts 16 and 24-25 in North Providence and western and northern Providence city (10 total)
7) Districts 22, 23 and 25 in central, eastern, and southern Providence city (10 total)
8*) Districts 2-3 in Newport County (8 total)
9*) Districts 1 and 17 in East Providence and Bristol County (10 total)

*One of the 5 terms, the extra representative from East Providence would be assigned to Newport County.  For that term both Newport districts would have the extra representative for a total of 9.  The other 4 terms Newport County would have a total of 8 representatives.  So the distribution would:

3 terms: LD2, 3 seats; and LD2, 5 seats.
1 term: LD2, 4 seats; and LD3, 4 seats.
1 term: LD2, 4 seats; and LD3, 5 seats.

[Antonio the Sixth]

Sound quite complicated... Why not just drawing districts so that they can have an integer number of representatives ?

[jimrtex]

Sound quite complicated... Why not just drawing districts so that they can have an integer number of representatives ?

Because then you would have to unnecessarily split towns in order to get sufficient equality.  This makes elections more difficult to administer, since voters in different precincts would have different ballots.  It opens up opportunities for gerrymandering as to which towns are split, or how they are split is somewhat arbitrary. 

Every redistricting cycle, boundaries will have to be adjusted.  If multi-member districts are used, the decision whether to expand the district and maintain its number of seats, or to reduce its area and its number of seats is also subject to manipulation.  If population change is not evenly distributed, then even districts that have near the desired population may still have to be modified in order to shift population from an overpopulated area of the state to an underpopulated area.

This may be particularly unforgiving under STV.  Imagine a member who is one of a 4-member delegation.  His residence is shifted into another district, which has 3 incumbents.  They will have represented most of the constituents, while he will be unfamiliar to most voters.  While he might get more votes from his area, those who have different political allegiances might still not vote for him.

Now compare this to the fractional alternative.  There are fairly simple rules for districts.  They have to have a magnitude between 3 and 5*; avoid splitting towns and counties if possible, or crossing county boundaries.  If larger cities or counties are split, all districts should be contained within the city or county.

*A city or county with a population equivalent to between 5 and 6 may be maintained in a single district.  The alternative would be to split it into two districts with fewer than 3 seats, or place part of the city or town in another district.

Because there are a wide range of acceptable magnitudes, district boundaries don't have to be adjusted as often.  Instead you can simply adjust the magnitude of the district.  Some growth, relative to other districts?  Then increase the magnitude from 4.2 to 4.4.   Some decline, drop it to 4.0.  The actual apportionment process can be automated.  Because of the range of acceptable magnitudes, it is reasonably easy to form districts within a county.  Instead of having to district an entire state, it is more like having to district individual counties, which can be done independently.  So the initial districting process is simpler, and reapportionment is much simpler.

Grouping the fractional members together is actually pretty easy.  If we assume an average district magnitude of 4.0 and an average fraction of 0.4, then typically the floating seats will amount to about 10% of the total seats.

The final assignment of which terms a district has its extra seat is done by lot.  If a district has a fraction of 0.6, there are 5 valid patterns of terms:

1) ++0+0 (district has extra seat in terms 1, 2, and 4; with base level in 3 and 5.
2) 0++0+
3) +0++0
4) 0+0++
5) +0+0+

These patterns ensure that the district does not have an extra seat for 3 consecutive terms, nor have the base number for 2 consecutive terms.

If a district has a fraction of 0.4, then there are also 5 valid patterns:

1) 00+0+
2) +00+0
3) 0+00+
4) +0+00
5) 0+0+0

These happen to be the complementary patterns of those for 0.6.  So if you have two districts, one with a fraction of 0.4 and the other with a fraction of 0.6 (such as the two Pawtucket districts LD20 and LD21), they can be paired together.  Choose (by lot) which of 5 patterns is used for the LD21 (fraction of 0.6) and the complementary patter for LD20 (fraction of 0.4) is automatically determined.

More complex patterns can also easily be handled.  For example, the fractional seats for the 3 Washington County seats are 0.4, 0.4, and 0.2.  But a valid pattern for a fraction of 0.6 can always be split into valid patterns for 0.4 and 0.2.  So instead of having to figure out a way to arrange patterns for fractions of 0.4, 0.4, and 0.2; it can be decomposed into

(0.6) 0.4
(0.4 0.2) 0.4

Once we have determined the number of seats for each district and term (fixed at the start of the decade) the rest is trivial.

The city clerks, parties and candidates, simply check a table and see that LD20 will have 4 representatives for the next term (and election).  The parties may have to figure out a strategy.  Perhaps one current representative will decide not to run for the current term.  Or perhaps they will let the voters decide.  STV is pretty good at handling intra-party contests.

The voters would have no reason to change their ranking procedure.  And while STV may be too complicated for most voters to really understand, that does not prevent them from having enough knowledge to vote in an STV race or to vote in an STV race for 4 seats one election and for 3 the next.

If they wonder why their district has 3 representatives some elections, and 4 at the next, a newspaper article in the Nimby Naysayer gives a simple explanation:  "There are about 10,000 persons per representative in Rhode Island.  Our district of Nimby Center has about 36,000 people or the equivalent of 3.6 representatives.  Instead of giving it 4 representatives (too many) or 3 representatives (too few), it gets 3 representatives some elections, and 4 representatives at other elections, for an average of 3.6 representatives over the decade which is just about the same as the district's fair share.  The alternative of changing district boundaries would mean that 6000 persons from Nimby Center would be placed in a district based in East Nimby, or perhaps 4000 persons from North Nimby would be moved into our district which would increase voter confusion."

[Antonio the Sixth]

Yes, it makes sense, though I don't think having an 4 or 3 representatives depending to the year of the election is really the equivalent of having 3.6. It can give uncorrect representations for some elections, which could result in a party winning a majority though getting less vote.
Anyways, the best system remains a statewide election without any district.

[jimrtex]

Yes, it makes sense, though I don't think having an 4 or 3 representatives depending to the year of the election is really the equivalent of having 3.6. It can give uncorrect representations for some elections, which could result in a party winning a majority though getting less vote.
Anyways, the best system remains a statewide election without any district.

Having an STV election for a single 102-member election is unworkable.  Using a list system simply results in the election of vapid placemen and not true representatives that a district system does.  STV combines mild proportionality, while maintaining local representation and local representativeness.

Fixed apportionment is equivalent to stealing 45 cents from someone every day, and giving it someone else, and claiming that you really aren't really stealing because it was less than a dollar per day.

Variable apportionment is like the Finns rounding cash transactions to the nearest 5 cents, or the change bowl next to a cash register, where if your purchase is a couple of cents over a multiple of 5, you take a couple of pennies from the bowl, and if you get a couple of pennies in change, you toss them in the bowl.  Over time, no one comes out ahead or behind.

Demanding exactly-sized districts will resulting in a lessening of local ties to representatives as voters are moved about like cows being herded to equalize grazing.  It treats the people as subjects rather than sovereign.   The voters are being chosen, rather than doing the choosing.

The geographic stratification of the floating seats will tend to reduce political effects.  It is unlikely that moving a seat across a town boundary will produce a radical change in representation, especially when only about 10% of seats float, and they don't necessarily float every election (a fraction of 0.8, means that a district will have the larger number of representatives 4 out of 5 terms).

[minionofmidas]

Write out the other NYC districts plz. And give em some better names. Come on. District 37 is simply "Harlem".

[Antonio the Sixth]

Yes, it makes sense, though I don't think having an 4 or 3 representatives depending to the year of the election is really the equivalent of having 3.6. It can give uncorrect representations for some elections, which could result in a party winning a majority though getting less vote.
Anyways, the best system remains a statewide election without any district.

Having an STV election for a single 102-member election is unworkable.  Using a list system simply results in the election of vapid placemen and not true representatives that a district system does.  STV combines mild proportionality, while maintaining local representation and local representativeness.

What about a State-wide (or nation-wide, or any other else division-wide) repartition of the seats between parties, but based on lists coming from smaller districts ?


Here's an example.
Let's say that that we have 3 districts. Here are the results with the traditional system :

District 1 : 4 seats
Democrats : 24 votes => 2 seats
Republicans : 16 votes => 2 seats

District 2 : 3 seats
Republicans : 16 votes => 2 seats
Democrats : 14 votes => 1 seat

District 3 : 6 seats
Democrats : 34 votes => 3 seats
Republicans : 26 votes => 3 seats

Republicans eventually get 7 seats and democrats only 6, even though they have more votes.

Instead, with the system I propose, votes are counted State-wide :
Democrats : 72 votes => 7 seats
Republicans : 58 votes => 6 seats

And only after, seats got by parties are dealt between districts :

For democrats :
District 1 : 24 votes => 2 seats
District 2 : 14 votes => 1 seat
District 3 : 34 votes => 4 seats

For Republicans :
District 1 : 16 votes => 2 seats
District 2 : 16 votes => 2 seats
District 3 : 26 votes => 2 seats


Basically, this system ensures that the representation is the best possible in the final Assembly, but also that list will be made in a small constituency. This system is used for French regional elections, and also for Italian legislative elections. It makes fractional representatives rather useless because uncorrect representation doesn't harm the partisan divide in the Assembly.

[Хahar 🤔]

The Italian electoral system is terrible.

[Antonio the Sixth]

The Italian electoral system is terrible.

It's far better than most of other countries'.

I am the first one to admit that Italy really sucks on most domains, but electoral system isn't among those.