Cube Root Rule Legislative Districts
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Author Topic: Cube Root Rule Legislative Districts  (Read 47276 times)
jimrtex
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« on: August 17, 2009, 11:37:46 PM »

There is a rule of thumb that a legislature should have a number of members equal to the cube root of the population being represented.  For Massachusetts this would mean a legislature of 185 members, each representing around 34,300 people.

The following maps were drawn using multi-member districts with an overall target of about 4 members.  All districts are contained within a single county, with an exception of the three smallest counties, Franklin, Dukes, and Nantucket.  Franklin is entitled to about 2 members and was combined with Hampshire.  Dukes and Nantucket, together with a population of about 0.7 members were combined with Barnstable.  Cohasset and Brookline were placed in districts with other towns in Norfolk County, even though they are discontiguous.

No cities/towns other than Boston were split.  Boston was divided into 4 districts based on  ward boundaries.  The wards are no longer are used for the city council and have a range in population of more than 5 to 1, with the largest wards in the south and smaller wards closer in to downtown area. Worcester is the 2nd largest city and has a single district with 5 members, the largest in the state.

Districts were apportioned a fractional number of members, with a resolution of 0.2.  If members were elected biennially, the number elected at each election could vary over a decade between census (eg a district entitled to 4.6 members would elect 4 representatives at 2 elections, and 5 members at 3 elections for an average of 4.6).

Alternatively, members could be elected to a fractional number of mandates, so that a popular representative might represent 1.4 mandates, and a less popular representative might represent 0.6 mandates.  In roll call votes, each candidate could vote the number of mandates he represented.








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jimrtex
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« Reply #1 on: August 24, 2009, 07:22:13 PM »
« Edited: September 07, 2009, 10:38:24 PM by jimrtex »

Edit: See modified plan which places Portland in its own district.
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Torie
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« Reply #2 on: August 25, 2009, 06:16:53 PM »

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.
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Verily
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« Reply #3 on: August 25, 2009, 07:55:42 PM »

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 theory is based on actual legislatures around the world. By coincidence, legislature size correlates strongly with the cube root of the population. (The US is, here, the exception rather than the rule.)
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Хahar 🤔
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« Reply #4 on: August 26, 2009, 12:54:39 AM »

Is America's aversion to legislators simply an outgrowth of the American individualistic ideology?
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True Federalist (진정한 연방 주의자)
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« Reply #5 on: August 26, 2009, 01:11:17 AM »

Is America's aversion to legislators simply an outgrowth of the American individualistic ideology?
More an aversion to paying for them.  The New Hampshire House is an exception to the rule as it has 400 members (roughly 1 per 3000 residents) but it pays them only $200 for the entire two tear term.
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minionofmidas
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« Reply #6 on: August 26, 2009, 12:05:19 PM »

I am not sure why the same rule should apply to state houses as to the federal tier, but please keep on with these districts. Smiley
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minionofmidas
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« Reply #7 on: August 26, 2009, 12:10:05 PM »

By that rule, the German Bundestag should have just 435 members, btw.
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jimrtex
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« Reply #8 on: August 26, 2009, 04:01:37 PM »

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.
It is more of an observation.  I don't know if there is an actual rationale for it. 

Perhaps if you started with a village with a 1000 people, and a council with 10 members each representing 100 people.  As the village grows to a town of 10,000; one side would argue for increasing the size of the council by 10-fold to maintain the level of representation, while the other side would argue that would result in too many nebbishes and losers.  So a compromise is reached, increasing the council to 21 or 22 members each representing about 465 people.

With the cube root rule, the number of persons represented is the square of the number of representatives, so that the number of persons represented increases at the 2/3 root of the total population.  If an area increased in population by 10% (about what the USA will this decade), the number of representative would increase by 3.2%, while the number each represents would increase by 6.5%.  If population growth is unbalanced you wouldn't have as dramatic a shift in representation to high growth areas.  Their share of the total representation would increase, but lower growth areas might not see an actual loss in the number of representatives.

California currently has 120 legislators, but because of the two chambers, the 40  senators each represent about 900,000 persons, and the assemblymen over 450,000, more than they can effectively represent.  And they end up with large staffs.  With a unicameral legislature, this would be reduced to 300,000 each.  With 330, they would represent 109,000 each.  You could have more of a part-time legislature and it might be possible for an ordinary citizen to get through to his representative, and the representatives may have more of a tie to the communities that elected them.
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jimrtex
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« Reply #9 on: August 26, 2009, 04:14:18 PM »

Is America's aversion to legislators simply an outgrowth of the American individualistic ideology?
When the number of federal representatives was "fixed" at 435 in 1910, the cube root rule would have suggested 451.  The USA did not reapportion after the 1920 census, because rural areas would for the first time have experienced loss of members, while industrializing areas further east would have gained representatives.  Eventually, President Hoover brokered legislation that would provide for an automatic determination of the apportionment based on the census.  Once Congress got out of the habit of considering the size of the House it has come to be seen as being set at a fixed number. 
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jimrtex
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« Reply #10 on: August 26, 2009, 04:17:49 PM »

I am not sure why the same rule should apply to state houses as to the federal tier, but please keep on with these districts. Smiley
New Hampshire just needs Rockingham County to completed.  New Hampshire and Maine have about the same population, but it is remarkable at how much more urbanized NH is.
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muon2
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« Reply #11 on: August 26, 2009, 05:07:31 PM »

Under the cube root rule IL should have about 235 legislators for 2010, compared to the actual number of total reps and sens of 177 so it isn't too far off. Interestingly IL had 236 legislators up to 1980. That year a constitutional amendment passed to cut back the number of house members from 177 to 118 based on the argument that it would save money by having fewer reps.
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Хahar 🤔
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« Reply #12 on: August 26, 2009, 10:19:15 PM »

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.

Yeah, it seems like 120 is far too much, though California really has one of the smallest legislatures per capita in the developed world.
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« Reply #13 on: August 27, 2009, 12:36:29 AM »
« Edited: August 27, 2009, 12:38:48 AM by ○∙◄☻tπ[╪AV┼cV└ »



2000 census 281M gives 655 members of Congress
2009 estimate of 307M gives 675 members of Congress

Of course, city councils are usually way off, for example, San Francisco has only 11 for a population of 800,000.
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« Reply #14 on: August 27, 2009, 08:13:54 AM »

And Ottawa has 23 + Mayor for a city of around 900,000 IIRC. And Montreal has 73 for a population of 1,600,000. But in Montreal's case, that's way too much since that gives 73 mafia crooks/Italian gangsters/egomaniacs/failures at life and politics and so forth.

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


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minionofmidas
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« Reply #15 on: August 27, 2009, 09:31:14 AM »


Of course, city councils are usually way off, for example, San Francisco has only 11 for a population of 800,000.
While Frankfurt has 93 for a population of 650,000.
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danny
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« Reply #16 on: August 27, 2009, 06:07:21 PM »

Israel would have 195.
Oh god, not another 75 of them.
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muon2
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« Reply #17 on: August 27, 2009, 09:06:26 PM »


Of course, city councils are usually way off, for example, San Francisco has only 11 for a population of 800,000.
While Frankfurt has 93 for a population of 650,000.

Similarly Chicago has 50 aldermen, one per ward, and the rule would predict 142 for 2.85 M people.

For smaller cities divided into wards IL state law provides a statutory number of aldermen (two per ward) on the city council, though that number can be changed in certain cases (and generally reduced) by referendum or ordinance. IL law seems to use just under half the number of aldermen predicted by the cube root rule.

Population Range  Aldermen  Cube Root Prediction
up to 3 K60 to 14
3 K to 15 K815 to 24
15 K to 20 K1025 to 27
20 K to 50 K1428 to 36
50 K to 70 K1637 to 41
70 K to 90 K1842 to 44
90 K to 500 K2045 to 79

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Hatman 🍁
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« Reply #18 on: August 27, 2009, 09:25:28 PM »

It's just ridiculous that California's Senate districts are larger than US House Districts.
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Torie
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« Reply #19 on: August 27, 2009, 10:39:26 PM »


Of course, city councils are usually way off, for example, San Francisco has only 11 for a population of 800,000.
While Frankfurt has 93 for a population of 650,000.

Similarly Chicago has 50 aldermen, one per ward, and the rule would predict 142 for 2.85 M people.

For smaller cities divided into wards IL state law provides a statutory number of aldermen (two per ward) on the city council, though that number can be changed in certain cases (and generally reduced) by referendum or ordinance. IL law seems to use just under half the number of aldermen predicted by the cube root rule.

Population Range  Aldermen  Cube Root Prediction
up to 3 K60 to 14
3 K to 15 K815 to 24
15 K to 20 K1025 to 27
20 K to 50 K1428 to 36
50 K to 70 K1637 to 41
70 K to 90 K1842 to 44
90 K to 500 K2045 to 79



Those numbers in a city council I think would generate chaos myself.
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muon2
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« Reply #20 on: August 27, 2009, 11:51:22 PM »
« Edited: August 27, 2009, 11:56:13 PM by muon2 »


Of course, city councils are usually way off, for example, San Francisco has only 11 for a population of 800,000.
While Frankfurt has 93 for a population of 650,000.

Similarly Chicago has 50 aldermen, one per ward, and the rule would predict 142 for 2.85 M people.

For smaller cities divided into wards IL state law provides a statutory number of aldermen (two per ward) on the city council, though that number can be changed in certain cases (and generally reduced) by referendum or ordinance. IL law seems to use just under half the number of aldermen predicted by the cube root rule.

Population Range  Aldermen  Cube Root Prediction
up to 3 K60 to 14
3 K to 15 K815 to 24
15 K to 20 K1025 to 27
20 K to 50 K1428 to 36
50 K to 70 K1637 to 41
70 K to 90 K1842 to 44
90 K to 500 K2045 to 79



Those numbers in a city council I think would generate chaos myself.

Not at all. With a strong committee system and a mayor who understands procedure, the full council meetings can be to the point. The council  where I live has 14 and rarely has a chaotic meeting. The same statement applies to the town next door which also has 14 on the council.

Granted, many large cities reduce the size through referendum. For example, Aurora has 188 K population but uses only 12 aldermen. They reduced the 10 wards to one alderman per ward and added two at-large aldermen.
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« Reply #21 on: August 28, 2009, 09:23:03 AM »

Paris has 163 seats in its city council. Marseille, IIRC, has 101 or something and the current makeup was similar to the one in the 2007-2009 US Senate.
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Torie
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« Reply #22 on: August 28, 2009, 10:21:33 AM »

muon2, when I used the word "chaos" I was thinking of Chicago having 142 aldermen. I "know" Chicago. Smiley
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Queen Mum Inks.LWC
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« Reply #23 on: August 28, 2009, 10:33:31 AM »

Michigan should have 215 instead of 148, according to the rule, so that would be a sizeable difference.
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Vepres
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« Reply #24 on: August 28, 2009, 05:43:37 PM »

Seriously, only as many gigantic egos as are necessary, any more and, well, *shudder*
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