Texas Weighted Voting
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jimrtex
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« on: June 09, 2016, 07:40:29 PM »

This is an experiment in use of weighted voting for the Texas House of Representatives. Basic rules:

(1) There will be 150 representatives, with a total of 150 votes.
(2) Each representative will have between 2/3 and 11/3 votes.
(3) A single county may have multiple representatives, who will evenly divide the county's voting weight.

To the extent possible:

(4) Each county with more than 1/150 of the population will have its own representative(s).
(5) Multi-county districts will have one representative.

To the extent practicable:

(6) Districts and number of representatives for a district will not change between censuses (that is, change will only occur to satisfy criteria (1) through (5).
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jimrtex
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« Reply #1 on: June 09, 2016, 11:30:53 PM »

1850

In the first census after accession, 58 of 78 counties had enough population for one representative and formed a single-county district. Eight other counties had a large fraction of a representative and also formed a single-county district, since there was no adjacent small counties to combine them with.

The remaining 12 counties were placed in five multi-county districts.

The 71 districts were apportioned floor(population/quota) representatives, for a total of 116 representatives. Districts with between:

0 < votes < 1
11/3 <= votes < 2
22/3 <= votes < 3

were apportioned an additional representative. This brought the total number of representatives to 150.

Medina County was only entitled to 0.641 representatives, but was still made a single-county district. It was totally surrounded by Bexar County. It it were combined with Medina it would have close to five votes shared among 5 representatives, and swamping Medina County. There were no nearby counties to combine with Medina County. It was felt that the small deviation below 2/3 of a vote was superior to any alternative.



Bexar County included the entire western part of the state, though it was likely very few persons were outside San Antonio.







Outline maps and population data courtesy of:

Minnesota Population Center. National Historical Geographic Information System: Version 2.0. Minneapolis, MN: University of Minnesota 2011.

NHGIS web site
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jimrtex
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« Reply #2 on: June 11, 2016, 05:49:12 PM »
« Edited: June 13, 2016, 04:01:51 PM by jimrtex »

1860

Texas grew by 184% during the decade, as the population grew from 1417 per representative to 4028. The number of counties increased from 79 to 154, though 21 were unpopulated.

When a county was created from another, the remainder of the original county was treated as a continuation of the representation unit, and the new county as totally new. Thus if there were a county that was entitled to two representatives was split in two, the remainder of the original county would be treated as losing a representative, and the new county being treated as a new county with a representative.

71 districts had been apportioned 150 representatives in 1850.

Of these, 16 had insufficient population to maintain the same number of representatives (voting weight per-representative less than 2/3. The number of representatives for these districts was reduced to the maximum possible. Three single-county districts: Jackson, Jefferson, and Medina no longer had enough population for their own district. With the reduction in representation, there were 128 representatives apportioned.

10 districts had increased in population share such that they required additional representatives to keep their voting weight per representative below 4/3. The number of representatives for these districts was increased to the minimum possible. With the increase in representation, there were 139 representatives apportioned.

12 counties now had enough population to form a single-county district with a total voting weight greater than one. 8 of these counties were new counties, and four had been part of a multi-county district. Three of the counties were large enough to require two representatives. The addition of these 15 representatives meant 154 representatives were apportioned.

None of the multi-county districts could be maintained. Three districts had counties promoted to single-county district, and one had to be divided because of its population increase. The fifth was in a location that it could not be maintained. For accounting purposes, these districts were dissolved, along with five additional representatives that they had been tentatively apportioned above, resulting in 144 apportioned representatives, though some residual population would need to be placed in new districts. The remaining population was equivalent to 20.69 representatives.

Three counties had population sufficient for a voting weight of more than 2/3, but less than one, but could not be combined into a multi-county district. In addition, Presidio because of its isolation was attached to El Paso, even though El Paso had a total voting weight greater than one. With these changes, there were 147 apportioned representatives, and a residual population equivalent to 17.75 representatives.

Because forming this additional population into new districts will result in more than 150 representatives, an attempt was made to keep their population on the high side. 15 new multi-county districts were created. Also additional counties were added to the Gillespie district. These new districts allocated the entire state to a district, but with 162 representatives apportioned, an excess of 12.

16 single-county districts were identified which could lose a representative, yet maintain an voting weight less than 4/3 per representative. For each of the 16 districts the harmonic mean between the current number of representatives, and one fewer was calculated, and divided into the population. The 12 districts with the smallest quotients lost a representative.

With all these changes, there are now 93 districts, with a net shift of 36 representatives.



Generally, growth was to the west, with also some northward growth away from the coast.

Districts that lost representatives are in red. They are generally in the east, with a few further west which lost representation as a result of being divided into new counties.

Districts in tan had no change in representation. Counties that formed a single-county district in 1850, but expanded in 1860 to include additional counties are in pale pink, and include districts based in Gillespie, Jackson, Jefferson, and Medina counties.

Districts in green gained representation. Districts in the brighter blue are new single-county districts. They are generally in the west. Freestone, Marion, Trinity, and Wood were newly created during the decade, and represent reorganization more than growth.

The two blue-green districts in the Coastal Bend area are a result of a division of a district as well as adding territory. The pale blue districts are new multi-county districts mostly on the frontier.



49 districts have a single representative. 44 districts have more than one representative, with 101 representatives among them. The multi-member districts are generally in an from San Antonio to Marshall, with addition districts towards the west south of the Red River.














Outline maps and population data courtesy of:

Minnesota Population Center. National Historical Geographic Information System: Version 2.0. Minneapolis, MN: University of Minnesota 2011.

NHGIS web site
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jimrtex
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« Reply #3 on: June 13, 2016, 12:50:14 PM »
« Edited: June 15, 2016, 12:14:38 AM by jimrtex »

1870

Texas grew by 35% during the decade, as growth on the frontier stalled during the Civil War. Only three counties were added, Hood, Kendall, and Wilson, one was deleted, and Bexar District was created. Cass and Buchanan counties were renamed Davis and Stephens.

93 districts had been apportioned 150 representatives in 1860.

Of these, 12 had insufficient population to maintain the same number of representatives (voting weight per-representative less than 2/3. The number of representatives for these districts was reduced to the maximum possible. Seven of these districts no longer had enough population for a representative. With the reduction in representatives, there were now 138 representatives apportioned.

15 districts had increased in population share such that they required additional representatives to keep their voting weight per representative below 4/3. The number of representatives for these districts was increased to the minimum possible. Five of the districts were multi-county districts which were slated for division. With the increase in representation, there were 153 representatives apportioned.

Brazos and Madison had formed a single-representative district, and were divided into single-county districts. Brazos was apportioned two representatives, resulting in one additional representative being apportioned.

Six districts along the coast which had fallen below the population need for a representative were merged, resulting in three addional representatives, for a total of 157 representatives.

One multi-county district along the southern border could not be split, and shed a county to remain a single-representative district. A multi-county district along the northern border which had fallen below the threshold for a representative was expanded to keep the representative. These two changes cancelled each other, leaving us at 157 representatives.

The addition of Kendall caused two Hill Country districts to be reorganized into three districts. South of San Antonio, the addition of Wilson caused a district to be divided into two districts. This resulted in apportionment of 159 representatives.

Four single-county districts were identified which could lose a representative, yet maintain an voting weight less than 4/3 per representative. These four districts lost a representative, giving us a total of 155 representatives, five more than the 150 permitted.

Thus after mandatory or possible reductions, required increases, straightforward mergers and division, and accommodating the three new counties, there were five too many representatives. More radical change was necessary.

In the northwest, there had been four districts. Two had been divided, and the addition of Hood permitted the other two districts to be maintained. All were on the small side. By adding Hood to the single-county Parker, it was possible to convert the two divisions into trims, maintaining the existing single-representative districts with less territory. The population trimmed off was added to other districts. As a result, two representatives were eliminated.

The addition of Kendall, had resulted in the reorganization of two Hill Country districts into three. By adding Kendall to the single-county Comal, it was possible to reduce the Hill Country districts back to two. The addition of Wilson had resulted in the division of a district south of San Antonio. By including a Goliad based district, it was possible to absorb Wilson without adding a district. These two changes resulted in 151 representatives, one more than the permitted.

No other simple modifications of multi-county districts were identified. Instead Guadeloupe was reduced to a single representative district. Guadeloupe had a population equivalent to 1.334, six persons more than 4/3 of the quota, so this was a minimal violation of the rules.

With all these changes, there are now 92 districts, with a net shift of 13 representatives. 73 of the districts were single-county districts with 131 representatives. This represents 87% of the representatives which were the result of simple apportionment. They form a solid block of counties generally east of the Balcones Escarpment, except for an area along the coast.

Of the 19 multi-county districts, nine are in West Texas, six in South Texas, and four along the coast.



Generally, growth continued to the west, with also some northward growth away from the coast. An exception was Harris and Galveston

Districts with no change in composition or number of representatives are in tan. For, these 54 districts with 94 representatives, the only change was in the voting weights.

Districts that lost representatives are in red. They are generally in the east, or closer to the coast. These nine districts lost 10 representatives, and were left with 14 representatives. Guadeloupe contributed some of its area to the formation of Wilson.

Three districts in salmon along the coast represent mergers of former single-representative districts, producing a loss of three representatives.

Five districts in pink expanded in area, and thus are larger, but still have one representative.

Districts in green gained representation. They were generally further from the coast along the axis of the Brazos River. Many had been created in 1860, and now surpassed the 4/3 of a quota needed for a second representative. The 11 districts gained 11 representatives for a total of 24.

Two districts in turquoise are new. Madison is a result of the split of the Brazos-Madison district, which had one representative. After the division, Brazos has two representatives and Madison one, for a net gain of two. The other new district is along the Rio Grande with its population concentrated in the Laredo area. It was formed from the district extend to the Hill Country, plus Zapata.

Four districts in light green shed part of their area. Rather than being divided, they shed part of their area to remain a single-representative district.

Four districts in blue can be regarded more as reorganizations rather than specifically areas that gained or loss representation.



44 districts have a single representative. 48 districts have more than one representative, with 106 representatives among them. The multi-member district area has shifted somewhat to the west.
















Outline maps and population data courtesy of:

Minnesota Population Center. National Historical Geographic Information System: Version 2.0. Minneapolis, MN: University of Minnesota 2011.

NHGIS web site
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jimrtex
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« Reply #4 on: June 15, 2016, 02:05:08 AM »
« Edited: June 15, 2016, 12:36:05 PM by jimrtex »

1880

Texas grew by 94% during the decade and 69 new counties were created. 54 of the new counties filled the Panhandle and South Plains with empty boxes - there were only about 2500 people counted here. 12 new counties were created in eastern Texas, these additions completed the modern map in this area except for minor boundary changes. With the growth came large-scale shifts, as only 61 of 92 districts remained intact, and 28 representatives shifted between districts.

92 districts had been apportioned 150 representatives in 1860.

Of these, 24 had insufficient population to maintain the same number of representatives (voting weight per-representative less than 2/3. The number of representatives for these districts was reduced to the maximum possible. Eleven of these districts no longer had enough population for a representative. With the reduction in representatives, there were now 125 representatives apportioned.

17 districts had increased in population share such that they required additional representatives to keep their voting weight per representative below 4/3. The number of representatives for these districts was increased to the minimum possible. Ten of the districts were multi-county districts which were slated for division. With the increase in representation, there were 147 representatives apportioned.

The population of the new counties and the districts that could no longer supported a representative amounted to the equivalent of 12.6 representatives, that will have to be accommodated by new or adjusted districts.

Four counties which had a voting weight of less than 2/3, had no neighbors with a voting weight less than one. So while the smaller counties could not support a representative, their neighbors would ordinarily be entitled to be a single-county district. This conflict was resolved by attaching the smaller county to their smallest neighbor, and treated for apportionment and electoral purposes as a single unit, sometimes sharing more than one representative. This has come to be known as the Rockwall Rule, after Rockwall County.

The Rockwall Rule districts were:

Rockwall attached to Kaufman (2 representative)
Delta attached to Hopkins (2 representatives)
Rains attached to Wood (2 representatives)
Madison attached to Walker (2 representatives)

In the first three instances, the smaller county had been created, at least in part from the county it was attached to.

In the eastern part of the state, 12 new districts were created, eight as the result of mergers of districts that no longer could support a representative; three new districts for new counties: Gregg, Lee, and Waller; and one for Hood which was detached from Parker plus the new county of Somervell.

In dividing districts in the west, one additional district was created beyond the additional estimate.

These changes resulted in an apportionment of 161 representatives, eleven more than the target.

Six single-county districts were identified which could lose a representative, yet maintain an voting weight less than 4/3 per representative. These six districts lost a representative, giving us a total of 155 representatives, five more than the 155 permitted.

Thus after mandatory or possible reductions, required increases, straightforward mergers and division, and accommodating all the new counties, there were five too many representatives. More radical change was necessary.

In the southeast and along the coast above the Coastal Bend, districts were rearranged to eliminate two representatives. These areas had lost population share, and thus the districts were a bit on the low side in population.

In the southwest, a representative was saved by converting two 2:1 splits, into a single new district formed from parts of the 1870 districts. The 1870 districts had only modestly qualified to be divided, so it was fairly easy to convert into a 3:2 split. A similar situation existed in the Hill Country.

The final representative necessary to reduce the total to 150 was in  the area west of Fort Worth, where three single-member districts had been divided into 12 districts electing 14 representatives. This area was treated as it it were entirely new, with the 3 existing districts ignored. A reduction to 11 districts electing 13 representatives achieved our goal of 150 representatives.

With all these changes, there are now 100 districts, an increase of eight with a net shift of 27 representatives. 67 of the districts were single-county districts with 113 representatives. In addition there were four Rockwall Rule districts with 8 representatives.

Of the 29 multi-county single-representative districts, 13 are in West Texas, six in South Texas, three above the Coastal Bend, five in the southeast, and two in East Texas, largely due to the creation of three small counties from Titus and Upshur.



Growth was concentrated in the northwest, particular from Dallas west. Texas had a different most populous county for the 4th census in a row: 1850 Harrison; 1860 Rusk; 1870 Washington; and 1880 Grayson.

Districts with no change in composition or number of representatives are in tan. For, these 39 districts with 66 representatives, the only change was in the voting weights. To maintain population share, a county needed to grow by 94%, so these counties are not low growth or no growth areas.

Districts that lost representatives are in red. They are generally in the east, or closer to the coast. These sixteen districts lost 17 representatives, and were left with 24 representatives. Some of the losses can be attributed to creation of new counties.

Six districts in deep pink, in the southeast and northeast represent mergers of district. Five districts in ligher pink expanded in area, and thus are larger, but still have one representative.

Districts in green gained representation. They were concentrated in the Dallas Area. This did not represent development of the Metroplex, but the opening of this area to farming which would later contribute to development of trading centers. Faced with a requirement to gain faster than 94% to gain representation, there were only six gainers. They had a total of 14 representatives, an increase of six.

17 districts were new, in a lighter green, including two new single-county districts, Cooke and Wise, with two representatives each. They were concentrated in the northwest, where an area with 3 representatives in 1870 now had 13 representatives. Three were new counties in the eastern part of state, where their creation contributed to the loss of representatives to the counties they had been created from.

Six districts in light green shed part of their area. Rather than being divided, they shed part of their area to remain a single-representative district (Parker shed Hood and gained a representative).

Four districts in blue are Rockwall Rule districts, where a smaller county has been attached to a larger county that would otherwise been a single-county district. The change in representative is relative to the area at the previous census.




53 districts have a single representative. 44 districts have two representatives, and only three have three representatives. 97 of the 150 representatives are elected from multi-member districts. The multi-representative area continued to shift westward.



















Outline maps and population data courtesy of:

Minnesota Population Center. National Historical Geographic Information System: Version 2.0. Minneapolis, MN: University of Minnesota 2011.

NHGIS web site
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jimrtex
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« Reply #5 on: June 16, 2016, 09:03:08 AM »

Starting Over

I found that the initial set of rules that required there be 150 representatives resulted in too many changes beyond those necessary to ensure each representative had between 2/3 and 11/3 votes.

For example if a multi-county district had increased in population share such that it was entitled to 1.5 representatives it would be split. But the resulting districts would tend to be on the small size (0.75 or so each), which would result in too many representatives, and require additional changes. For example, if two adjacent districts had a total voting weight of 3.0, they might be first divided into four districts of roughly 0.75 voting weight, and then reorganized into three districts of roughly 1.0 voting weight.

If the initial division into four districts had remained in place, then if the area continued to grow, the new districts might stay in place for a census or two. But the three larger districts would likely require more changes in subsequent censuses. Thus we are violating the principle of stability.

This is an experiment in use of weighted voting for the Texas House of Representatives. Basic rules:

(1) There will be approximately 150 representatives, with a total of 150 votes.
(2) Each representative will have between 2/3 and 11/3 votes.
(3) A single county may have multiple representatives, who will evenly divide the county's voting weight.

To the extent possible:

(4) Each county with more than 1/150 of the population will have its own representative(s).
(5) Multi-county districts will have one representative.

To the extent practicable:

(6) Districts will not change between censuses (that is, change will only occur to satisfy criteria (1) through (5).
(7) The number of representatives for single-county multi-representative districts may change if it will result in the total number of representatives becoming closer to 150.
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jimrtex
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« Reply #6 on: June 16, 2016, 09:35:33 AM »

1850

In the first census after accession, 58 of 78 counties had enough population for one representative and formed a single-county district. Seven other counties had a large fraction of a representative and also formed a single-county district, since there was no adjacent small counties to combine them with.

Medina County was only entitled to 0.641 representatives, but was still made a single-county district. It was totally surrounded by Bexar County. It it were combined with Medina it would have close to five votes shared among 5 representatives, and swamping Medina County. There were no nearby counties to combine with Medina County. It was felt that the small deviation below 2/3 of a vote was superior to any alternative.

Bexar County included the entire western part of the state, though it was likely very few persons were outside San Antonio.

The remaining 12 counties were placed in five multi-county districts.

The 71 districts were apportioned floor(population/quota) representatives, for a total of 116 representatives. Districts with between:

0 < weight < 1
11/3 <= weight < 2
22/3 <= weigh < 3

were apportioned an additional representative. This brought the total number of representatives to 150.

1850 Apportionment



1850 Vote Weight/Representative



Ideally, this would be randomly distributed, with more extreme values for single-member districts.



Outline maps and population data courtesy of:

Minnesota Population Center. National Historical Geographic Information System: Version 2.0. Minneapolis, MN: University of Minnesota 2011.

NHGIS web site
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