Measuring Deviation in Hudson
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  Measuring Deviation in Hudson
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jimrtex
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« on: May 11, 2015, 03:06:14 AM »

I am experimenting with Google Sheets.  Does the following link work?

Measurement of Deviation

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smoltchanov
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« Reply #1 on: May 11, 2015, 05:47:40 AM »

Seems so
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jimrtex
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« Reply #2 on: May 11, 2015, 09:26:20 AM »

Can you see the formulas?
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smoltchanov
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« Reply #3 on: May 11, 2015, 11:14:35 AM »


Yes
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jimrtex
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« Reply #4 on: May 11, 2015, 06:20:12 PM »
« Edited: May 16, 2015, 06:20:12 AM by jimrtex »

The first spreadsheet, 'Hudson Common Council, Corrected Population, Dunn Proposed Weights' is based on a plan proposed by Torie, based on the correct ward lines, but apparently dividing the population of the Firemen's Home between wards 4 and 5.

This presentation is to examine the measurement of deviation, and show it to be consistent with the measurement of deviation for other apportionment methods, such as equal population districts, rather than to critique Torie's proposed weights.

The basis of "one man, one vote" is that each voter has equal influence over decisions of a representative body.  Typically, "voter" is interpreted to mean each person who lives in a district, regardless whether they are old enough to vote, or eligible to vote.   There has never been a definitive answer by the SCOTUS of what should or must be used.

It is presumed in a representative democracy that each voter in a district has equal influence over his district's representative, with the exception of stranded minority voters, whether political or racial (ethnic).  In turn, in a legislative body, where each representative has one vote, they are presumed to have equal influence.  Thus when comparing the influence of voters from throughout a city or state, they have should approximately equal influence over legislation regardless where they live, just as they would have equal influence in a direct election for mayor or governor, or a ballot measure.

The SCOTUS has accepted the use of multi-member districts, so long as they don't strand minority voters.   If a district has roughly seven times the population of an ideal district, and elects seven representatives, then it comports with one man, one vote.  While the influence of a voter in the district is only 1/7th of that of a voter in a single-member district, the collective influence of the legislators from the district is seven times as great as the influence of a legislator from a single-member district.  The principle of one man, one vote is upheld when representation is proportional to population.

It is a small step, mathematically at least, to go from seven legislators exercising one vote each, to one legislator from the larger district exercising seven votes.  Or perhaps if the district actually had a population 7.2 times the ideal, having seven representatives with 1.03 votes each, or perhaps 3 representatives with 2.4 votes each, or 2 representatives with 3.6 votes each.  In any case, the principle of one man, one vote is upheld when representation is proportional to population.

Our analysis begins with the population of each ward (Column B).  When comparing population to representation, it is simple to compare population share (percentage of the total population) and representation share (percentage of total representation).  Column C is the population share of each ward.

Allocation of Council President's Vote

Each ward in Hudson has two alderman who exercise the weighted vote shown in Column D.  In addition, the Council President is elected citywide, and has his own weighted vote (624).  The total weighted vote is 7024.

We can allocate the president's voting among the five wards based on their population share.  For example, Ward 1, with 9.26% of the population, is allocated 9.26% of the president's weighted vote of 624 (624 x 9.26% = 57.79).  The allocation of the president's vote is shown in Column E.  The total weighted vote for each ward is the sum of the weighted vote for the two aldermen from the ward, and the ward's allocated share of the president's weighted vote.  This is shown in column F.  The representation share (percentage of the total weighted vote) is calculated in column G.

While this allocation of the president's vote is reasonable, the legal precedents for doing so are not overwhelmingly strong.   Andrews v Koch concerned the New York city council.  It had 35 members elected from single-member districts of roughly equal population; 2 members elected from each of the five boroughs; and the council president who was elected citywide.  The single-member districts did not totally conform to borough boundaries.  Two districts were shared between Manhattan and Bronx boroughs, and one was shared between Staten Island and Brooklyn.  80% of the population of this latter district was on Staten Island, and thus 0.80 of the district was attributed to that borough, and 0.20 to Brooklyn.  Staten Island had another district wholly to itself.  Adding two members elected borough-wide gave the borough a total representation of 3.80 members of 45 total (8.44%), even though, in 1980, it only had 4.98% of the city population, and was thus grossly overrepresented.  But New York was not making the case that the borough members were representing the people who lived in the borough, but rather that they represented the political interest of the borough since they were elected in a way that ensured minority political representation in each borough (a Democrat on Staten Island, and a Republican in the other 4 boroughs).  

Had New York City stopped at apportioning Staten Island 1.80 of 35 districts total (5.14%), they would have been well within the the safe harbor of relative deviation less than 5% (at 3.27%).  It was when they added the borough members that they violated equal protection.  In addition, the court did not factor in the council president who was elected citywide.  In any case, his effect would have been quite small, serving only to reduce Staten Island's share of representation from 8.44% to 8.36%.

Board of Estimate v Morris concerned the composition of the Board of Estimate of New York City, which was comprised of the 5 borough presidents, the mayor, the city controller, and the the city council president.  None of the eight board members were directly elected to the board, but rather served in an ex officio capacity.   The borough presidents had one vote, while each of three officials elected citywide each had two votes.  

New York had originally argued that the Board of Estimate was not a legislative body, and therefore was not subject to one man, one vote.  After the courts had rejected this argument, New York made the argument, based in part on the Banzhaf power index, that the citywide officials could effectively control the board, so that it did not matter that Staten Island and Brooklyn each elected one member, despite Brooklyn having more than six times the population.  They simultaneously argued that the board usually went along with the borough president with regard to expenditures in their district.  The district court and the 2nd circuit rejected the use of the Banzhaf power index, and also found that the citywide officials should not be considered in determining whether one man, one vote was satisfied.  To these lower courts, the five boroughs were treated as single-member districts with widely disparate populations, with the citywide officials simply ignored in determining whether one man, one vote was satisfied.

The SCOTUS upheld most of the decision by the 2nd Circuit and the district court, but overturned the part of the decision that said that the citywide officials should be ignored.  The method of calculating the effect of the citywide officials had not been adjudicated by the lower courts, but the SCOTUS found a calculation in some of the briefs, that showed a deviation far beyond that permitted by the court.  In essence, the SCOTUS said that the lower court should have included the citywide officials in calculation, but that for compliance with one man, one vote, it did not matter.

In a city council that has members elected from single-member districts, and also members elected citywide (or which the mayor is an ex officio member of the council), the inclusion of the citywide members has little effect on the one man, one vote analysis.  For example, if Hudson had five equal-population districts, each of which elected two alderman, it would be expected that the districts would have between 19% and 21% of the city population (19% is 95% of 1/5th of the population, 21% is 105% of 1/5th of the population, so that the relative deviation of the district populations would be within 5% of the ideal district population.  This would permit a range of districts populations from 1220 t0 1348, with 1281, the ideal.  If the council president is factored in, the permitted range would be expanded slightly to 1214 to 1355.

Summary: Though the practical effect is quite small, the election of the council president should be included as part of a comprehensive analysis of one man, one vote that is applicable to both weighted and unweighted configurations, and legislative bodies where members are elected from overlapping areas.  The method used is consistent with that used in the two New York City cases of Andrews v Koch and Morris v Board of Estimate.


 
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