THE EXPERT WITNESS: Allegorical economics: The gerrymander shuffle (part 4)

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By John F. Sase, Ph.D.
Gerard J. Senick, general editor
Julie Gale Sase, copyeditor

“Political gerrymandering makes the incentive for most members of Congress to play to the extremes of their base rather than to the center.”
—Barack Obama, 44th President of the United States of America

Gerrymandering is the practice of manipulating the boundaries of an electoral constituency in order to favor one party or class. In the United States, Gerrymandering has been practiced since the founding of the country in order to strengthen certain political interests within the House of Representatives. Recently, in the Federal lawsuit of Gill v. Whitford, the plaintiffs alleged that voting districts were Gerrymandered unconstitutionally. The court found that the unequal treatment of Democratic and Republican voters violated the First and Fourteenth Amendments to the U.S. Constitution. Meanwhile, an anti-Gerrymandering coalition has been organized in Michigan. Common Cause Michigan (CCMI) is a nonprofit, nonpartisan advocacy organization that seeks to ensure that public officials and public institutions are both accountable and responsive to citizens. It will advocate for the passage of “Voters Not Politicians,” a Michigan-initiated anti-Gerrymandering Constitutional Amendment (votersnotpoliticians.com). This initiative hopes to create an independent redistricting commission while “removing the ability of legislators to draw district lines for partisan gain and handpick their constituents to ensure their reelection” (www.commondreams.org/newswire/2018/01/26/). In addition, State Representatives Jeremy Moss (D) of Southfield and Jon Hoadley (D) of Kalamazoo recently reintroduced legislation that they assert would end Gerrymandering in Michigan by creating a nonpartisan commission. Instead of State Legislators, this new group would have the responsibility to draw boundary lines.

Gerrymandering Defined

The term Gerrymander originated in the early 19th century as a hybrid of the name of Massachusetts Governor Elbridge Gerry and the word salamander. The name was coined to describe the supposed similarity between a salamander and the shape of a new voting district that was drawn on a map and that took effect while Governor Gerry held office in 1812.

Today, Gerrymandering may emerge through the decennial Redistricting Process that takes place in the United States. Our Census of the Population provides the measure for determining the population-distribution throughout the states. This census data is employed on the Federal level to allocate the 435 seats of the U.S. House of Representatives equitably among the fifty states. Once the decennial census has been completed, each state has the responsibility for redrawing its district borders in order to ensure equal levels of population within the districts in the state. As a result, the potential for Gerrymandering surfaces at the state level.

Michigan is one of more than thirty states in which the legislature retains the responsibility for redrawing Federal and State voting districts. Therefore, the majority party in the State Legislature controls the determination of district boundaries. This power has often resulted in Gerrymandered districts such as the following one in Southeast Michigan.

(image 1)

Typically, the majority party may attempt to manipulate the shapes of districts in order to create a more favorable map to help its party in future elections. Occasionally, the “art” of Gerrymandering results in odd-shaped districts, as politicians draw lines in order to maximize their electoral potential. Matt Grossmann, a professor of Political Science at Michigan State University, explains, “You’re trying to elect as many people from your party and as few people from the other party” (Capital News Service, 15 March 2015). If state districts can be Gerrymandered effectively, then the dominant political party may win a number of seats, disproportionately reflecting the total of votes for their party statewide.

In Michigan and the other states to the west of the original thirteen, maps are drawn generally in accordance with acceptable population-variance by using counties as the “basic building blocks” of these legislative districts. However, we note that state citizens often exhibit politico-socio-economic preference as to their place of residence. This practice results in a self-clustering of the population.

Back to Our Roots

Benjamin Franklin, George Washington, John Adams, Alexander Hamilton, Thomas Jefferson, and James Madison formed the core of the early leadership of the United States of America. In specificity to our current topic, let us consider Franklin and Jefferson. Historical records indicate that Jefferson liked and respected Franklin. Furthermore, these two polymaths shared a deep love of, and genius for, experimental science. Jefferson owned copies of numerous scientific treatises written by Franklin, a man who promoted and contributed to the useful sciences of mankind. Both men had a strong interest in the development of the compass and related tools for surveying the new country.
As well as excelling in multiple fields of study, both Franklin and Jefferson had a fascination for squares and grids. Franklin wrote about his self-amusement in the creation of Magic Squares. In 1771, he stated that, during sessions of the Continental Congress, “I was at length tired with sitting there to hear debates, in which, as clerk, I could take no part, and which were of so entertaining that I was induc’d to amuse myself with making magic squares...” (The Autobiography of Benjamin Franklin, 1793, reprinted by Dover, 1996).

Franklin referred to Magic Squares, which also are known as normal magic squares (mathworld.wolfram.com). These squares date back to Emperor Yu the Great of China in around 3000 BCE and as later detailed by Yang Hui in his book “The Continuation of Ancient Mathematical Method for Elucidating the Strange Properties of Numbers,” which was first published around 1275 CE. In modern times, such squares have been generalized in numerous ways, including the multiplication of, rather than the addition of, cells and the replacement of numbers with geometric operations. Perhaps we may find a solution to the conundrum of Gerrymandering through the work and play of Franklin and Jefferson as we consider square-mile grids and townships for the basis of redistricting.

In the following tutorial, we focus on the simple, additive 3 x 3 square along with the 6 x 6 square as used in the township design created by Thomas Jefferson for his application of the “grid” survey to the growing United States west of the Appalacians. This grid divided land into plots one mile square, each consisting of 640 acres. The grid forms the latticework that divvies fields, forests, and small towns of America into perfect square-mile sections. This plan allowed for the assemblage of 36 square-mile sections into townships and multiple townships into counties. In 1785, Jefferson drafted his survey into an ordinance to extend government authority across the Mississippi River and the Great Lakes regions. Furthermore, he suggested that this new grid-system would be less confusing than the “metes-and-bounds” method applied in the original thirteen colonies. The Land Ordinance of 1785 was the first of its kind in America and continues to affect urban, suburban, and farmland planning to the present day.

Congress passed the subsequent Land Act of May 18, 1796. It provided that “sections shall be numbered, respectively, beginning with number one in the northeast section, and proceeding west and east alternately, through the township, with progressive numbers till the thirty-sixth be completed.” The initial survey of Michigan commenced in 1815, with the Federal government contracting Douglass Houghton, Bela Hubbard, and other surveyors. The crews here usually conducted surveys in the winter because their line of sight was less hampered and they could walk across frozen lakes and ponds.

Per the 1796 Act, Michigan townships measured six miles by six miles. The survey of townships commenced at the crossing of the Michigan-Ohio Meridian, which remains apparent as Meridian Road east of Lansing, and the state Baseline, also known as Eight Mile Road. The origin point of these axes lies in a wooded area twelve miles north of Jackson, MI.

A “standard” county in the lower pennisula of Michigan contains 16 townships in a four-township-by-four-township configuration. However, the layout of the state contains a number of exceptions to this rule due to the establishment of early cities that predated the survey as well as the counties along the coast of the lakes. In respect to rectangular counties, examples include Oakland County, which contains 25 townships, and Calhoun County (between the cities of Jackson and Kalamazoo), which is composed of 20 townships.

Preliminaries

The decennial Census of the United States is mandated by Article I, Section 2 of the U. S. Constitution. This Article notes that Representatives and direct Taxes shall be apportioned among the several States according to their respective Numbers within every subsequent Term of Ten Years. The next census, which is scheduled for 2020, will be conducted largely by using the Internet.

Following our Jeffersonian line of thought, we will be able to use data from the digitally stored Census of the Population. Aggregate statistical data derived from the census is released as soon as it becomes available. Generally, the Census Bureau makes data available at the Tract level with a varying number of Tracts, depending on population density. For example, Oakland County has twenty-five Townships with between two and more than fifty Tracts per Township. However, for serious research and applications such as determining voting districts, data may be obtained in smaller units as long as summaries contain a large enough number of individuals so as not to violate personal confidentiality.

A Tutorial on Magic Squares

Our Magic Squares contain whole numbers of one to two digits. However, larger Squares may contain larger numbers. In using the Squares to equalize population, we may replace these ordinal whole-numbers with census-values while maintaining an acceptable level of variance. We can substitute mathematical algorithms to express population density in the Squares. This technique may help us to achieve higher degrees of precision. Nevertheless, we will keep our illustrative examples as simple as possible for the benefit of our wider readership within the community of Law.

Let us start with the simple 3x3 “Saturn” Square. Through rotations and reflections, we can produce eight outcome variations. In addition to the simplicity of the Saturn Square, we can extend it to create the 6x6 “Sun” Square of 36 square miles.

Following the progression for numbering implemented in the Jeffersonian survey-plan discussed above, the sequence of nine values commences at the top-right corner and concludes at the lower-left. If we add the digits in each of the three rows, we obtain the unequal sums of 6, 15, and 24. Similarly for the columns, we obtain sums of 16, 15, and 14, though the sums of the rightward and leftward diagonals both equal 15.

(image 2)

In order to determine eight equal sums, we need to rearrange the nine values in our Magic Square. We move the “1” to the middle of the bottom row, the “2” to the upper-right corner, and so forth in order to follow the inscribed path that starts at “1” and ends at “9” at the middle of the top row.

(image 3)

In performing this operation, we have rearranged the nine sub-squares. This action produces eight sets of three numbers, for which each of the sums all equal one another with a value of “15.” If our goal is to construct three districts of equal size, we have two feasible sets of nonrepeating values. Of course, the “population” residing in each of the sub-squares would not need to move. The “residents” of each sub-square would be assigned to a meta-district for voting such that the population of “4,” “9,” and “2” would be members of the same district. If the population shifts from one decennial census to the next, reassignments can be made easily without creating one of the Governor Gerry salamanders.

(image 4)

The 3x3 example is the simplest Magic Square to construct. However, let us consider the larger 6x6 version. This one parallels the conceptual layout of Thomas Jefferson’s Grid Township. Though there are many ways to number these 6x6 “Sun” Squares, we will use the sequence prescribed in the Land Act of May 18, 1796 discussed above.

The original township-layout produces a square for which the column sums equal one another. Though this aspect may be curious in its alignment, it may leave the use of the township-base open to “rigging” in respect to election outcomes if taken at face value. Nevertheless, none of the row sums of “21,” “57,”, “93,” “129,” “165,” and “201” or the diagonal sums of “108” and “114” are equal to any of the others.

(image 5)


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