Creative Math

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Heroes / Repairing the System

I believe that imagination, not logic, is the essential ingredient in good legal reasoning.  But imagination need not be vague or dreamy. Sometimes the imaginative solution to a thorny legal problem can be as clear and simple as 1,2,3.

A good example is found in a recent case involving the recurring evil of political gerrymanders. This NYT editorial tells the story well.

“Gerrymander” is a term most people have heard of, but few understand. It’s the name history has assigned to the dishonorable tradition of political parties in power drawing the lines for election districts to favor their chances of winning.

Here is a simplified example of political gerrymandering. The State of Dairyland has a total of 100 voters, 60  Democrats and 40  Republicans. They are to be divided into 10 election districts of 10 voters each. If the Republicans are in power, they can decide how many Democrats and how many Republicans will be in each district by use of sophisticated computer programs. By clever drawing of the district lines they can turn their 40% of the total vote into the election of 60% of their candidates. Let’s be clear—when Democrats are in power, they do the same.

Here is how it works in my fictional Dairyland. The Republicans draw district lines so that the Democrats “waste” votes in a few landslide victories—they might draw the lines in Districts 1-4 so the Democrats win all four races by a 9-1 vote. That means that there are only be 24 Democratic votes (60-36)) left for the other 6 districts. This will enable the Republicans to win the  six districts 6 votes to 4 by also gerrymandering those districts.

The Republicans have transformed their 40 % of the votes into victory in 60% of the races. The reason the Republicans can perform this magic is that they have designed the system to ensure that the Democratic voters cast 12 “wasted” votes. These are the 12 votes in Districts 1-4 that they did not need to win. They needed six to win, but got 3 surplus votes in each of the four districts, 12 votes that would have brought them victory in two or more of Districts 5-10. The voters voted democratic, but the gerrymandered system created Republican legislators who will enact Republican policies.

This is not an occasional freak occurrence in the United States, but pretty much business as usual. My Dairyland example is a simplified hypothetical, but it does show  how Republican-controlled state houses can and have in the recent past  drawn election district lines that permit them to transform a minority of the votes into a majority of elected state representatives in states all across the country. Wisconsin is a good example. Wisconsin Republicans in 2012 were able to create the election districts that allowed them to elect over 60 percent of the members of the Wisconsin Assembly even though they received only 49% of the votes.

This sad situation exists despite the fact that partisan gerrymandering clearly violates the basic democratic principle that each voter should have equal voice. But persuading courts to mandate effective remedies for partisan political gerrymanders has proved difficult because it is impossible to draw districts that in no way favor one party or the other to some degree, and therefore you get into messy arguments about how much unfairness is too much.

That’s where the creative math comes in. Democrats in Wisconsin challenging the 2012 Wisconsin election were represented by University of Chicago law professor Nicholas Stephenopolous who made an argument that was not in the least “messy”; it introduces a mathematical formula that quantifies the discriminatory effects of the Republican gerrymander and provides the court a simple numerical answer to when the discriminatory effects violate the Equal Protection Clause.

The Democrats’ lawyers argued that that court should take all the “wasted” Democratic votes in the districts Democrats won and subtract from this number all the votes Republicans “wasted” in the districts they won. Here’s the math. The Democrats received 3 more votes than the 6 they needed to win in each of districts 1 -4 while the Republicans got  only the six votes they needed to win in Districts 5-10. The Democrats “wasted” 12 votes and the Republicans didn’t waste any.  Subtract 0 from 12 and you get 12.  That is the  total  number of “wasted votes.”  If you want to find out how great a percentage the “wasted” votes were of the total votes cast, you divide that 12 by 100, the total number of votes cast.  You arrive at an “efficiency gap” of 12%. a percentage well above what could be explained by factors other than intentional gerrymandering.

I want to emphasize the creative aspects of Stephenopolous’ argument. One is its ability to identify and isolate the constitutional evil perpetrated by political gerrymanders. Twelve Democratic voters in those heavily democratic districts had no real voice in the election, and their silence was a direct and intentional consequence of how the Republicans set the district lines. These votes were not so much “wasted” as nullified by design. Twelve percent of Wisconsin voters (and 20% of the Democratic voters) in the election were silenced by gerrymander, a result completely out of synch with our constitutional ideal of “one person, one vote.”

Stephenopolous’ second creative move was to translate the constitutional injury into a simple numerical formula easy to apply and difficult to ignore. Judges in these cases are faced with scores of varying fact situations. The “equity gap” formula provides them  a simple formula that focuses on the constitutionally relevant factors.

I am happy to report that a three judge U.S. District Court panel in Wisconsin has agreed with plaintiffs in the Wisconsin case by a 2-1 majority– both on the methodology and the conclusion. It’s important to note that all three judges were Republican appointees. The case might be appealed to the Supreme Court which has been looking for an objective norm to decide partisan gerrymander cases. The “efficiency gap” argument might just become the law of the land.

If so, we will have to credit a very creative law professor. Of course, Stephenopolous’ argument is also rigorously logical, but it is logic in the service of imagination. That’s the way it  is with a good legal argument.


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