When and How Should Courts Use Math?

In Gill v. Whitford, the Supreme Court will decide whether and when partisan gerrymanders violate the First and Fourteenth Amendments.  Plaintiffs claim that Wisconsin’s electoral map, drawn to afford Republicans a significant partisan advantage in the legislature, deliberately dilutes the votes of certain voters and penalizes them for their viewpoints/political beliefs.  Gill‘s threshold question of whether the longstanding but corrosive practice of partisan gerrymandering is unconstitutional is a difficult one.  However, the question of how courts should determine whether an unconstitutional partisan gerrymander has occurred is even thornier.

Some scholars propose using a test called the “efficiency gap,” which measures how many votes are “wasted” by each party.  Wasted votes are defined as votes above the number needed to win in a winning district and all votes in a losing district.  The fewer the votes a party wastes, the more likely it has engaged in partisan gerrymandering.  Those who object to the use of the efficiency gap argue that it does not measure the fair translation of votes to representatives in single-member districts.

One reason the Justices have been reluctant to declare partisan gerrymandering unconstitutional is because of the Court’s wise skepticism about incorporating math and statistics into its jurisprudence.  Law is a methodology that relies mostly on analogy, logical reasoning, and critical interpretation of text.  Lawyers and judges are not trained as experts in math, or in any social science.  The assessment and application of complex, mathematically-based concepts is not within their institutional expertise.  However, law and math share many similarities, even if the law has normative elements and math aims to be purely descriptive.  Mathematical principles, like legal rules, are explanatory abstractions that provide guidance, uniformity, and consistency to whatever fits within its parameters.  Statistics, like law, tries to fairly account for a large number cases with a small amount of data, and ultimately is open to subjectivity and interpretation.  In addition to these similarities, courts already incorporate math and statistics in a wide-ranging number of contexts, from the evaluation of scientific evidence of causation in toxic torts cases to the examination of the false positive rate of drug-sniffing dogs.  Cataloging some of the instances where courts incorporate math helps illuminate how the Court should proceed in Gill v. Whitford.


Math as evidence:   Courts cannot avoid using math to determine the strength of certain types of evidence.  Although courts may botch using math as evidence, this task is inevitable in an increasingly quantifiable world.

Most routinely, trial courts serve as gatekeepers, determining when a scientific expert witness’s testimony is scientifically reliable, and is not “junk science.”  Although jurors ultimately weigh the credibility of the evidence, the judge determines whether an expert is sufficiently qualified to present to the jury.  Under the Daubert test, judges consider factors such as whether the expert uses the scientific method and whether its known error rate is acceptable.

As an example, plaintiff, afflicted with cancer, sues a factory that dumped waste into the water near her home.  Plaintiff needs to prove not only a breach of duty (negligently dumping waste) but that this breach of duty caused her injury – i.e.  that she would not have gotten cancer absent the negligence.  Defendant will argue that plaintiff’s cancer was caused by other factors (smoking, diet, the fact that a high number of people get cancer anyway).  Both parties will present experts relating studies on the causal links between the pollution at issue and the cancer at issue, and the judge must decide whether these experts have a solid enough scientific basis to present their opinions to the jury.

Judges also use math as evidence in cases where they — and not the jury — are the ultimate arbiters of an issue.  For example, in deciding whether a police officer has the probable cause, required by the Fourth Amendment, to search a vehicle, a court will consider the accuracy of a drug-sniffing dog that alerted positively for drugs in the presence of the vehicle.  Courts have generally concluded that a drug-sniffing dog with a low false positive rate provides sufficient probable cause for police to then conduct a search of a vehicle.  This is bad math.  The false-positive rate measures the likelihood of a positive alert given that there are no drugs in the vehicle.  What judges need to determine probable cause is actually the likelihood of drugs in the vehicle given a positive alert.  These are two distinct probabilities, yet judges continue to get this wrong and misapply Bayes’ Rule.  This error has serious implications for our Fourth Amendment rights, because the police are permitted to use dug-sniffing dogs at certain drug checkpoints without any suspicion.   If nothing else, this context reveals how much more education lawyers and judges should receive in probability and statistics — because these disciplines are necessary to assess almost everything we know about the world.

Math as rule: Another area where judges cannot escape incorporating math is when math is necessary to the articulation of a legal rule.  Some legal rules must be expressed quantitatively, with the language of math.

For (a completely fictional) example, let’s say Brew Bar serves Cal alcohol until he is drunk.  Cal then drives on Dayton’s negligently maintained roads and crashes into Egon, texting and driving, who suffers a broken leg.  A jury in Egon’s suit will allocate percentages of responsibility, if it decides every party is negligent.  Let’s say the jury finds Brew Bar 20% responsible, Cal 40% responsible, Dayton 30% responsible, and Egon 10% responsible.  In a several liability jurisdiction, Egon will collect the percentage responsibility from each defendant.  So, if his total damages are $100,000, he will receive 20% from Brew Bar, etc.  His own contribution will be deducted from that $100,000 — leaving him with $90,000 in total from the defendants.  If any defendant is insolvent, Egon cannot go after a defendant for more than his percentage contribution.

However, in a joint and several liability jurisdiction, the other defendants bear the burden of a defendant’s insolvency.  So, let’s say Cal is insolvent.  The $40,000 Cal owes will be redistributed back to Brew Bar, Dayton, and Egon.  Brew Bar will owe $20,000 plus (20/60) (40,000).  The $20,000 is what Brew Bar originally owed, and the denominator of 60 is the percentage of fault left after Cal, insolvent, is removed.  Dayton will owe $30,000 plus (30/60) (40,000).  The remaining 10/60 of Cal’s $40,000 is deducted from Egon’s verdict, under the rules in many jurisdictions.

There is no way to articulate or conceptualize the rules related to reallocation in a joint and several liability district without using math.  Here, though, the math is relatively straightforward, and the translation from the rule a judge prefers and its expression in math is objective, without room for interpretation.

Math as a way to enforce and delineate the contours of a rule: In contrast to the joint and several liability rules, Gill v. Whitford requires the Court to use math to determine whether a rule has been violated.  The rule itself, if the Court goes this way, would be that partisan gerrymandering is unconstitutional.  The way to define unconstitutional partisan gerrymandering would be through, perhaps, using a mathematical formula such as the efficiency gap — or by closely examining electoral maps or using statistics in another way.

Incorporating the efficiency gap into First or Fourteenth Amendment jurisprudence is different than, say, deciding that a positive alert by a drug-sniffing dog is sufficient to establish probable cause under the Fourth Amendment.  In the drug-sniffing dog case, math is used as a simple measuring device, as evidence to decide a test that already is about the probability of committing an offense.  In partisan gerrymandering, a mathematical concept would be used not simply to straightforwardly decide the probability of an event (like drugs in a car), but to determine which events are relevant in the first place.  Determining which formula to select as evidence of partisan gerrymandering is not an objective, purely descriptive inquiry, but is heavily contested.  The rule itself, unlike joint and several liability re-allocation, is not necessarily expressed in mathematical terms, and there isn’t a straightforward mathematical way of measuring when the rule has been violated.

So what then, is the probability that judges are going to get this right?

[Edit: Just a note. There are other, more qualitative tests that could also assess whether a partisan gerrymander is unconstitutional.]




6 thoughts on “When and How Should Courts Use Math?”

  1. Perhaps the first step to ending gerrmandering is to require the electoral map be picked from one of three or four that gets closest to making all districts square-shaped. And from those, we pick the square-shaped one where all districts are closest to the same racial/ethnic make-up as the state.

    So if in one square-shaped electoral map, there’d be a district that’s 60% black and six districts that are 0% black, and there’s one map where nearly all the districts are 12% black with one or two rural districts that are 1% black–we pick the latter map. (Just like we’d prefer each university to have the same % of blacks, rather than have one state university with all the blacks and three without any blacks.)

    That is, we pick the electoral map that makes each district as similar as possible in respect to shape, then size, then racial demography.


Comments are closed.