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Motivation: Loius Pojman mentions in What Can We Know? (2001) of a certain Carneades (ca. 214-129 B.C>) who must have been a "remarkable dialectician"because " in 155BC he was sent on a diplomatic mission to Rome and in his spare time he gave two lectures. On first day he eulogized justice, making a profound impression on his audience. To their amazement on the second day he gave a diatribe against justice, arguing that there were equally good reasons for not adopting it".

Research yielded the Carneades argumentation framework. However I am interested in the more recent ones. Here's one:

The Mathematical Proof that got a Physicist out of a Traffic Ticket

Dmitri Krioukov, a UC San Diego physicist, was recently given a ticket for running a stop sign. He went to court to argue the ticket, armed with a scientific paper that mathematically demonstrated that he really had stopped. He won.

Krioukov has since posted the entire paper, rather immodestly called "The Proof of Innocence", on the arXiv server. It's probably debatable how much his ironclad mathematical reasoning really helped determine his innocence - it's just as likely the judge threw out the ticket when it was demonstrated another car had obstructed the ticketing police officer's view. Still, let's take a look at...

Full ezine article

Here is the arXiv paper.

Are there any similar cases?

EDIT: Peter Suber has a description of the case on the famous Paradox of Court here.

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    $\begingroup$ I would love to see answers to this, but I fear that any minute now the army of "serious" users will try to close this question. I would like to pre-emptively request: please guys, can we leave this one alone? $\endgroup$ Jul 10, 2012 at 21:39
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    $\begingroup$ @Vel Nias: as a general advice if you want something from somebody, maybe try to avoid implicit insults and belitteling in formulating it. But, well, let's say it asks for papers similar to a certain arXiv...relative to some other recent things it's not even that bad. $\endgroup$
    – user9072
    Jul 10, 2012 at 23:10
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    $\begingroup$ Dear quid, thanks for your general advice. However, (1.) I was not belittling anyone either implicitly or otherwise, and (2.) as a general advice, there is only one 'e' in belittling. $\endgroup$ Jul 11, 2012 at 0:46
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    $\begingroup$ Am I the only one who noticed that the article was originally submitted on April 1? $\endgroup$ Jul 11, 2012 at 11:01
  • $\begingroup$ Related: en.wikipedia.org/wiki/John_F._Banzhaf_III $\endgroup$ Mar 16, 2013 at 8:03

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This is perhaps a borderline example. I heard this story from BCnrd a few years ago, so I hope it hasn't been too mangled in my head since then.

One day, Ken Ribet got a phone call in his office:

  • "Is this Professor Ribet?"
  • "Yeah."
  • "Could you tell me what one tenth of one percent means?"
  • "One part in a thousand."
  • "Are you willing to give that answer under oath?"

It turns out that someone around Berkeley had rented some property, and the rental contract specified that the landlord could not increase the rent by more than one tenth of one percent each year. When the landlord tried to raise it by more, the tenant sued.

At the trial, the tenant's lawyer called in the expert witness. They swore him in, asked him about his job and his qualifications, then came the key question:

  • "Professor Ribet, what, in your expert view, is one tenth of one percent?"
  • "It's one part in a thousand."

Before he could give a rigorous proof, the landlord's lawyer said, "Objection! Anyone reading the contract can tell that it obviously meant one part in 10." The judge agreed, and threw out the case.

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    $\begingroup$ This is incredibly sad if true. $\endgroup$ Jul 11, 2012 at 6:31
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    $\begingroup$ Reminds of the Verizon controversy where they are unable to distinguish between 0.002 dollars and 0.002 cents. verizonmath.blogspot.kr/2007/08/… Pretty painful to listen to. $\endgroup$
    – Tony Huynh
    Jul 11, 2012 at 9:14
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    $\begingroup$ I cannot see anything objectionable about what the landlord's lawyer said! It is quite obvious what was meant; that it is something else than what is written is a different issue. So, to infer from this story that lawyer and judge did not understand the math problem is IMO bold, without detailed knowledge of the underlying legal system. What I do however find sad is that somebody tries to exploit and obvious error somebody made (or that somebody would be so foolish as to actually think 1 in 1000 was intended). $\endgroup$
    – user9072
    Jul 11, 2012 at 14:48
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In France some roadside apparatus will take a picture of you at point A and another apparatus will take a picture at point B on the same highway. They will then apply the mean value theorem to determine if you deserve a ticket for speeding.

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  • $\begingroup$ Yes, I use this example when teaching first-semester calculus. $\endgroup$
    – HJRW
    Jul 11, 2012 at 10:11
  • $\begingroup$ Actually I am curious about how far this can go. I can imagine that the axiom of choice is needed to prove the mean value theorem --- what would happen if I went to court and argued that I do not believe the axiom of choice, and thus the mean value theorem upon which my fine is based? $\endgroup$ Jul 11, 2012 at 10:47
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    $\begingroup$ The axiom of choice is not needed to prove the mean value theorem. $\endgroup$ Jul 11, 2012 at 12:19
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    $\begingroup$ Our students (at the ENS de Lyon) like AC very much when they hear about it, to the point that they feel that they need it in order to choose one element from a set of two. $\endgroup$ Jul 11, 2012 at 12:29
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    $\begingroup$ One could be an ultrafinitist, and claim that you don't believe in the consistency of the real numbers, hence no MVT... $\endgroup$ Jul 11, 2012 at 23:35
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There are several famous cases of fallacious statistical arguments leading to wrongful convictions, where recognition of the error was a major or contributing factor in the eventual overturn of the decision. Such errors are broadly grouped under The Prosecutor's Fallacy - the fallacy of calculating $P(evidence|innocent)$, which is typically tiny, and equating it to $P(innocent|evidence)$, which may not be small when the unconditional probability $P(evidence)$ is itself small.

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    $\begingroup$ An example I have seen which makes this evident to everybody, is the following: P(hanged | death) is usuallly small P(death | hanged) is usually very much larger! $\endgroup$ Jul 12, 2012 at 1:02
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This is not exactly an answer to the question but interesting none-the-less.

In 2005 the British model Kate Moss was filmed putting some kind of white powder, allegedly cocaine, up her nose. The police wanted to press charges for possessing illegal drugs. However the pictures could not demonstrate exactly what the substance was, in particular whether it was a Class A or Class B drug, each of which would require different charges to be brought. The British legal system does not allow a person to be tried on a disjunction of two charges so the case was dropped.

Legal reasoning is often different to mathematical reasoning, but I found it amusing to see the courts employing intuitionist logic in this case, whereas mathematicians would usually be satisfied with a classical proof.

Details: http://news.bbc.co.uk/2/hi/5082546.stm

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  • $\begingroup$ If both charges result in the same verdict and same sentence, then it would be intuitionistically valid! $\endgroup$
    – Zhen Lin
    Jul 11, 2012 at 10:08
  • $\begingroup$ Even given A -> "10 years" and B -> "10 years", one would still need an (intuitionistic) proof of A v B to conclude "10 years" unconditionally, luckily for Moss. $\endgroup$ Jul 11, 2012 at 15:25
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    $\begingroup$ If it could have been drug A or drug B then it could just as well have been baking soda, so I don't think classical logic would have saved their case. $\endgroup$ Jul 18, 2012 at 20:40
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For a case which very nearly came to court disputing a claim made by a company to have built a computer chip mathematically proven to meet its specification, take a look at this section of an article by Donald MacKenzie: http://books.google.co.uk/books?id=rx3oUTzjh8sC&pg=PA134. It would have been wonderful to have had barristers contest the nature of mathematical proof. Mackenzie writes about the case at greater length in 'Mechanizing Proof: Computing, Risk, and Trust' MIT Press 2001.

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Note: Firstly, I apologize for asking the question without spending substantial amount of time doing research. After posting OP, I found the following resources to be a good starting point. As it turns out there are mostly game-theoretic approaches through argumentation theory.

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A new book titled Math on Trial: How Numbers Get Used and Abused in the Courtroom was published on March 12, 2013 that exclusively seems to address this question. It may not involve "rigorous proofs" but the book contains cases where math was (ab)used.

Here's the blurb from Amazon:

In Math on Trial, mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used—and disastrously misused—as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt’s will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge’s misunderstanding of probability led him to discount critical evidence—which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison.

A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn’t always enough to prove a person innocent.

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