Ethics and responsibility · Ethics
How can mistakes in mathematical reasoning lead to injustice?
Numbers carry authority in courtrooms and public decisions. When a calculation is presented confidently by an expert, few people are in a position to question it. This question asks who is responsible for making sure mathematical evidence is understood correctly.
Claims
- Statistical reasoning can protect justice by replacing vague impressions with clear evidence, as long as it is done correctly.
- Professional bodies of statisticians can and do correct misuse, as in the case below.
Counterclaims
- Juries and judges often cannot evaluate mathematical evidence, so they trust the expert, and a single error can decide a case.
- Presenting a number gives a false sense of precision about uncertain situations, which can be unfair to the accused.
Real-life situations from mathematics
Sally Clark
In 1999 Sally Clark was convicted in England of murdering her two baby sons. An expert witness told the court that the chance of two sudden infant deaths in such a family was about 1 in 73 million, a figure obtained by squaring the chance for one death as if the two deaths were independent. The Royal Statistical Society publicly criticised the reasoning, and her conviction was overturned in 2003.
The prosecutor's fallacy
Confusing the probability of the evidence given innocence with the probability of innocence given the evidence is a known error, called the prosecutor's fallacy. Conditional probability shows why the two can be very different.
Check dates and figures in a reliable source before you use them, and cite that source.
Use this in your TOK work
Essay. Fits titles about the responsibilities of experts, ethics of knowledge, or trust.
Exhibition. A newspaper report of a court case involving statistics is a serious object for a prompt about the consequences of knowledge.
Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.
Themes and study heading
Knowledge and politics Knowledge and the knower Ethics
Responsibility in making and using mathematics.