The Paradox of Unanimity

The Paradox of Unanimity


Under ancient Jewish law, if a suspect on trial was unanimously found guilty by all judges, then the suspect was acquitted. This reasoning sounds counterintuitive, but the legislators of the time had noticed that unanimous agreement often indicates the presence of systemic error in the judicial process, even if the exact nature of the error is yet to be discovered. They intuitively reasoned that when something seems too good to be true, most likely a mistake was made.

So begins a summary of a forthcoming paper in The Proceedings of The Royal Society A on the “paradox of unanimity.” One of the authors, physicist and electronic engineer Derek Abbott (Adelaide), says:

Unanimity is often assumed to be reliable. However, it turns out that the probability of a large number of people all agreeing is small, so our confidence in unanimity is ill-founded. This ‘paradox of unanimity’ shows that often we are far less certain than we think.

While widespread unanimous agreement may remain reliable in cases in which there is zero or near-zero bias, “the researchers say that this paradox crops up more often than we might think,” providing a number of examples. Here’s one from law enforcement:

the researchers showed that even a tiny bit of bias can have a very large impact on the results overall. Specifically, they show that when only 1% of the line-ups exhibit a bias toward a particular suspect, the probability that the witnesses are correct begins to decrease after only three unanimous identifications. Counterintuitively, if one of the many witnesses were to identify a different suspect, then the probability that the other witnesses were correct would substantially increase.

What’s the philosophical significance of this? Well besides a nod the authors make to the Duhem-Quine thesis, there’s the question of whether the paradox of unanimity could be used as a heuristic for determining questionable philosophical claims. One might say that we just need to look at where there’s (a) the possibility of bias and (b) widespread consensus.

Yet even where there is consensus, it is rarely (if ever) unanimous. Indeed, one of the ways in which the discipline is attacked is by pointing to the persistence of disagreement. Many find this disagreement embarrassing, or attempt to explain it away. But what if philosophical disagreement is instead, as this research suggests it might be, a sign that we should be confident in popular philosophical views?

Thanks to Andrew Stephenson for the pointer.

(image: detail of “Human Structures” by Jonathan Borofsky)

Borofsky - Human Structures crop

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