## Tuesday, January 05, 2016

### Too much evidence

In keeping with point 3 of an earlier post, unanimity can be suspicious.
"If many independent witnesses unanimously testify to the identity of a suspect of a crime, we assume they cannot all be wrong," coauthor Derek Abbott, a physicist and electronic engineer at The University of Adelaide, Australia, told Phys.org. "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."

You know that the probability of two people sharing a birthday is not very large: 1/365 (let's forget about leap year). But in a room of 30 people, what is the probability that at least 2 will share a birthday? (If you want to check it for yourself, I'm fond of Pari/GP. The author had a fix within 2 days when I reported a bug.)

As the article says, distinguishing an apple from a banana in a lineup has a vanishingly small failure rate--the rule against unanimity isn't 100%--but for most circumstances unanimity is suspicious. Voters spoil ballots (I've heard people swear and ask for a new one while I was there voting) and I've run into people who weren't quite sure which party controlled the candidate they were supposed to vote for. When I hear of a community going 98% for one party, I suspect assistance was involved.

Have a look at the article.