Tuesday, 5 January 2016

The FOAF test

We're usually fairly good at estimating frequencies of things that happen a lot. But the evidence suggests that we're not very good at judging frequencies of rare events, with the result that we fall back on heuristics involving availability, recency, or saliency rather than underlying frequency.

We might think that we don't have very much personal data about rare events. But in fact we do. First, we may have several decades of experience: if events of a certain kind have happened to us, or never happened to us, this is useful information. Second, we may have a hundred or so friends and associates, each with a similar lifetime of experience. The friends of our friends (our FOAFs) might number ten thousand or so, each with decades of experience - and provided we are talking about relatively-unusual events, there's a good chance you'll hear about them when they happen to one of these people. This is a lot of data.

We can use these observations to estimate frequencies of experiences of relatively rare personal events - such as burglaries, plane accidents, or winning the lottery - which will, unless you're particularly lucky or unlucky, give us (on average) a good enough idea, most of the time, to inform the decisions we need to make, until we can back them up with more-reliable sources of data:
  • If something's happened to you several times in your life, the event probably occurs on an order-of-magnitude (OOM) of around 1 in 10 people a year.
  • If something's happened to you once, the event probably occurs on an OOM of around 1 in a 100 people a year.
  • If something's happened to a few of your friends, the event probably occurs on an OOM of around 1 in 1000 people a year.
  • If something's happened to one of your friends once, the event probably occurs on an OOM of around 1 in 10,000 people a year.
  • If something's happened to a some friends-of-friends, the event probably occurs on an OOM of around 1 in 100,000 people a year.
  • If something's happened once to a friend-of-a-friend, the event probably occurs on an OOM of around 1 in 1,000,000 people a year.
  • If something's never happened to a friend-of-a-friend, the event probably occurs on an OOM of less than around 1 in 1,000,000 people a year.
Give this test a try on these types of event (statistics are all for the UK):
  • Getting divorced: about 1 in 300 per year
  • Being the victim of a burglary: about 1 in 50 people per year
  • Having coronary artery bypass surgery: about 1 in 3,000 people per year
  • Having a baby: about 1 in 100 people per year
  • Being killed by lightning: about 1 in 25,000,000 people per year
  • Appearing on 'University Challenge': about 1 in 600,000 people per year
  • Being admitted to hospital due to a dog attack: about 1 in 9,000 people per year
There are, of course, many many caveats - which we won't list here. Usefully, the inference works both ways. For example, around 1 in 1000 people in the UK are imprisoned each year. This means that, on average, each of us has a few friends who have been imprisoned at some point (of course, some people will have lots of friends who've been to prison, some will have none). Is that true of you? How well do you know your friends?

"Apparently, 1 in 5 people in the world are Chinese. And
there are 5 people in my family, so it must be one of them.
It's either my mum or my dad. Or my older brother Colin.
Or my younger brother Ho-Cha Chu. But I think it's Colin." 

Tommy Cooper
[Edit: correction to burglary figure]

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