Just how important in this?

I seem to get much inspiration from the TV news. Today (late July 2010) a set of Churchill's dentures is being auctioned. “So just how important is this item?” asks the news person of the auctioneer, after expounding on how Churchill had the top plate specifically engineered to preserve his speech impediment, as he thought that it was vital to the war effort to have the same, highly distinctive voice. This before TV, of course, when most people only knew him through radio.

An interesting question. Just how important are a set of Churchill's dentures? 0.5? 17.6? This is a quantitative question – it deserves a quantitative answer. I turned off the TV before the auctioneer could give the inevitable, and enormously unsatisfying, answer “Oh, this is very important ….”

One can measure importance by how much effect something has on you. I think one could come up with a reasonable scale, like the Richter scale for earthquakes or the Beaufort scale for wind (both of which are logarithmic in terms of impact). For example, if we chose a 0-10 scale, we might say:-

Event

Effect on me

Importance

About to be hit by bus

kill me now

10

Chinese peasant trips over chicken

none

0

and so on. The Chinese Premier dying comes in at about 1 (putting cheap tee-shirts at risk), millions of Chinese peasants dying in an earthquake comes in on 0.25 (a few moment's distraction on the news).

Thinking about this more, though, one can be further quantified by asking what fraction of my remaining life does something materially alter? Onrushing bus – terminally alters all of it. Diagnosis of cancer – pretty much all of it. Chinese earthquake story, 10 minutes of TV watching. And so on. We will define I as Importance, a measure from 0 to 10 of the amount of  QuALY I lose as a result of something happening.

I is not additive (neither are Richter magnitudes). But they are multiplicative, as are the probabilities of things happening of course, which has a pleasing aspect – the importance and of two unlikely things happening together is therefore the sum of their individual importances, and the chance is the product of their chances.

Of course, this only applies to me. What about you? Well, it depends on how similar or closely associated you are with me, and here we bring in Kevin Bacon, who, as we all know, is separated from any random person on the planet by six steps. (Not sure this applies to Chinese peasant or Peruvian llama farmers, but it will do for the moment). So we can work out what the I is for the most affected person, and I for the least affected person, and then network theory will tell us how connected the average person is to both, and hence what the importance will be to them, and so define a Proximity-Adjusted Just-How-Important-ness scale corrected for proximity.  So – the Bains PAJIT scale (Proximity-Adjusted Just-how Important is iT). Me being run over by a bus has minimal effect on nearly everyone, for example, no matter how distressing it is for me, and so has a rather low PAJIT. And of course there are global and local PAJITs. The UK PAJIT of me being run over by a bus is marginally higher than the Chinese PAJIT.

I expect to see this universally taken up, and next time part of Winston Churchill comes up for auction and the newsperson asks the auctioneer 'so just how important is three feet of Winston's pickled colon?' the man will be able to answer with confidence “2.3” This will be a great improvement. Won't it? Indeed, it will be a Very Important Improvement. Indeed, one of the highest PAJITs calculated will be that for – PAJIT.

Quality-Adjusted Life Years, the standard (and very vague) measure for how useful a heath treatment is. Thus having a stroke has a higher I than getting a mortgage because, even though a mortgage lasts much longer than the average post-stroke survival, it does not leave you unable to walk or talk.