Statistical crimes [UPDATED]

09/03/2012 § 8 Comments

Time for the Dominion Post to refresh their statistics capabilities. The headline is Capital burglaries most likely in day. The reporting is based on ‘figures from AA Insurance’.

Exhibit A:

Wellingtonians were far less likely to be burgled than their Auckland counterparts, with 31 per cent of all burglaries taking place in the Auckland region, compared with just under 9 per cent in Wellington.

Let’s consider the probabilities. At the 2006 Census, Auckland had 1.3 million of the 4.0 New Zealanders, or 32.4 per cent of the population. Wellington had 0.45 million, or 11.1 per cent. That gives us 32.4:11.1 versus 31:9. Wellingtonians are a bit less likely to be burgled, but (a) it isn’t ‘far less likely’, and (b) there’s no basis for the assessment without the base population figures.

Exhibit B:

Security alarms had proven effective for preventing burglaries, with 60 per cent of claims between 2009-11 coming from homes without alarm systems.

This is meaningless by itself. How many houses have alarm systems? I don’t know. How many readers do know? What we’d need to know is the proportion of burglaries versus the proportion of house with alarms. That second bit of data is crucial.

This reminds me of an old Dilbert comic. They wind up the pointed-haired manager by telling him that 40 per cent of absences happen on a Monday or Friday.

Base probabilities — they aren’t just a good idea, they’re Bayes’s law.

UPDATE: Eric Crampton nominated this story and blog post for the University of Auckland Department of Statistics’ Stats ChatStat of the Week‘ competition. We won! Very cool. Thanks, Rachel and the others at Stats Chat, and thanks to Eric, too. I highly recommend the Stats Chat blog for thinking about how stats are used and misused.

We all do stupid things

08/02/2012 § Leave a comment

I’ve been looking at disease rates. Interesting project but depressing, because I’m looking at several terminal diseases as well as, well, depression. It was specifically with the HIV/AIDS statistics that I started thinking about responsibility, stupidity, probability, and safety nets.

You see, we all do stupid things. We all do things we shouldn’t, even though or perhaps because we know we shouldn’t. And some of us sail on through and laugh about it later. Others contract terminal diseases or fall off cliff faces or drown or otherwise bear a personal cost for that stupidity.

And that raises the question, what should be the size of the consequence?

I think it breaks down in two ways. First, there is the major role that luck plays. Secondly, there is the actual utility created by the fact that people are getting hurt and killed.

Let’s take luck: how much should the economy reward good luck or penalise bad luck? I think we have general agreement that the economy should reward good decisions. But, as I’ve pointed out, we all make bad decisions (‘do stupid things’). All the people who decided to do something stupid and got away with it haven’t paid a price. Instead, the cost has fallen on the few with the bad luck. In some ways, this could be analysed with a Harsanyi-Vickrey framework: we don’t know a priori whether we’ll have bad luck, so we might opt for a system that insures us.

The problem looks a bit like a tournament theory problem, but inverted. There are lots of entrants, but only a few bear the costs. We would therefore expect a different result if we compared it to a situation in which each entrant had to pay the expected value of the marginal disutility up front.

Issue number two: people who do dangerous things and live to tell the tale get some extra utility from the danger. Death-defying acts by definition require some positive probablity of death. Otherwise, they are merely acts. The extra utility is created by the people who are injured, maimed, and killed.

So, is there some compensation due? Should the lucky ones pay the unfortunate ones for making their lives more meaningful? Taking the logic even further, perhaps we aren’t producing the socially optimal amount of dangerous past-times because of market failure caused by the public good aspect. Perhaps.

There are several secondary questions. Improving the safety net reduces the individual cost of such decisions. This creates moral hazard, which increases the social cost. There are also institutional questions — how to transfer payments from the lucky to the unfortunate. That is obviously one reason for safety nets in the first place. Whether they could be improved is a reasonable question.

I guess my point is that when we are arguing about social safety nets, we are arguing about responsibility. We are arguing about how much people should individually bear the costs of poor decisions. And then, we have to be honest with ourselves: we all do stupid things. Only sometimes do we really pay the consequences. As my mother would say, ‘There but for the grace of God go I.’

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