Posted by: TomA | 20 January 2010

Utterly Dismal (Growing Irrationally Statistical)

When I’m feeling a bit geeky, there are a few things I find a bit annoying. The first is when people start talking about “rational”. I was explaining something at work to someone and they kept stating, that if people were “rational” in a market (in this case for boats), they’d forsee that if the price was historically low and ship owners weren’t ordering new ships, the fleet will dwindle as boats are retired and lead to a shortage, and hence a price rise. So, if they were “rational”, they would build boats now and beat the rush, having fresh new boats just in time.
Would they? What’s to say that the past will repeat itself? It often does but to assume it will seems foolhardy. Moreover, I’d assume the folks that own these ships are suffering from low incomes from their current fleet and probably aren’t able to (cheaply) raise the cash for what would be a large and speculative position. So far, so simple. But consider a bit of game theory and what might be “rational”. We’re talking basic prisoners dilemma here: my best strategy is to do what my competitors do. In doing so, we maintain the status quo, I don’t take the large risk of going out of business but may miss out on windfall profits. Isn’t my long term survival also in my “rational” interests?  This is before we ask what to be “rational” is and most definitely before we consider whether anyone can truly behave in the cold sober state of the mythical “rational” agent neo-classical economics takes as its core .

On to maths for the second. I like it when people use maths properly. Maths is fun y’know. The mis-use of statistics though is everywhere, headline grabbing figures that upon reflection make little sense.
Listening to the Today programme on Radio 4 this morning, one comment bugged me in a discussion between the Families Secretary Ed Balls and the Tory shadow David Willetts. They were discussing policy on how the state should be assisting the “family” [another arbitrary concept no one seems to be able to satisfactorily define]. With the Tories focussing on providing income tax benefits for married couples, being an easy and economic first step, the question was raised as to how non-traditional families are considered – unmarried couples with children, widows and widowers, single parents – and how this would effectively penalise these groups for not being subscribing to a religious view of partnership. And it was put forward as a question, what is the proportion of teenage mothers in the country (with an implied base of mothers, age non-specific)? Numbers spectacularly forwarded included 50%. FIFTY PERCENT! I know politicians are prone to hyperbole and ludicrous use of statistics, but that would be absurd.
No, the real figure is 2%, as they pointed out shortly after. But to even suggest 50% – what would it mean for 50% of mothers (single or otherwise) to be in their teens?
Assume you class a mother as such when she has a (dependent) child under 16 – the age at which I believe legally they can act on their own behalf and not under a guardian. We’ve already set a cap on the proportion of teenage mothers it is possible to have (mathematically, not physically): 62.5%. And that would rely every mother in the country having given birth on the day she becomes a teenager, or before.
If every mother gave birth a little later, say at the age of 12, their child will have a teenage mother for half of their life as a child dependent – which’d give our ludicrous 50% statistic.
Yes, the figure was undoubtedly thrown out in the heat of a debate to provide emphasis to the 2% that was to follow but such blatant disregard for statistical possibility, for me at least, undermined anything else that was to come.
[A few caveats as and when I think of them. One: This assumes, for simplicities sake, a constant birth rate (see below for digressions on this). Two: my statistical abilities aren’t amazing, so please point out if there are flaws in my logic, it is more than possible].

While I’m here talking statistics and economics, here’s one a conundrum that has continually wound me up since starting to study economics well over a decade ago, that got a mention on Radio 4’s More Or Less the other week. I’m not aware of any economy that doesn’t set out to achieve economic growth (and possibly only implicitly). We live in a world of finite resources. Are the two not entirely incompatible? You’re about to point out population growth, technology and productivity. Possibly… but what if any of those factors use finite resources, say energy? That growth can’t go on forever. You can probably spot the problem in indefinite population growth (go read some Malthus if not); economic growth must face the same limitations – at some point, the consequences will force us to stop. Consequences? Um, let me think of an example… climate change perhaps?
I’ll leave you with two theorems  from economist Kenneth Boulding, which should leave you with a warm fuzzy feeling in your heart:

Dismal Theorem
If the only check on population growth is misery, then the population will grow until it is miserable enough to stop the growth.

Utterly Dismal Theorem
Any technical improvement can only relieve misery for a while, for so long as misery is the only check on population then technology will allow population to grow, and allow more people to live in misery than before. Thus the result of technological improvement is to allow more people to live in misery, i.e. increase the sum total of human misery.


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