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Showing posts with the label mathematics

Links: A few thoughtful pieces

I'd like to write a full article on each of today's links, but I may never get around to it. In the meantime, you may have your own conclusions to draw: Tim Haab has a good defence of economics as a mathematical discipline. While the particular maths we have to use will evolve, as we incorporate more psychology, theory of organisations and financial institutions into the orthodoxy, economics will and should still use lots of mathematics - because that's the only way we can build and apply successful models. In this review of Create Your Own Economy , Henry Farrell starts to build an argument that the internal mental orderings which add value to our own lives, can also add value to other people's. My own review (not out yet) touches on the converse idea - can ready-made (or at least part-cooked) mental orderings be provided to us as a service? A mini-Easterlin paradox from Stephanie Flanders : as a country, are we more interested in comparative measures of GDP (against ...

Mathematics with Carol (and Danica?)

From the irrelevant-policy-of-the-week department: David Cameron has set up a mathematics taskforce with Carol Vorderman. I think mathematics is a hugely important subject and skill and becoming more so, but this does sound like policy-by-press-release. How can this be tackled without an overall strategy for education? And don't the Tories risk trivialising themselves by announcing this kind of thing in the middle of an economic crisis, nationwide anti-European strikes, Middle East tension and a new American administration? However, if Labour is tempted to respond, I hope they get Danica McKellar to front their version of the campaign. I think she'll stimulate a lot more interest than Carol.

Lottery rollover - fewer players, bigger prizes? Bad maths

I was sceptical of a claim on Free Exchange today: "...if there is no winner the prize is carried over to the following week. A smaller participant pool can then result in infrequent, higher jackpots." This struck me intuitively as unlikely. So I thought I would work it out. Probability theory has been unpopular among economists this year - everyone quotes Nicholas Taleb and slowly, loudly explains to us how the financial markets don't behave like a normal distribution after all, and we don't have enough historical data to give us a predictable distribution for the future. Insufferable. Fortunately lottery draws do  obey standard probabilities and we do  have enough data (and enough theory) to predict how they will behave. So we can use some standard results. Assume that a lottery has 10 million participants each paying $1, with a 50% payback. The prize fund in a typical week is $5 million. Let's say the odds of getting the right numbers are 1 in 14 million; then...

Three kinds of structure

The motivation principle : People act in their best interest, in the light of the information available to them, over a time period that they can accurately foresee. The first two of these statements seem relatively obvious but perhaps the third is not so clear. It means that people will not take an action today, for some nebulous potential benefit one day in the future. They must gain something in return for the action either immediately, or within a time horizon that they can clearly grasp. How long is that? If I make a calm and considered decision, the time horizon may be as much as a few hours; while in the heat of the moment it may only be a few seconds. Either way, in order to act in my longer-term interest, I must get some kind of short-term payoff or else it's too easy to sell out on my decision. For example, if I want to lose ten pounds and be able to run a marathon in six months, I won't succeed unless I give myself incentives that keep paying off for all those early ...