Saturday, May 22, 2010

Angles In Real Life Project

The victory of the France team, televisions Kahneman-Tversky and reimbursed

Several commercial brands of supermarkets (including one with a name similar to Galaxy Venus) and brands of televisions offer to pay more or less partially purchases TV depending on the performance of the team of France in World football future in South Africa.
Arthur (Charpentier) has already mentioned this problem here . Well, if I want to do evil spirit, I would say the risk is not great for these signs appear. But as I said before, the thing footballing awakening my interest about as much as Peter Gabriel listening to the last title of Celine Dion, one must say that I feel unable to make myself a moderate on trial the magnitude of the risk taken by Venus Galaxy and others. Let

elements "objective".
probability "revealed by the victory of paris sport is, if I understood everything, one chance in 22 (France is given to winning 21 against 1).

[drive, I put quotation marks around "objective" because the use of the coast from Paris returns to the sport by definition contrary to the notion of subjective probability defined by Leonard Savage in the 50s]

If we consider the probability and the average budget for a TV purchase, say, 1000 euros, the expected loss for retailers who offer a full refund is about 45 euros, which you confess, reader, not much. This amounts to a discount of less than 5% on the price of nine. So the signs say we are all about marketing based on a spectacular but probably cheap at all ex ante.
course this expected loss has certainly been balanced with the demand response television to such an operation. This is not what I mean now, what interests me is you are slipping reader doubts, the perception of this operation by potential buyers and their incentive to buy these TVs. Well, I put aside the possibility that the buyer finds the sympathetic concerned that teachers support the blues by being willing to suffer a cost in case of victory, as this is surely the crux of the marketing operation. Suppose that the probability
revealed by paris sport is known enough buyers and represents a relatively rational assessment of the probability of victory for France. Will he act if the account on an expected gain of just under 50 euros may seem ridiculous?
The answer is probably positive. Thousands of people buy a daily ticket lottery tickets or other game based on chance when they face some cost by buying them is much higher than the expected gain, that is to say the probability of winning multiplied by the gain on success . If they adopted a decision on the basis of a comparison "rational" expected gains and losses, they would not buy, they buy or by being rational, it would mean that contrary to the national lottery would go to ruin a business perspective and financial. This is not the case, thank you for her, she is doing very well otherwise.
I put aside preferences vis-à-vis the risk to explain the daily behavior of paris. In fact, to rationalize such behavior, it should be assumed that most bettors are risk-lovers, which is not apparent, far from it, empirical studies. These lines, whether based on experimental data or field data, show instead that most people like you and me are risk averse and even highly risk averse (this is also the problem posed by the famous "equity premium puzzle (" enigma of the risk premium on shares, the yield spread between stocks and bonds in financial markets observed over a long period involving very high levels of "timidity" of investors).

One of the most plausible explanations for these behaviors, which may motivate the act of purchase in the case of televisions refundable in case of victory, is the distortion of probabilities by individuals (and not by their preferences vis- toward risk).

I mentioned the cumulative prospect theory of Kahneman and Tversky in this post, and if reader, you need a refresh, you can go read ...
[Especially since the ticket in question is based on developments in the series "Lost" (translation of "lost" in English) that the final season of this series going on right time on a large national chain, and this post will do you absolutely no help to understand the tortuous twists enough of this final season, sorry.]
An interesting feature of this theory is that it stands the expected utility theory of Von Neumann & Morgenstern in that it raises the possibility that individuals distort probabilities. More precisely, in prospect theory, the concept of probability is replaced by a broader concept of "weight" (also proposed by Edwards in 1954), implying that weight in the presence of objective probabilities, they are transformed by individuals. This transformation has been proven time and again in the experiments, especially in the quasi-experiment of Allais in 1954 which highlights the effect of certainty, as explained elsewhere Kahneman and Tversky in their seminal article in 1979.
For example, if you are offered in a lottery which you can earn 1000 euros or nothing, depending on the outcome of throwing a coin (face wins, loses battery), it seems reasonable to assign a probability of 50% gain, which gives, assuming the individual neutral vis-à-vis the risk of an expected gain of EUR 500. However, experiments show that this objective probability of 50% is processed by most individuals in a weight (a "belief") smaller than 50%.
More generally, Drazen Prelec, starting from the experimental work, proposed in 1998 (in the journal Econometrica) a functional form of transformation of probabilities. This functional form is quite flexible, but adapts well to many experimental results which show that the weight of small probabilities tend to be more important than the weight of large probabilities (we tend to overestimate our chances of winning the lottery and to underestimate our probability of having a hangover after a drunken party to make a telling example). Roughly, it looks like this:


The dotted line represents the cumulative probability 0 to 1 and the red curve the weight given to objective probabilities. Small probabilities are overweighted effectively against major odds. For example, in the chart above, and assuming that my individual distorts the probabilities as shown in the red curve, the probability of winning is about 5% for the France team is transformed into a "belief" about 15%, a difference "subjective" objective of the order of 10 points.

In the example of Galaxy Venus, it seems obvious that we play here over to sell us televisions : The probability of winning is in fact very low, but the weight given to this probability, the belief that we give the win, probably even more distorted by our latent chauvinism, inevitably moves us to buy these TVs in stores that know very well handle our emotions and our inconsistencies.

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