Comments on: Defining Probability in Prediction Markets http://www.midasoracle.org/2008/01/13/defining-probability-in-prediction-markets/ Prediction Markets For All Mon, 01 Dec 2008 22:35:23 +0000 http://wordpress.org/?v=2.6.5 By: ABC 20/20 — A good (but servile) explainer on the wisdom of crowds and the prediction markets | Midas Oracle .ORG http://www.midasoracle.org/2008/01/13/defining-probability-in-prediction-markets/#comment-18651 ABC 20/20 — A good (but servile) explainer on the wisdom of crowds and the prediction markets | Midas Oracle .ORG Fri, 16 May 2008 07:51:35 +0000 http://www.midasoracle.org/2008/01/13/definining-probability-in-prediction-markets/#comment-18651 [...] I’m not happy he served InTrade’s past forecasting successes in absolute terms —and not in terms of probabilities. That shows James Surowiecki can’t be the ultimate leader of the field of [...] [...] I’m not happy he served InTrade’s past forecasting successes in absolute terms —and not in terms of probabilities. That shows James Surowiecki can’t be the ultimate leader of the field of [...]

]]> By: Chris. F. Masse http://www.midasoracle.org/2008/01/13/defining-probability-in-prediction-markets/#comment-16687 Chris. F. Masse Tue, 15 Jan 2008 08:20:52 +0000 http://www.midasoracle.org/2008/01/13/definining-probability-in-prediction-markets/#comment-16687 Are you a Bayesian or a Frequentist? http://behind-the-enemy-lines.blogspot.com/2008/01/are-you-bayesian-or-frequentist.html Are you a Bayesian or a Frequentist? (Or Bayesian Statistics 101) http://behind-the-enemy-lines.blogspot.com/2008/01/are-you-bayesian-or-frequentist-or.html Are you a Bayesian or a Frequentist?
http://behind-the-enemy-lines......ntist.html

Are you a Bayesian or a Frequentist? (Or Bayesian Statistics 101)
http://behind-the-enemy-lines......st-or.html

]]> By: Panos Ipeirotis http://www.midasoracle.org/2008/01/13/defining-probability-in-prediction-markets/#comment-16683 Panos Ipeirotis Mon, 14 Jan 2008 17:33:31 +0000 http://www.midasoracle.org/2008/01/13/definining-probability-in-prediction-markets/#comment-16683 True, efficiency is an issue and you know that I am not convinced that the markets are efficient :-) <p> However, we should try to separate two things: Market efficiency and market accuracy. Efficiency is the rate in which the market incorporates new information and prevents any arbitrage opportunities. Accuracy is the probability in which the market predicts the correct outcome of an event. The main claim to fame for the markets is that they self-report their accuracy, and that "the prices are probabilities". <p> We can measure the effectiveness of the market by following the outline discussed above. One axis is the price of the contract at time <i>t</i> before the expiration of the contract and the other axis is the rate in which this event happens. (...60% of the cases the event that trades at 0.6 happens, 30% of the cases the event that trades at 0.3 happens, and so on...). A perfectly accurate market should have a straight line as an outcome when time <i>t</i> gets close to 0. Any deviation of the experimental results indicates an accuracy bias. There are many papers that indicate the favorite-longshot biases in the market (underprice the favorite, overprice the longshots) so there is no need to really repeat this here. An interesting thing is to see how big <i>t</i> can be and still have reasonable accuracy. Furthermore, if we have systematic and robust biases, then we can use a calibration function that will adjust the market prices, compensating for the biases, to reflect real-life probabilities. <p> Measuring efficiency is a trickier concept. The general definition of efficiency is that "the market immediately incorporates all available information". Being able to predict price movements indicates inefficiency. Having prices for an event summing up to anything other than 1, indicates inefficiency. However, it is difficult to have a definite proof that the market is efficient. We can only say that "we were not able to spot inefficiencies". It is very difficult to prove that "the market is efficient". <p> The two metrics are, of course, highly connected close to the expiration of the contract. If the market is not efficient, then it will not be accurate, as it will not have had incorporated all the available information, if any material information becomes available just before the expiration of the contract. True, efficiency is an issue and you know that I am not convinced that the markets are efficient :-)

However, we should try to separate two things: Market efficiency and market accuracy. Efficiency is the rate in which the market incorporates new information and prevents any arbitrage opportunities. Accuracy is the probability in which the market predicts the correct outcome of an event. The main claim to fame for the markets is that they self-report their accuracy, and that “the prices are probabilities”.

We can measure the effectiveness of the market by following the outline discussed above. One axis is the price of the contract at time t before the expiration of the contract and the other axis is the rate in which this event happens. (…60% of the cases the event that trades at 0.6 happens, 30% of the cases the event that trades at 0.3 happens, and so on…). A perfectly accurate market should have a straight line as an outcome when time t gets close to 0. Any deviation of the experimental results indicates an accuracy bias. There are many papers that indicate the favorite-longshot biases in the market (underprice the favorite, overprice the longshots) so there is no need to really repeat this here. An interesting thing is to see how big t can be and still have reasonable accuracy. Furthermore, if we have systematic and robust biases, then we can use a calibration function that will adjust the market prices, compensating for the biases, to reflect real-life probabilities.

Measuring efficiency is a trickier concept. The general definition of efficiency is that “the market immediately incorporates all available information”. Being able to predict price movements indicates inefficiency. Having prices for an event summing up to anything other than 1, indicates inefficiency. However, it is difficult to have a definite proof that the market is efficient. We can only say that “we were not able to spot inefficiencies”. It is very difficult to prove that “the market is efficient”.

The two metrics are, of course, highly connected close to the expiration of the contract. If the market is not efficient, then it will not be accurate, as it will not have had incorporated all the available information, if any material information becomes available just before the expiration of the contract.

]]> By: Niall O'Connor http://www.midasoracle.org/2008/01/13/defining-probability-in-prediction-markets/#comment-16682 Niall O'Connor Mon, 14 Jan 2008 10:58:46 +0000 http://www.midasoracle.org/2008/01/13/definining-probability-in-prediction-markets/#comment-16682 All well and good in theory. But this does not really deal with the question of market inefficiency. Nor does it take into account the innumerable occasions when the probabilities in the market do not sum up to 1. All well and good in theory. But this does not really deal with the question of market inefficiency. Nor does it take into account the innumerable occasions when the probabilities in the market do not sum up to 1.

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