2 min and 36 sec to read, 650 words

There is a story about Thales, I think, where he is essentially asked why, if he is so clever, he has no money. So Thales goes ahead and observes the world a little, finds that with the great weather they are having there is a great olive crop coming and so corners the market on olive presses – essentially rents them all – and then charges healthy fees for anyone that wants to use them. The value of his prediction – that the presses would be needed – seems simple to assess: it is the most valuable action his prediction allowed him to take (in this case cornering the market for olive presses). This value, of course, depends on the prediction not being widely known, because when it is, well, then everyone will have tried to rent the presses.

Today, trade in predictions is more or less common place in so-called futures. Financial futures contracts are standardized agreements to buy or sell a specific financial asset at a predetermined price on a future date. These contracts allow investors and businesses to hedge against price fluctuations or speculate on market movements. The underlying assets can include currencies, stock indices, commodities, or interest rates. When entering a futures contract, parties commit to the transaction without immediate exchange of the asset or full payment. Instead, they make initial margin deposits and adjust them daily based on market price changes, a process known as “marking to market.” As the contract’s expiration date approaches, participants can either close their position by taking an offsetting contract or proceed with the physical delivery or cash settlement as specified in the contract terms.

But there also seems to be a lot of value in not having to predict a situation, but essentially making sure that an event can be accommodated in one’s plans no matter how it turns out. In this model we are paying to not have to predict, and the value of the prediction is arguably what we would not have had to pay if we had been able – at some probability – to predict the event. This model – hedging – is done at what we could call the price of certainty.

Now, the price of certainty and the value of a prediction are closely related, it seems — the more certain a prediction is, the more it approaches the value of certainty, in some possible curve.

Now, this raises another possible avenue of exploration: maybe events can be characterized by different probability curves? Some may be smooth like this, others may be binary and just shift from zero to 1 in a single moment, and yet others may be quickly growing towards 1 and then increasingly nudging upwards. Could we use this prediction / probability profile to categorize events in different ways? Some may even be random noise until they settle. What would a taxonomy of events based on the nature of the predicted probability look like?

We could imagine a few of the categories:

• Binary events that move from 0 to 1, where a single data input point decides and that is not know at all. Or, perhaps more common, it moves from 0.5 to either 1 or 0.
• Smooth gradient events like aging processes.
• Step functions where probability changes in steps.
• Exponential growth events with fast growing probabilities.
• Plateau events – quick initial growth that levels off.
• Cyclical events with, say, seasonal probabilities. ¨
• Random events, where probability shifts like a random walk.
• Threshold events with points where the probability shifts radically.
• Decay events where probability is increasingly high or low but then decays.
• Compound events of different kinds.

Or in a picture:

The prices of certainty and prediction will then vary with the kind of event it really is — and knowing what kind of event it is in itself may be an advantage for whoever is thinking this through.