On an alternative prediction scoring rule

 The main idea: allocate a prediction pool based on the product of the probability and sum contributed 


0. Posts on this blog are ranked in decreasing order of likeability to myself. This entry was originally posted on 09.02.2024, and the current version may have been updated several times from its original form. 


1.1 You and a bunch of others have recorded your expectations that a given event will happen or not in the future, with the event being binary, and predictions in the form of 0 – 100%. 

1.2 Further, each of you has put some money towards the pool. No odds were given to you when you did either of these things.

1.3 Now how you score the predictions and allocate the pool: the pool is allocated in weighted fashion, where each participant’s weight is the product of their contribution and the probability they assigned to the event (probability of occurrence if the event occurred, and one less that if the event didn’t occur).

1.4 With bets were made at different points in time, a bit more thought is required. Naively, one may just add a third term to the weight product there, this being the total time outstanding, but I fear there may be a gamable glitch in there. 

1.5 So, instead of that, you virtually allocate the pool as above at the moment immediately prior to the new participant's entry, and then use the new virtual stakes to calculate payouts at the end. Iterate for every new participant.


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