I am having trouble grokking the above example in the numeraire whitepaper, and I am hoping to get some guidance from this community,
If we only consider those who achieved logloss < -ln(0.5), we see that XIRAX, PHIL_CULLITON and ABRIOSI receives cash rewards. What I don’t understand is the intuition behind the s/c formula for calculating payouts. It seems strange to me that XIRAX gets paid less than ABRIOSI even though XIRAX staked more numeraire than ABRIOSI. What is the intuition behind the s/c formula?
Further, why is it that data scientists are compelled to reveal their true confidence level? It seems to me that if you have a great model that leads you to be VERY confident of your model, you will still think twice before submitting a high confidence score since it decreases your payout. If XIRAX somehow knew that his model was the best, wouldn’t he be motivated to submit the lowest confidence score possible? I understand the dutch auction mechanism here counters this somewhat because submitting a low confidence score means you might risk not getting paid at all. In practice, how has everyone been setting their confidence, and how does that relate to how much numeraire you stake?
The paper claims “The higher p, the higher c a data scientist will submit, and the more dollars the data
scientist can win from the auction.” Then why didn’t XIRAX stake more numeriare than PHIL_CULLITON?
Lastly, why are payouts not simply inversely proportional to the logloss? Is this just a convenience?
Thanks in advance!