Many people have different definitions of rational delegation. This is not to argue their points, but to compare Cardano’s design assumptions with the real world. Cardano’s design defines rational delegation as trying to maximize rewards. So long as >50% of delegates are trying to maximize their rewards Cardano can be ‘proven secure’.
A rational delegate will evaluate all pools and order them with the highest reward potential at position 1. They would delegate to the highest rewarding pool that has room for their stake as to not oversaturate it. As pools fill up, new stakers have to choose pools lower on the list. The list would fill from top to bottom.
So, how rational is Cardano’s stake?
For this evaluation we will consider any stake within the top 500 pools to be rational
First, we find all private pools that are fully pledged. Subtract that number from 500. This is how many rational public pool choices there are. Now we add up the stake within all of these highest reward potential pools, including the stake pledged to private pools. This is the amount of rational stake within the system.
I calculated only 14% of the total stake is acting rationally. This is a far cry from the >50% required for Oroborous to be secure.
There is some ambiguity that can cause errors in this calculation, like underperforming pools put in the top 500. I do not suspect any errors to be in the range of 36%.
This evaluation method is overly conservative as it’s irrational to choose the 500th highest rewarding pool when there is room in the 10th. I believe this would be more accurate if we just ordered the pools from highest to lowest and then found how many down from 1 saturation stops. That is the amount of truly rational stake. That’s only like 2 public pools down the list.