Yes the stake taken into acount is σ’=min( σ , 1/k). Which means that you will be able to have more than 1/k stake but it will not count for more than 1/k in the reward formula, that’s what I meant. (We could formulate it “the stake taken into account is limited”)
Can you say more about this?
We have demonstrated this in the technical post:
https://forum.cardano.org/t/understanding-shelley-reward-formula-and-k-a0-parameters/
Quick example from this post with 2 pools with 100% pledge ( s’=σ’ to simplify things), and let’s take a0=5 (So that we can streess the effect with high a0)
One big pool which is saturated (s’=σ’=z0) :
f= R * σ
One small pool saturated at 1% :
f~= R/6 * σ’
I.e RoS will be 6 times higher in the large pool than in the small one, even though all of them have 100% pledge.
I had always understood pledge to be measured in absolute terms. And pools were compared based on the total amount of ADA pledged.
In the formula f= R ( σ’ + a0* s’ ), before adding the strange factor, the impact of the pledge on RoS, is not in absolute terms but in relative terms: the optimal RoS= cste*( 1 + a0 * s/σ ).
When you talk bout a “pledge ratio,” what is being compared?
The pledge to the total amount of stake in the pool. I’m talking about s/σ. To prevent sybill attacks we need to keep this ratio above a certain threshold.