@anderselowsson.bsky.social
The appendix provides simple approximations of the validator count under a Zipfian distribution of stakers. The log adjusted D/(20*ln(D)) gets very close and the loglog adjusted measure is almost perfect, as indicated in the plot. Check out the post for further details!
January 26, 2025 at 1:55 PM
The appendix provides simple approximations of the validator count under a Zipfian distribution of stakers. The log adjusted D/(20*ln(D)) gets very close and the loglog adjusted measure is almost perfect, as indicated in the plot. Check out the post for further details!
The scale parameter f_y determines how much the yield should change given a specific consolidation force (the scale of the incentive). The appropriate scale depends on the currently offered yield and MEV, the perceived risk of being active as a staker, deposit size, etc.
January 26, 2025 at 1:55 PM
The scale parameter f_y determines how much the yield should change given a specific consolidation force (the scale of the incentive). The appropriate scale depends on the currently offered yield and MEV, the perceived risk of being active as a staker, deposit size, etc.
Validators might congregate at sizes that produce the best risk-adjusted rewards and the protocol’s priorities might change with consolidation level. For these reasons, validators can as an alternative be given an f2 based on their position in a sorted list of validator sizes.
January 26, 2025 at 1:55 PM
Validators might congregate at sizes that produce the best risk-adjusted rewards and the protocol’s priorities might change with consolidation level. For these reasons, validators can as an alternative be given an f2 based on their position in a sorted list of validator sizes.
The blue line is equidistant in the log domain and the yellow line weighs together the green and red line, in this example by averaging them. These options are less “lopsided” and will see a more or less equal impact on f2 when a validator doubles in size or activity rate.
January 26, 2025 at 1:55 PM
The blue line is equidistant in the log domain and the yellow line weighs together the green and red line, in this example by averaging them. These options are less “lopsided” and will see a more or less equal impact on f2 when a validator doubles in size or activity rate.
As an example, 4096 ETH can be divided into (A) 1 2048-ETH validator and 64 32-ETH validators or (B) 4 1024-ETH validators. With Orbit thresholded at 2048, active stake is roughly equal (so green sets A=B), but the protocol might prefer 4 validators over 65 (so red favors B).
January 26, 2025 at 1:55 PM
As an example, 4096 ETH can be divided into (A) 1 2048-ETH validator and 64 32-ETH validators or (B) 4 1024-ETH validators. With Orbit thresholded at 2048, active stake is roughly equal (so green sets A=B), but the protocol might prefer 4 validators over 65 (so red favors B).
The green line estimates the assumed risks based on activity rate and is neutral w.r.t. the active stake of some endowment. The red line simulates a validator fee and is inversely proportional to validator size. Given some endowment, it is neutral w.r.t. occupied validator spots.
January 26, 2025 at 1:55 PM
The green line estimates the assumed risks based on activity rate and is neutral w.r.t. the active stake of some endowment. The red line simulates a validator fee and is inversely proportional to validator size. Given some endowment, it is neutral w.r.t. occupied validator spots.
The force distribution f2 is unique to each validator and varies with activity rate or size or both. It distributes the collective f1 across the validator set through f1*f2 to produce individual incentives. Several options are reviewed in the post, a summary plot shown here.
January 26, 2025 at 1:55 PM
The force distribution f2 is unique to each validator and varies with activity rate or size or both. It distributes the collective f1 across the validator set through f1*f2 to produce individual incentives. Several options are reviewed in the post, a summary plot shown here.
It consists of the two shape variables f1 and f2 in the range 0-1 and the scale variable f_y. The combined incentive attenuates the yield by f1*f_y(c+f2). The consolidation force f1 is the same for all validators and varies with consolidation level, i.e., validator count V.
January 26, 2025 at 1:55 PM
It consists of the two shape variables f1 and f2 in the range 0-1 and the scale variable f_y. The combined incentive attenuates the yield by f1*f_y(c+f2). The consolidation force f1 is the same for all validators and varies with consolidation level, i.e., validator count V.