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!

26.01.2025 13:55 — 👍 0    🔁 0    💬 0    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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).

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

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.

26.01.2025 13:55 — 👍 0    🔁 0    💬 1    📌 0

Consolidation incentives in Orbit/Vorbit SSF 1. Introduction 1.1 Background A key proposition of Orbit SSF is that validators rotate based on size, such that those with larger balances are active more frequently, while still giving all validator...

In Orbit SSF, validators rotate based on size, leading larger validators to take on greater risks. We must therefore provide some incentives to ensure consolidation in the staking set. This post offers a systematic framework for designing such incentives. ethresear.ch/t/consolidat...

26.01.2025 13:55 — 👍 1    🔁 1    💬 1    📌 0