tl;dr: make the APYs persevere the relative standing of delegates before IDTs go live to avoid a “robin hood” effect
In my conversations with various delegates, a potential issue was flagged with even distribution of delegations which I would like to suggest a correction for.
Imagine if a whale is delegating to a delegate. Once IDTs go live there is incentive for them to undelegate, and redelegate through IDTs to collect some additional yield. This would not be problematic if they redelegated to the same delegate they did before*. However, if token emissions are spread evenly between all qualifying delegates, then they have incentive to spread out these delegations evenly. This would result in a redistribution of delegations from single delegates to all delegates. This “robin hood” redistribution is not the objective of this proposal so the following mathematical model is suggested.
*(There is likely to be some APY being distributed to token holders who have already entered the votable supply but this is likely to be a small percentage of the overall delegators tracked in IDTs as these redelegators didn’t need incentive to delegate in the first place. Sidelined tokenholders, by contrast, are more likely to respond to economic incentives by comparison.)
So in order to preserve the relative weighting of each delegates voting power prior to the launch of IDTs a snapshot of the delegations of all included delegates will be taken. The objective of this proposal is to preserve the relative standing of each included delegate while increasing the votable supply. The purpose of this proposal is not to boost small delegates. This is a worthy initiative but out of scope for this proposal, for now at least. Now onto the model:
The Model
The goal is that the APY for each selected delegate incentivizes rational actors to delegate in proportions which maintain the relative standing of each delegate. To do so, let’s first define some terms:
We want to preserve the relative ratio of each delegate’s delegation at the time of snapshot T_0. We can express this relative ratio of delegate i as the ratio of tokens that delegate i has delegated to them out of the total tokens delegated to all delegates included. Formally, the target weight of each delegate i can be expressed as:
Contrast this with the actual weight of each delegate i at time t once IDTs are live:
So the difference between the target weight, and the actual weight of delegate i can be expressed as the following quantity which indicates to us how far off we are from the ideal delegation ratio:
With the previous definitions in hand, we can adjust the base rate APY r_base to an updated rate r_i(t) at time t by the following model:
K is a parameter ranging from 0.01-0.05 indicating how sensitive we want this model to be to changes in delta_i(t)
Intuition building
To build some intuition for this model consider the following cases:
This model ensures that APY creates incentives which results in rational agents delegating to each delegate in proportion to the standing they had prior to IDTs.