Staker population target (m) #2
Description
One of the biggest endeavors ostensibly facing the Threshold network is the (major) recruitment drive to increase the staker population ahead of tBTCv2’s Q2 launch. Today we have ~50 stakers, albeit before any announcement, or certainty, regarding incentives in this interim era.
Choosing a target m – i.e. what size staker population we require – is a major determinant of:
(a) the interim monthly issuance
(b) other governable parameters such as min. stake size
(c) the eventual split of issuance between full applications (PRE vs. RB vs. tBTCv2)
(d) the % community effort allocated to staker recruitment (marketing, etc.)
Q: If the genesis x-of-n is fixed at 51-of-100, even temporarily, should we actually be aiming for 1,000 stakers for launch?
Assuming uniform stake sizes, the relationship between x, n & m and the failure probability is shown below. The blue curve shows a fixed x-of-n (i.e. 51-of-100, irrespective of m). Conversely, the red curve assumes that x and n have a fixed dependency on m (i.e. x - 1 = m / 20 & n= m / 10 – e.g. when m = 500, x = 25 and n = 50). Note that in the first case, security marginally as the staker population grows.
Note that with respect to both models, x-of-n and x - 1 = m/a & n= m/b – all the parameters are governable (including a and b!). This suggests that we may not wish to simply maximize the target staker population – rather, it depends on weighing up realistic recruitment scenarios against thresholds of acceptable hypergeometric risk. In theory, the network could retain a fixed x-of-n until the staker population reached 1,000, then DAO-upgrade to a variable x-of-n, in order to minimize the probability of a collective absconding event. If insurmountable communication/latency issues arise in groups significantly larger than 100, then that's a (further) argument against targeting a large m.
Of course, the missing piece here is the unequal distribution of stake, and the weighted sampling of heterogenous stake sizes in order to form signer groups. However, it's not yet clear what impact this has on the ideal m at genesis.