OK, so this is what I in my previous paper call the p=1 approach. The formula was
interest_rate = k / total_deposits^p
With p=1, that becomes a simple
interest_rate = k / total_deposits
The other main alternatives are p=0 (fixed interest rate), p=0.5 (what we’re currently doing) and p=infinity (consider this as the limit of k and p going to infinity at the same time; basically, this is a policy that targets some specific total deposit size, and if the actual deposit size is different then it keeps lowering or raising the interest rate as much as needed to achieve the given target).
As I see it, the main tradeoffs are as follows:
(i) As p gets closer to 1, you maximize certainty of the issuance rate.
(ii) As p goes higher, you maximize certainty of the deposit size (note that for p<1, (i) and (ii) are in harmony, for p>1 they are in conflict)
(iii) As p goes lower, you reduce effects where if validators drop out remaining validators’ revenue goes up, which could create selfish mining-like attacks.
Personally¸ my intuition still favors 0.5 
, but I’d be interested in seeing the case for different values of this hashed out.