Hyperbolic discounting is a ‘time inconsistent’ form of discounting where delays early on are penalised more than delays later on. This results in a ‘fat tail’ where it takes a long time for a hyperbolic function to get near zero. Over a long enough time period, an exponential function (for example growth in happiness driven by population growth) will always be more extreme than a hyperbolic function (for example discount rate in this scenario).
So actually the title should perhaps be reworded; the shape of the discount function matters just as much (if not more so than) the parameterisation of that function. A hyperbolic discount function will always result in longtermism dominating neartermism.
Having said that, I don’t think anyone believes hyperbolic discount rates are anything other than a function of time preference, and the consensus amongst EAs seems to be that time preference should be factored out of philanthropic analysis.
ADDENDUM: There is an excellent post here about why the discount rate is probably not zero based on an analysis of existential risk rates. However, I think the post assumes a lot of background familiarity with the theory of discount rates, and doesn’t – for example – explicitly identify that existential risk is probably not the biggest reason to discount the future (even absent time-preference). Would an effortpost which is a deep dive into discount rates as understood by economists be helpful?