Thanks Basil! That’s an interesting idea. The constant hazard rate model is just comparing two uses of the same model over different task lengths, so if using that to work out the 99% time horizon, it should cost 1/70th as much ($1.43). Over time, I think these 99% tasks should rise in cost in roughly the same way as the 50%-horizon ones (as they are both increasing in length in proportion). But estimating how that will change in practice is especially dicey as there is too little data.
Also, note that Gus Hamilton has written a great essay that takes the survival analysis angle I used in my constant hazard rates piece and extended it to pretty convincingly show that the hazard rates are actually decreasing. I explain it in more detail here. One upshot is that it gives a different function for estimating the 99% horizon lengths and he also shows that these are poorly constrained by the data and his model disagrees with METR’s by a factor of 20 on how long they are, with even more disagreement for shorter lengths.
Thanks Basil! That’s an interesting idea. The constant hazard rate model is just comparing two uses of the same model over different task lengths, so if using that to work out the 99% time horizon, it should cost 1/70th as much ($1.43). Over time, I think these 99% tasks should rise in cost in roughly the same way as the 50%-horizon ones (as they are both increasing in length in proportion). But estimating how that will change in practice is especially dicey as there is too little data.
Also, note that Gus Hamilton has written a great essay that takes the survival analysis angle I used in my constant hazard rates piece and extended it to pretty convincingly show that the hazard rates are actually decreasing. I explain it in more detail here. One upshot is that it gives a different function for estimating the 99% horizon lengths and he also shows that these are poorly constrained by the data and his model disagrees with METR’s by a factor of 20 on how long they are, with even more disagreement for shorter lengths.