That makes sense. I was imagining inputs which are broader than car pieces, but narrower than just people (labour) and money (capita), like people in specific roles, or certain production equipment.

Hi David. Are you implying this post is neglecting non-empirical evidence? If so, which type of evidence do you have in mind?

Actually, this comes down to how we define the boundaries. If the difference is truly imperceptible, it remains within the same region where numerical comparisons are perfectly valid.

Do you think there is a temperature T, and duration t for which the pain of T for t + 0.1 s is infinitely (lexically) worse than pain of T for t - 0.1 s?

However, my claim is based on a discontinuous graph. Just as water undergoes a qualitative jump at 100 °C and turns into steam, I believe consciousness undergoes a phase transition at specific thresholds which creates a qualitative leap in the nature of pain.

What do you mean by "qualitative leap"? A large, but finite increase in pain intensity for a small increase in temperature or duration? If so, it would still be the case that a sufficiently long time in pain of level i would be worse than any given time in pain of level i + 1, as argued in Bentham's Bulldog's post.

I am not entirely certain, but maybe we might also consider the following hypothesis: This qualitative shift in experience morally corresponds to the tradability status of the experience itself.

This is how I would think about it. I do not know if there are large increases in pain intensity for small increases in temperature or duration. However, I agree pain intensity increases superlinearly with temperature for some ranges of temperature. Note the above goes very much against prioritising higher levels of pain infinitely (lexically) more.

But at a certain critical threshold (the point of systemic collapse where the subject entirely loses its rationality) this tradability factor effectively hits zero. In such a model, while Level 3 and Level 4 pain might possess vastly different coefficients due to the hidden tradability factor, they remain theoretically comparable. However, once we reach Level 5, we encounter a state of incomparability.

Imagine 53 ºC for 1 min separates the levels of pain 4 and 5, as it is roughly the case in the graph above (which assumes the temperature ranges you mentioned apply to a duration of 1 min). Would you prever averting i) 53 ºC for 60.1 s (maximum pain level of 5) for 1 person with probability 10^-100 over ii) 53 ºC for 59.9 s (maximum pain level of 4) for the 8 billion people on Earth with certainty? i) corresponds to 6.01*10^-99 s (= 60.1*1*10^-100) of level 4 pain in expectation, and ii) to 4.79*10^11 s (= 59.9*8*10^9*1) of level 5 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 5 pain infinitely (lexically) more than averting level 4 pain. I do not understand this. People would not distinguish between 53 ºC for 60.1 s (maximum pain level of 5), and 53 ºC for 59.9 s (maximum pain level of 4).

Thanks for the great post, Rory. In reality, I think the intended output often increases as any of the input factors increases. However, your point remains that increasing the most limiting input factor may increase the output much more than increasing other input factors.

Level 1: Ignorable (40°C – 43°C)

I think you meant 44 ºC instead of 43 ºC. Level 2 starts at 44 ºC.

1-) As I stated earlier, duration is not just a multiplier; it is a catalyst for a qualitative shift. ( In the context of my Five-Phase Model, after a certain threshold, a prolonged Level 3 experience does not simply "add up" to a large Level 3 sum, it undergoes a functional priority shift, effectively transforming into a Level 4 state for example.)

It makes sense the maximum level of pain increases with duration, but I do not think this solves the core issue. There will still be very small changes in temperature or duration leading to a change in the level of pain. Consider the function f(T = "temperature of the water", t = "time with a hand under water") which outputs the highest level of pain (1 to 5). Below is an illustration from Gemini. It assumes the temperature ranges you provided apply to a duration of 1 min, and the level of pain increases with duration as you mentioned. The specific shape of the boundaries between pain level is not important. What matters is that boundaries exist. Imagine 45 ºC for 3 min separates the levels of pain 2 and 3, as it is roughly the case below. Would you prever averting i) 45 ºC for 3 min 0.1 s (maximum pain level of 3) for 1 person with probability 10^-100 over ii) 45 ºC for 2 min 59.9 s (maximum pain level of 2) for the 8 billion people on Earth with certainty? i) corresponds to 1.80*10^-98 s (= (3*60 + 0.1)*1*10^-100) of level 3 pain in expectation, and ii) to 1.44*10^12 s (= (2*60 + 59.9)*8*10^9*1) of level 2 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 3 pain infinitely (lexically) more than averting level 2 pain. I do not understand this. People would not distinguish between 45 ºC for 3 min 0.1 s (maximum pain level of 3), and 45 ºC for 2 min 59.9 s (maximum pain level of 2).

You are welcome. Feel free to get in touch in the future if you want me to have a look at other CEAs of animal welfare interventions.

Hi Alfredo. Thanks for the great post.

I think your question was relevant. I did not feel like you were derailing the post. Thanks for the support.

Hi Cynthia. Thanks for the helpful clarification. Are there any medical conditions that make people regularly experience excruciating pain (for example, for a few minutes per week)? Maybe people suffering from cluster headaches?

Thank you too for making me understand your perspective better. I think it is shared by many people.