Caledonian,
Your comments seem to me to increasingly be of the "gotcha" variety that focus on noncrucial details. There's value to keeping posters honest but you're on the slippery slope of irrelevancy. JMHO.
Joseph et al, I appreciate your thoughts. I think, though, that your objections keep coming back to "it's more complicated." And in reality it would be. But the simple thought experiment suggests that any realistic derivative of the specks question would likely get answered wrong because our (OUR!) intuition is heavily biased toward large (in aggregate) distributed harm. It appears that we personalize individual harm but not group harm.
Ben, I assume that we would all vote that way, if only because the thought of having sentenced someone to torture would be more painful than the punch. But you've changed the question. How would you choose if faced with deciding that either 1) every person on earth receives a painful but nonfatal punch in the face or 2) one random person is chosen to be tortured? That's the specks question.
Joseph,
The point of using 3^^^3 is to avoid the need to assign precise values, which I agree seems impossible to do with any confidence. Once you accept the premise that A is less than B (with both being finite and nonzero), you need to accept that there exists some number k where kA is greater than B. The objections have been that A=0, B is infinite, or the operation kA is not only nonlinear, but bounded. The first may be valid for specks but misses the point - just change it to "mild hangnail" or "banged funnybone." I cannot take the second seriously. The third is tempting when disguised as something like "you cannot compare a banged funnybone with torture" but becomes less appealing when you ask "can it really cause (virtually) zero harm to bang a trillion funnybones just because you've already banged 10^100?"
It was the need for a "magical line" as in Unknown's example that convinced me. I'm truly curious why it fails to convince others. I admit I may be missing something but it seems very simple at its core.
Neel, I think you and I are looking at this as two different questions. I'm fine with bounded utility at the individual level, not so good with bounds on some aggregate utility measure across an unbounded population (but certainly willing to listen to a counter position), which is what we're talking about here. Now, what form an aggregate utility function should take is a legitimate question (although, as Salutator points out, unlikely to be a productive discussion), but I doubt that you would argue it should be bounded.
I have really enjoyed following this discussion. My intuition to the initial post was "specks" but upon reflection I couldn't see how that could be. My intuition couldn't scale the problem correctly - I had to "do the math." Magically diminishing unit harm from the same action across an increasing number of individuals was not convincing. The notion that specks are not harm in the same sense that torture is harm is appealling in practice but was ruled out in the thought experiment, IMHO. Bottom line, if both specks and torture are finite harm (a reasonable premise, although the choice of "specks" was unfortunate because it opens the "zero harm" door), I can't see how there is not some sufficiently large number of specks that have to outweigh the torture. This is very uncomfortable because it implies that there is also (in theory) a sufficiently large number of specks that would outweigh 10^100 people being tortured. Ouch, my brain is trying to reject that conclusion. More evidence that I need to do the math. Luckily, this is all hypothetical. But scaling questions are not always hypothetical and nothing in this discussion has convinced me that intuition will give you the right answer. To the contrary...
I share El's despair. Look at the forest, folks. The point is that you have to recognize that harm aggregates (and not to an asymptote) or you are willing to do terrible things. The idea of torture is introduced precisely to make it hard to see. But it is important, particularly in light of how easily our brains fail to scale harm and benefit. Geez, I don't even have to look at the research El cites - the comments are enough.
Stop saying the specks are "zero harm." This is a thought experiment and they are defined as positive harm.
Stop saying that torture is different. This is a thought experiment and torture is defined to be absolutely terrible, but finite, harm.
Stop saying that torture is infinite harm. That's just silly.
Stop proving the point over and over in the comments!
/rant/
Steven wins:
"How many Overcoming Bias readers does it take to change a lightbulb?"
Actually it's 3^^^3 + 1 (the first 3^^^3 have something in their eye).
I am sympathetic to the counter-comments but need to point out that most of us (those who are not perfect 10s) want to believe that there is something else underlying the evidence that looks matter. Who wants to accept that their talents are dominated by appearance?
Doug S,
You have to use ex ante probabilities - just because the fat dude stops the trolley once in a million times doesn't make it a moral act that one time. In practice we almost never know the probabilities, which leads to the ends-means conclusion. What's interesting is how many folks are willing to, in the face of not knowing the probabilities, substitute intentions. Which has its own saying.
Reminds me of the time that my daughter asked me how to solve a polynomial equation. Many moons removed from basic algebra I had to start from scratch and quickly ended up with the quadratic equation without realizing where I was going until the end. It was a satisfying experience although there's no way to tell how much the work was guided by faint memories.
Caledonian,
I'm suggesting that you ask yourself "does this really matter?" before you post. You've made contributions to past threads but now we get comments like "a tendency on the part of the authors to make incredibly sloppy, poorly-supported, and ..." that signal an attack dog mentality. Why is "incredibly" part of this sentence? Does it add anything except flame? Do you really find the "errors" you comment on incredible?
You may care more about the methods than the conclusions but, personally, I visit OB more for the questions than the answers.
Sorry to highjack the thread but I think that increased civility warrants attention.