All of tobycrisford's Comments + Replies

Saving Average Utilitarianism from Tarsney - Self-Indication Assumption cancels solipsistic swamping.

I think this is a really interesting observation.

But I don't think it's fair to say that average utilitarianism  "avoids the repugnant conclusion".

If the world contains only a million individuals whose lives are worse than not existing (-100 utils each), and you are considering between two options: (i) creating a million new individuals who are very happy (50 utils each) or (ii) creating N new individuals whose lives are barely worth living (x utils each), then for any x, however small, there is some N where (ii) is preferred, even under average utili... (read more)

1wuschel5moI think you are correct, that there are RC-like problems that AU faces (like the ones you describe), but the original RC (For any population, leading happy lives, there is a bigger population leading nearly worth living lives, whose existence would be better) can be refuted.
6MichaelStJules5moIndeed, whether AU avoids the RC in practice depends on your beliefs about the average welfare in the universe. In fact, average utilitarianism reduces to critical-level utilitarianism with the critical level being the average utility, in a large enough world [https://globalprioritiesinstitute.org/christian-tarsney-and-teruji-thomas-non-additive-axiologies-in-large-worlds/] (in uncertainty-free cases). Personally, I find the worst part of AU to be the possibility that, if the average welfare is already negative, adding bad lives to the world can make things better, and this is what rules it out for me.
Incompatibility of moral realism and time discounting

This is a beautiful thought experiment, and a really interesting argument. I wonder if saying that it shows an incompatibility between moral realism and time discounting is too strong though? Maybe it only shows an incompatibility between time discounting and consequentialism?

Under non-consequentialist moral theories, it is possible for different moral agents to be given conflicting aims. For example, some people believe that we have a special obligation towards our own families. Suppose that in your example, Anna and Christoph are moving towards their res... (read more)

What are some low-information priors that you find practically useful for thinking about the world?

I think I disagree with your claim that I'm implicitly assuming independence of the ball colourings.

I start by looking for the maximum entropy distribution within all possible probability distributions over the 2^100 possible colourings. Most of these probability distributions do not have the property that balls are coloured independently. For example, if the distribution was a 50% probability of all balls being red, and 50% probability of all balls being blue, then learning the colour of a single ball would immediately tell you the colour of all of t... (read more)

1NunoSempere1yAs a side-note, the maximum entropy principle would tell you to choose the maximum entropy prior given the information you have, and so if you intuit the information that the balls are likely to be produced by the same process, you'll get a different prior that if you don't have that information. I.e., your disagreement might stem from the fact that the maximum entropy principle gives different answers conditional on different information. I.e., you actually have information to differentiate between drawing n balls and flipping a fair coin n times.
What are some low-information priors that you find practically useful for thinking about the world?

I think I disagree that that is the right maximum entropy prior in my ball example.

You know that you are drawing balls without replacement from a bag containing 100 balls, which can only be coloured blue or red. The maximum entropy prior given this information is that every one of the 2^100 possible colourings {Ball 1, Ball 2, Ball 3, ...} -> {Red, Blue} is equally likely (i.e. from the start the probability that all balls are red is 1 over 2^100).

I think the model you describe is only the correct approach if you make an additional assumption that all b... (read more)

1AidanGoth1yThanks for the clarification - I see your concern more clearly now. You're right, my model does assume that all balls were coloured using the same procedure, in some sense - I'm assuming they're independently and identically distributed. Your case is another reasonable way to apply the maximum entropy principle and I think it's points to another problem with the maximum entropy principle but I think I'd frame it slightly differently. I don't think that the maximum entropy principle is actually directly problematic in the case you describe. If we assume that all balls are coloured by completely different procedures (i.e. so that the colour of one ball doesn't tell us anything about the colours of the other balls), then seeing 99 red balls doesn't tell us anything about the final ball. In that case, I think it's reasonable (even required!) to have a 50% credence that it's red and unreasonable to have a 99% credence, if your prior was 50%. If you find that result counterintuitive, then I think that's more of a challenge to the assumption that the balls are all coloured in such a way that learning the colour of some doesn't tell you anything about the colour of the others rather than a challenge to the maximum entropy principle. (I appreciate you want to assume nothing about the colouring processes rather than making the assumption that the balls are all coloured in such a way that learning the colour of some doesn't tell you anything about the colour of the others, but in setting up your model this way, I think you're assuming that implicitly.) Perhaps another way to see this: if you don't follow the maximum entropy principle and instead have a prior of 30% that the final ball is red and then draw 99 red balls, in your scenario, you should maintain 30% credence (if you don't, then you've assumed something about the colouring process that makes the balls not independent). If you find that counterintuitive, then the issue is with the assumption that the balls are all c
What are some low-information priors that you find practically useful for thinking about the world?

The maximum entropy principle can give implausible results sometimes though. If you have a bag containing 100 balls which you know can only be coloured red or blue, and you adopt a maximum entropy prior over the possible ball colourings, then if you randomly drew 99 balls from the bag and they were all red, you'd conclude that the next ball is red with probability 50/50. This is because in the maximum entropy prior, the ball colourings are independent. But this feels wrong in this context. I'd want to put the probability on the 100th ball being red much higher.

4AidanGoth1yThe maximum entropy principle does give implausible results if applied carelessly but the above reasoning seems very strange to me. The normal way to model this kind of scenario with the maximum entropy prior would be via Laplace's Rule of Succession, as in Max's comment below. We start with a prior for the probability that a randomly drawn ball is red and can then update on 99 red balls. This gives a 100/101 chance that the final ball is red (about 99%!). Or am I missing your point here? Somewhat more formally, we're looking at a Bernoulli trial - for each ball, there's a probability p that it's red. We start with the maximum entropy prior for p, which is the uniform distribution on the interval [0,1] (= beta(1,1)). We update on 99 red balls, which gives a posterior for p of beta(100,1), which has mean 100/101 (this is a standard result, see e.g. conjugate priors [https://en.wikipedia.org/wiki/Conjugate_prior] - the beta distribution is a conjugate prior for a Bernoulli likelihood). The more common objection to the maximum entropy principle comes when we try to reparametrise. A nice but simple example is van Fraassen's cube factory (edit: new link [https://plato.stanford.edu/entries/probability-interpret/]): a factory manufactures cubes up to 2x2x2 feet, what's the probability that a randomly selected cube has side length less than 1 foot? If we apply the maximum entropy principle (MEP), we say 1/2 because each cube has length between 0 and 2 and MEP implies that each length is equally likely. But we could have equivalently asked: what's the probability that a randomly selected cube has face area less than 1 foot squared? Face area ranges from 0 to 4, so MEP implies a probability of 1/4. All and only those cubes with side length less than 1 have face area less than 1, so these are precisely the same events but MEP gave us different answers for their probabilities! We could do the same in terms of volume and get a different answer again. This inconsistency is the
What is the reasoning behind the "anthropic shadow" effect?

Thank you for your answer!


I think I agree that there is a difference between the extinction example and the coin example, to do with the observer bias, which seems important. I'm still not sure how to articulate this difference properly though, and why it should make the conclusion different. It is true that you have perfect knowledge of Q, N, and the final state marker in the coin example, but you do in the (idealized) extinction scenario that I described as well. In the extinction case I supposed that we knew Q, N, and the fact that we haven't ... (read more)