This weekly roundup thread is intended for all culture war posts. 'Culture war' is vaguely defined, but it basically means controversial issues that fall along set tribal lines. Arguments over culture war issues generate a lot of heat and little light, and few deeply entrenched people ever change their minds. This thread is for voicing opinions and analyzing the state of the discussion while trying to optimize for light over heat.
Optimistically, we think that engaging with people you disagree with is worth your time, and so is being nice! Pessimistically, there are many dynamics that can lead discussions on Culture War topics to become unproductive. There's a human tendency to divide along tribal lines, praising your ingroup and vilifying your outgroup - and if you think you find it easy to criticize your ingroup, then it may be that your outgroup is not who you think it is. Extremists with opposing positions can feed off each other, highlighting each other's worst points to justify their own angry rhetoric, which becomes in turn a new example of bad behavior for the other side to highlight.
We would like to avoid these negative dynamics. Accordingly, we ask that you do not use this thread for waging the Culture War. Examples of waging the Culture War:
-
Shaming.
-
Attempting to 'build consensus' or enforce ideological conformity.
-
Making sweeping generalizations to vilify a group you dislike.
-
Recruiting for a cause.
-
Posting links that could be summarized as 'Boo outgroup!' Basically, if your content is 'Can you believe what Those People did this week?' then you should either refrain from posting, or do some very patient work to contextualize and/or steel-man the relevant viewpoint.
In general, you should argue to understand, not to win. This thread is not territory to be claimed by one group or another; indeed, the aim is to have many different viewpoints represented here. Thus, we also ask that you follow some guidelines:
-
Speak plainly. Avoid sarcasm and mockery. When disagreeing with someone, state your objections explicitly.
-
Be as precise and charitable as you can. Don't paraphrase unflatteringly.
-
Don't imply that someone said something they did not say, even if you think it follows from what they said.
-
Write like everyone is reading and you want them to be included in the discussion.
On an ad hoc basis, the mods will try to compile a list of the best posts/comments from the previous week, posted in Quality Contribution threads and archived at /r/TheThread. You may nominate a comment for this list by clicking on 'report' at the bottom of the post and typing 'Actually a quality contribution' as the report reason.
Jump in the discussion.
No email address required.
Notes -
There's also the problem that 50-50 is not actually a neutral probability, if you're a coherent Bayesian and you don't have an ultra-simple sample space. For example, if I think that the probability of each possible bloxor being greeblic is 50%, then I am committed to thinking that the probability that 70/100 bloxors being greeblic is 0.004%. So my "neutral" prior commits me to extremely strong confidence that the distribution of greeblic among those 100 bloxors is not 70!
If I set my prior for each bloxor being greeblic to 69.5%, then it is approximately neutral with respect to 70/100 bloxors being greeblic. But now I'm obviously far from neutral with respect to any individual bloxor being greeblic.
This is one of the limitations of Bayesianism as a formalism: it can model neutral belief with respect to any individual partition of the sample space, but not all partitions of the sample space. So, Scott is just wrong and frankly hasn't understood the mathematics, given his statement "If you have total uncertainty about a statement (“are bloxors greeblic?”), you should assign it a probability of 50%," since this norm implies incoherence, but coherence is a fundamental Bayesian norm.
Put briefly, what Scott is saying requires that you reject Bayesian epistemology/decision theory. I haven't read the whole post yet, but I would be surprised if he realised that.
A different model solves this. If you treat the proportion of greeblic bloxors as an unknown parameter, then assign a prior to that parameter, you can have both
a single bloxor has a 50% chance of being greeblic
the chance of 70/100 bloxors being greeblic is not negligible
This works because the bloxors are no longer independent; they are related through the proportion parameter. Observing one bloxor would change your belief about the parameter, and thus about the other bloxors.
A sufficiently large number of conjunctions of single-case hypotheses of the "bloxor x is greeblic" regenerates the problem. I put it in terms of proportions for familiarity's sake, but formally it's easier to understand the point if you consider Boolean operations on the elements of partitions, and note that in Bayesian epistemology the sample space is assumed to be closed under Boolean operations.
More options
Context Copy link
More options
Context Copy link
That was one of the objections listed in the post, Scott's response was that you should only be neutral about elementary propositions, not about compound ones ("bloxors are greeblic AND bloxors are grue").
I personally think that this entire kind of objections can be dismissed by pointing out that Bayesian math works correctly and without contradictions, and when looking at actual priors there's not much disagreement about how to choose them either, in practice. Nobody actually has arguments against assigning a symmetric prior to a coin bias, or even can muster a lot of enthusiasm to argue that you should use a gaussian instead of a uniform prior.
People get hot and bothered when they feel that someone tries to hide how much information they have actually updated on and how much is their prior.
How do I know that "bloxor-1 is greeblic" is elementary, if I am totally uncertain about this proposition, and I don't even understand the terms? Additionally, it's arbitrary to say that one should be neutral about the elementary propositions.
What do you mean "correctly"?
Depends. If you interpret the probabilities as subjective degrees of belief and interpret degrees of belief in terms of idealised betting dispositions, then it's not obvious that people can introspect their own odds. Experimental work from about the Allais paradox onwards doesn't suggest that Bayesianism is a good fit with how humans actually reason under uncertainty, and without some evidence of reliability of personal introspection of priors, "My prior is X" is potentially just hot air.
How many of the arguments in probability theory have you read to come to this judgement? Because I can think of large parts of the literature dedicated to exactly this point.
Skill issue.
That I, doing Bayesian math about some bets against you, will leave you poor and destitute in the long run, unless you're using Bayes too. What do you want to use instead of Bayes for the record?
My point is not that the poors are always instinctively right. My point is that they have well-honed instincts for when someone is trying to take advantage of them, and the usual Bayesian reasoning like the above rightfully triggers it, even if they don't have the concepts or the introspection to communicate to us what was that, that triggered them.
My point is that a Bayesian megamind is entirely justified in asking the yudkowsky what fraction of his prediction came from the data, and basing his bet amount on that, and grumbling about the yudkowsky being useless if he refuses to answer.
Huh?
It's possible to set up some types of games where this is true, as well as some types of games when using Bayesian math can lead to disasters. See this paper for a pretty simple example of how setting up the game in a way that Bayesianism looks good is more complex than you seem to think: https://www.jstor.org/stable/40210799
If you're thinking of conditionalization as part of "Bayesian math" and alluding to diachronic Dutch Book Arguments, the problems here are particularly vexing. See here: https://link.springer.com/article/10.1007/s10670-020-00228-1
Richard Pettigrew, who has a background in both mathematics and philosophy, has done a lot of great work on these issues. Here's a brief and relatively simple introduction: http://m-phi.blogspot.com/2018/10/dutch-books-and-conditionalization.html
Basically, the literature thus far has been a long series of failed attempts to squeeze Bayesian epistemological juice out of pragmatic rocks.
The task is underspecified and hence so is your question. Can you explain more?
I agree.
One strand: Bayesians tend to be subjectivists, so symmetric priors are only a personal decision. Another strand: imprecise probabilists (like set-based Bayesians) tend to deny that any additive prior is mandatory (and perhaps not even permissible). Another strand: frequentists are critical of the whole Bayesian enterprise; note that criticisms of frequentists' positive claims are beside the point here.
Of course, all those criticisms of symmetric priors (as mandatory) might be wrong, but it's not true that symmetric priors are controversial, even among people with apparent expertise in the relevant mathematics and logic.
You might say, "Well, obviously if I asked you what the probability of heads is with this perfectly ordinary coin, you'd say 50%." However, we are both far from lacking any evidence with respect to that coin, and "The probability is 50%" can be interpreted in all sorts of different ways, e.g. a frequentist would want to interpret it in terms of hypothetical frequencies in a mathematical model of the coin tossing; some Bayesians would interpret it in terms of degrees of evidential support; other Bayesians would interpret it in terms of degrees of belief; some Bayesians would interpret it in terms of the degrees of belief that a rational person should have given the evidence...
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link
The idea that you can have a prior on bloxors being greeblic strikes me as a type error. The domain of priors are propositions, that is, assignments of truth values to possible world-states, not strings of words; to the extent that we pretend assign a probability to a string of words, this is only enabled by us having an understanding that the string encodes a world->bool map (or at least a distribution on such maps, to allow for linguistic uncertainty). Without knowing the definition of "bloxors" and "greeblic", I'm not aware of any canonical interpretation this sequence of words has that yields a truth value; and it does not seem reasonable to expect that any string actually encodes a valid map, any more than it is to expect that any line noise encodes a valid polynomial.
In fact, my prior on strings of Latin characters tells me that the bloxors statement is very likely to not encode a map/proposition, and therefore to not have a probability.
From a mathematical point of view, you can have a probability function defined over all sorts of domains. IIRC, Rudolf Carnap initially defined probability functions over sentences (in the sense of strings of symbols in an artificial language) while John Maynard Keynes and Harold Jeffreys did so over propositions (meanings of sentences) and later Carnap over models (in the formal logic sense). Then there's frequentism and other event-based definitions...
However, I agree with your comment, as we are thinking from the point of view of probability as an epistemologically meaningful magnitude, e.g. a measure of degrees of belief or evidential support. "Bloxers are greeblic" is not part of my languages. In general, I shall have at least some background evidence about any proposition in a language I speak, and thus not have pure uncertainty.
I mean, of course I'm not saying it's impossible to define a distribution on arbitrary strings or anything; but I don't think that this is the intended interpretation of any putative "anything has a probability" maxim one would ascribe to LW-style Bayesianism.
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link
That math only applies if “greeblic” is an independent event. If it’s a category, then either (almost?) all bloxors are greeblic, or they aren’t. I think that’s what the original article uses.
Fair point, I was assuming that Scott would think you should also assume independence unless you have evidence otherwise, but I should have stated that assumption.
Scott's claim is about statements, so there's still the problem I mention: 50% with respect to the hypothesis "Almost all bloxors are greeblic" implies very non-neutral beliefs about other statements. Similarly, if it's all bloxors that are being described, then that leaves just 50% of the probability mass to allocate among all the other possible statistical distributions, so e.g. "50% of bloxors are greeblic" and "0% of bloxors are greeblic" can't both have 50% probability as well.
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link