The colloquial definition is "Useless but impressive and flatters my vanity".
Useless to whom?
Newton was respected for coming up with useful theories and natural science, not just pure philosophy or non-applied math. You could maybe argue that his work was rarely useful to him personally, so he only did it as "signalling" to get respect from others to whom it was useful. But under that theory, any division of labor where people are paid money for their work which is only useful to others would be called "signalling".
The probabilistic definition is "Observable thing X signals quality A means P(A|X) > P(A)".
That's true: that Newton came up with good theories in the past is evidence he'll come up with more good theories in the future. It signals his quality as a scientist.
But this is a good thing (as opposed to the usual negative implied connotations of "mere signalling"). And the reason it's a good thing is that his scientific work was actually useful, so it's a good thing others could identify this and reward him to make him do more useful work.
The economic definition is [...]
That's just saying "people will choose to signal if benefits exceed costs". It's true, but it doesn't explain to me the original statement:
With the worst privileged questions I frequently find that the answer is "nothing," sometimes with the follow-up answer "signaling?"
Which says "signalling' in this instance is something that motivates people in the absence of things being useful in their own right.
Related to: Privileging the Hypothesis
-- Paul Graham
-- Doug Henwood
-- Eliezer Yudkowsky
Here are some political questions that seem to commonly get discussed in US media: should gay marriage be legal? Should Congress pass stricter gun control laws? Should immigration policy be tightened or relaxed?
These are all examples of what I'll call privileged questions (if there's an existing term for this, let me know): questions that someone has unjustifiably brought to your attention in the same way that a privileged hypothesis unjustifiably gets brought to your attention. The questions above are probably not the most important questions we could be answering right now, even in politics (I'd guess that the economy is more important). Outside of politics, many LWers probably think "what can we do about existential risks?" is one of the most important questions to answer, or possibly "how do we optimize charity?"
Why has the media privileged these questions? I'd guess that the media is incentivized to ask whatever questions will get them the most views. That's a very different goal from asking the most important questions, and is one reason to stop paying attention to the media.
The problem with privileged questions is that you only have so much attention to spare. Attention paid to a question that has been privileged funges against attention you could be paying to better questions. Even worse, it may not feel from the inside like anything is wrong: you can apply all of the epistemic rationality in the world to answering a question like "should Congress pass stricter gun control laws?" and never once ask yourself where that question came from and whether there are better questions you could be answering instead.
I suspect this is a problem in academia too. Richard Hamming once gave a talk in which he related the following story:
Academics answer questions that have been privileged in various ways: perhaps the questions their advisor was interested in, or the questions they'll most easily be able to publish papers on. Neither of these are necessarily well-correlated with the most important questions.
So far I've found one tool that helps combat the worst privileged questions, which is to ask the following counter-question:
What do I plan on doing with an answer to this question?
With the worst privileged questions I frequently find that the answer is "nothing," sometimes with the follow-up answer "signaling?" That's a bad sign. (Edit: but "nothing" is different from "I'm just curious," say in the context of an interesting mathematical or scientific question that isn't motivated by a practical concern. Intellectual curiosity can be a useful heuristic.)
(I've also found the above counter-question generally useful for dealing with questions. For example, it's one way to notice when a question should be dissolved, and asked of someone else it's one way to help both of you clarify what they actually want to know.)