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A note about calibration of confidence
isionous00

sorry if I went a little overboard. I didn't mean it to sound confrontational.

You didn't. I appreciated your response. Gave me a lot to think about.

I still think there is some value to my strategy, especially if you don't want to (or it would be unfeasible) to give full probability distribution for related events (ex: all the possible outcomes of an election).

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0jbay
You're welcome! And I'm sorry if I went a little overboard. I didn't mean it to sound confrontational.
A note about calibration of confidence
isionous00

Could you comment about how my strategy outlined above would not give useful information?

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1jbay
The calibration you get, by the way, will be better represented by the fact that if you assigned 50% to the candidate that lost, then you'll necessarily have assigned a very low probability to the candidate that won, and that will be the penalty that will tell you your calibration is wrong. The problem is the definition of more specific. How do you define specific? The only consistent definition I can think of is that a proposition A is more specific than B if the prior probability of A is smaller than that of B. Do you have a way to consistently tell whether one phrasing of a proposition is more or less specific than another? By that definition, if you have 10 candidates and no information to distinguish them, then the prior for any candidate to win is 10%. Then you can say "A: Candidate X will win" is more specific than "~A: Candidate X will not win", because P(A) = 10% and P(~A) = 90%. Since the proposition "A with probability P" is the exact same claim as the proposition "~A with probability 1-P"; since they are the same proposition, there is no consistent definition of "specific" that will let one phrasing be more specific than the other when P = 50%. "Candidate X will win the election" is only more specific than "Candidate X will not win the election" if you think that it's more likely that Candidate X will not win. For example, by your standard, which of these claims feels more specific to you? A: Trump will win the 2016 Republican nomination B: One of either Scott Alexander or Eliezer Yudkowsky will win the 2016 Republican nomination If you agree that "more specific" means "less probable", then B is a more specific claim than A, even though there are twice as many people to choose from in B. Which of these phrasings is more specific? C: The winner of the 2016 Republican nomination will be a current member of the Republican party (membership: 30.1 million) ~C: The winner of the 2016 Republican nomination will not be a current member of the Republic
A note about calibration of confidence
isionous10

The method described in my post handles this situation perfectly well. All of your 50% predictions will (necessarily) come true 50% of the time, but you rack up a good calibration score if you do well on the rest of the predictions.

Seems like you're giving up trying to get useful information about yourself from the 50% confidence predictions. Do you agree?

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0jbay
Yes, but only because I don't agree that there was any useful information that could have been obtained in the first place.
A note about calibration of confidence
isionous40

For the problem of how to phrase the 50% confidence predictions, it might be useful to use the more specific proposition (or one that has the smaller uninformative prior probability). For instance, if you have a race between 10 candidates, and you think candidate X has a 50% chance to win, you should phrase your prediction as "Candidate X will win the election" rather than "Candidate X will not win the election".

If you consistently phrase your 50% confidence predictions this way, then your prediction results tell you something useful. ... (read more)

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0jbay
"Candidate X will win the election with 50% probability" also implies the proposition "Candidate X will not win the election with 50% probability". If you propose one, you are automatically proposing both, and one will inevitably turn out true and the other false. If you want to represent your full probability distribution over 10 candidates, you can still represent it as binary predictions. It will look something like this: Candidate 1 will win the election: 50% probability Candidate 2 will win the election: 10% probability Candidate 3 will win the election: 10% probability Candidate 4 will win the election: 10% probability Candidate 5 will win the election: 10% probability Candidate 6 will win the election: 2% probability ... Candidate 1 will not win the election: 50% probability Candidate 2 will not win the election: 90% probability ... The method described in my post handles this situation perfectly well. All of your 50% predictions will (necessarily) come true 50% of the time, but you rack up a good calibration score if you do well on the rest of the predictions.
Wear a Helmet While Driving a Car
isionous00

What do you think of watching car crash compilations to counteract the Peltzman effect?

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1James_Miller
It might work.
Wear a Helmet While Driving a Car
isionous50

Risk compensation is one potential problem with wearing a helmet... I imagine seat belts have a similar effect, as might drivers wearing helmets. Based on this idea backwards, I've read a proposal to add a spike to steering wheels to reduce dangerous driving.

I recommend watching car crash compilations. They definitely help you feel the risk of driving on an emotional level. I feel I've learned some things that improve my driving safety, but probably the biggest safety gain is I just tend to drive more cautiously due to car collisions being very present in my mind.

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1btrettel
Great suggestion. I've watched a fair number of these, along with bike crash videos. The mental simulation value is fairly high, because you won't be in every situation on the road, and you should have some idea about what happens if you take certain actions.
Green Emeralds, Grue Diamonds
isionous10

Only if you decide you're defining a sensation and not some physical phenomenon...That, to me, makes defining color through qualia a definition that isn't useful all that often.

That's the definition used in the overwhelming majority of cases. Careful, technical texts often make it clear that color is a sensation. Even Isaac Newton stressed that "the rays [of light] are not colored".

Even wikipedia goes with the sensation definition of color: "Color...is the visual perceptual property corresponding in humans to the categories called red, ... (read more)

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2Lumifer
I do not believe that to be so. An example: all color management in digital photography. Another example: color swatches (e.g. Pantone).
Green Emeralds, Grue Diamonds
isionous20

it's not hard to make pretty rigorous (as Lumifer suggested, with the radiation frequency, and some outside conditions added to it).

Taking "outside conditions" into account to produce an objective definition of color that does a good job of corresponding to human color sensations is actually extremely complex and a very difficult task. Human color sensations are the result of extremely complex and highly contextual processing. I have studied color vision a great deal, and it is very, very common for people to underestimate the complexity and... (read more)

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Green Emeralds, Grue Diamonds
isionous00

You are now dealing in circular logic. If you criterion for "red" is a "color sensation in humans", you have already defined red. That's it, we're done.

We would run into the same problem for any description of a quale/sensation. For example, we would describe/identify nausea, bitterness, and redness in similar ways - it's hard to directly describe sensations, so we often indirectly identify sensations by pointing to conditions that lead to humans experiencing the sensation, or pointing to how the sensation relates to other sensation... (read more)

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0Lumifer
Only if you decide you're defining a sensation and not some physical phenomenon. Yes, I understand that very well. But all that tells you is that different definitions will diverge in many cases. "Subjective" was probably the wrong word. I distinguish: * A physical approach which defines color through spectral power distributions * A human objective approach which defines color via the tristimulus model (the CIE color space, etc.) * A human subjective approach which defines color as a particular perception The human subjective approach has -- as you have pointed out -- all the issues associated with talking about subjective sensations, that is, they are essentially unobservable and it's very hard to get a good handle on them. That, to me, makes defining color through qualia a definition that isn't useful all that often.
Green Emeralds, Grue Diamonds
isionous00

Neat, I recognize your username. I always liked your choice of username, and I've often enjoyed your comments. Thanks.

you could mean it as shorthand for "that object emits or reflects electromagnetic radiation with a pronounced peak around 700nm wavelength".

Except that is not sufficient nor necessary to ensure that the object would typically generate a red color sensation in humans, even in "neutral or typical conditions". So, I would not mean it as shorthand for that. Color sensations can not be boiled down to or predicted by s... (read more)

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0Lumifer
Thanks :-) You are now dealing in circular logic. If you criterion for "red" is a "color sensation in humans", you have already defined red. That's it, we're done. My point is that you do not have to define "red" in terms of human qualia. Definitions should be judged by their usefulness. Sometimes "a human would call that red" is the right defintion, sometimes "this light peaks at ~700nm" is the right definition. For example, if the sensor in your telescope captured a few photons from a dim distant star, you might call them "red" even if the human visual system will be unable to process these photons (or associate with them the qualia of "red"). It is easy to make color an objective creature -- just define it a particular mixture of wavelengths of visible light. To produce a workable definition of subjective color is much harder -- this is a practical matter in photography and graphics and whole books are written on the subject.
Green Emeralds, Grue Diamonds
isionous00

I'm going to raise an issue, and it could be fair to consider it a nitpick, but considering that you're trying to be rigorous, perhaps it is okay to be unusually technical.

Blue and green are not natural categories, or at least they are as natural as "sour tasting" or "stinky". To quote Bruce MacEvoy, "color is a complex judgment experienced as a sensation"; color is not an objective property of things in the world. When a human gazes at something, the color sensation they experience is highly dependent on all sorts of visual... (read more)

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0Stuart_Armstrong
Cheers! I used blue and green because the grue and bleen example is a standard philosophical one, and it's not hard to make pretty rigorous (as Lumifer suggested, with the radiation frequency, and some outside conditions added to it). The pretty rigorous definition is only a partial match for the subjective blue and green, as you pointed out, and I'll try and make that clearer in any subsequent write-up.
2Lumifer
You could mean that. Or you could mean it as shorthand for "that object emits or reflects electromagnetic radiation with a pronounced peak around 700nm wavelength".
2014 Less Wrong Census/Survey
isionous380

Took the survey. I loved the calibration questions; it takes ~20 times more effort to come up with the confidence level than the answer, and I always feel I learn about myself. I've messed with some calibration question games before and was downright astonished at how well calibrated I was (the irony is not lost on me); but the questions were all in A-vs-B format rather than free form. The A-vs-B format is much easier to appear to be well calibrated.

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5TobyBartels
Once you choose your answer, you can still calibrate yourself in A vs B form: ask if your answer is correct (A) or incorrect (B).
Uncertainty
isionous00

The wolfram alpha links in the article and previous comments seem to be broken in that the parentheses in the mathematical expression are missing, meaning that the links present readers with the wrong answer. It was rather confusing for me for a bit. You might want to update the links to something like this:

S pdf: http://www.wolframalpha.com/input/?i=integrate+3%2F2+*+%281+-+2*x+%2B+2*x^2%29+++from+0+to+1
D pdf: http://www.wolframalpha.com/input/?i=integrate+6+*+%28x+-+x^2%29+++from+0+to+1
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