Thank you for your response.
Could you comment about how my strategy outlined above would not give useful information?
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?
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. If your 50% confidence predictions come true only 10% of the time, then maybe your problem is overconfidence in your reasons to deviate from uninformed priors or overconfidence in concocting reasons to believe a certain hypothesis in the vast hypothesis space.
edit: The biggest weakness of this approach is what do you do when you're choosing between something like "this coin flip will come up heads" and "this coin flip will come up tails"? Or when it is unclear what an uninformed prior would even be.
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.
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, blue, yellow, etc...The color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain."
In everyday use, when a person says things like "hand me the blue towel", that person usually does not care, know, or even think about reflectance profiles and spectral power distributions. Usually all that person cares about is that the towel "looks blue" to him and the person he's talking to. He'll say "that towel is blue" just like he'll say "that chocolate is bitter".
It's very useful to have definitions that depend on human sensations. You and I are both humans, and we often have conversations with other humans.
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 contextual nature of color perception.
Also, you're already conceding that color is not a property of a single object, which would make color a poor example of a property of an object.
Anyway, I'll take your response as a sign that you are comfortable with the problematic nature of your example, and the more pressing concern is playing nice with philosophical tradition/convention. So, I consider the issue closed.
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 sensations. That's the unfortunate business of qualia/sensations.
So, the criterion isn't circular, it's just unsatisfying in that we basically end up saying, "in situation X, you will probably feel the sensation I'm talking about, and we've labeled that sensation 'red'".
Definitions should be judged by their usefulness.
Agree 100%. Sometimes you can pretend that color is a simple objective creature and it turn out okay, just like we can use Newtonian physics when relativistic effects are small enough for our purpose.
just define it [color] a particular mixture of wavelengths of visible light
As I said before, you CAN come up with a simple objective definition of color, but it will do a "very poor job of corresponding to human color sensations".
A particular spectral power distribution can lead to many different color sensation depending on visual context, and even the expectation and memory of the human experiencing the color sensation. This fact makes that sort of definition unfit for a lot of purposes.
Look at these two scenes. The left-hand scene contains "blue" pixels that use the same RGB value (0x6e6f73) as the right-hand scene's "yellow" pixels. And in the context of the legend at top, that RGB value produces a third color sensation: gray.
So, any definition of color that only depends on spectral power distributions will not correspond very well with actual human color sensations. The linked picture demonstrates that "the light mixture your monitor produces for an RGB value of 0x6e6f73" is nowhere near enough information to predict what color sensation a human will experience from viewing pixels with that RGB value, even within the limited range of conditions of looking at something on a monitor.
Also, the two-scene picture is not an unusual case. The highly contextual nature of color perception is ubiquitous. Human color processing is always making contextual adjustments from scene illumination. The picture of a fruit basket in this section does a good job of showing how contextual adjustments are the norm. The overwhelming importance of context in color perception massively shrinks the situations where simple objective definitions of color are useful. Treating color as a simple objective creature gets you into trouble fairly quickly.
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.
Yep, which is why I urged the author of the post to choose something other than color as an example of a simple/natural category.
Also, don't you mean objective? The color model work you're talking about is an effort to come up with objective mathematical models that exist outside of human minds (thus considered objective) that give outputs that correspond to sensations that exist inside human minds (those sensations being subjective). I don't want us to get hung up on what "objective" and "subjective" means, but if this conversation continues much more, it might be good to spend a bit of time making sure we understand each other when we use those words.
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).