I'm confused; why don't you just pick black with probability 100%? (Assuming that your utility is 1 if you make the on-further-reflection-correct choice, 0 else.)
This isn't the same thing as knowing what you're going to think at the end of your fretting -- you still don't know -- but the correct response to uncertainty is not half speed, and just picking the 40%-to-be-right option all of the time is the expectancy-maximizing response to uncertainty.
I also use a simple version of this, with a key extra step at the end:
1) have a decision you are unsure about. 2) perform randomisation (I usually just use a coin). 3) notice how the outcome makes you feel. If you find that you wish the coin landed the other way, override the decision and do what you secretly wanted to do all along.
You might think the third step defeats the purpose of the exercise, but so long as you actually commit to following the randomisation most of the time, it gives you direct access to very useful information. It also sets up the right incentive, wherein you never really need to work your willpower against your desires (except, I guess, the desire to deliberate more).
I mostly use this for a slightly different use case – inconsequential decisions like where to eat or small purchases, where taking a lot of time to optimise isn’t worth it. Your mileage may vary with more important decisions, but I see no reason in principle this couldn’t work.
Never leave the house without your d20 :-P
But I agree with you. This seems a simple way to do something like satisficing. Avoiding the great computational cost of an optimal decision.
In terms of prior art that is probably the field you want to explore: https://en.m.wikipedia.org/wiki/Satisficing
One problem I run into when making decisions that impact my life substantially (say, making a big purchase) is that I spend a lot of time staring at decision becoming increasingly anxious. Usually, this is accompanied by only very minor amounts of information being acquired.
There is a well-known solution to this: flip a coin.
Flipping a coin is nice in that it allows you to substantially compress the amount of time during which you are anxious. However, it is not without its flaws.
1. Flipping a coin does not allow you choose among more than two options. That's often enough, but more often than not, it's not enough.
2. Flipping a coin does not allow you to include any of the information that is pertinent to the decision you are making.
So while flipping a coin is nice because it allows you to skip lengthy pointless fretting, it also does not really lead to an optimal outcome. Now of course, if you're at that point, you don't already know the optimal outcome. Otherwise you'd just do that. Right? If you know what you're going to do at the end of the fretting, just do it. The problem is that you don't know.
So I'm proposing the following approach:
1. Estimate the probability that you will end up selecting each of the options.
2. Pick one of the outcomes randomly in accordance with the probability you assigned to it.
e.g. I'm trying to purchase pants. Either black or navy. They cost a few hundreds of dollars so it is an anxiety-generating purchase. I've analyzed the pros-and-cons of the two pairs of pants and at this point, I'm just worrying about whether or not I'm making the best choice.
Step 1. I assign a 0.4 probability to getting the black pants. A 0.3 probability that I will get the navy pants. And a 0.3 probability that I will abandon the purchase.
Step 2. I compute the intervals: 0-0.4 is black, 0.4-0.7 is navy, 0.7-1.0 is no purchase.
Step 3. I generate a random number. I just search Google for "random number between 1 and 100" and divide the result by 100.
Step 4. Compare the result to the intervals to figure out what I just decided.
Step 5. Implement the decision.
I figure I can't be the first person to have thought of this. If you know of prior art on this, let me know.