Free Will Paradox

Let's suppose that as part of an experiment, 100 genetically similar people are offered a choice: accept a red hat or accept a blue hat. They may, statistically, have a preference toward one color or the other. Now, if you only saw one of these people, and you saw that they accepted a red hat, would you assume that red hats or blue hats were more commonly chosen among the other 99? It's only one data point, but gun to your head, you would probably assume that among the other 99, red hats were more popular.

Here's where it gets weird. What if you were one of the 100, and you chose the red hat? Would you make the same assumption? I argue you probably could. Even if you chose it for some obscure reason, knowing that reason led you to choose the red hat means that others might pick it for the same reason. But if you picked the blue hat, then it would similarly seem more likely that blue hats were probably more likely overall.

Now, knowing this, what if you wanted to influence what hats the others picked? If you pick the red hat, then you can logically conclude that red hats are more likely to be popular. If you pick the blue hat, then you can logically conclude that blue hats are more likely to be popular. Based on this choice, you can change the expected outcome of events you don't participate in. Suppose everyone read this thought experiment before participating. If you pick the red hat to influence the group, it increases the expected likelihood that the majority picked the red hat to influence the group.

I suspect that a possible answer to this paradox is that picking the hat doesn't give you any new information: even before you pick it, you could guess your own thought process and then make your best guess as to what the other 99 pick. Then that would be the most accurate guess you could make regardless of what color you choose. I don't know if this answer would hold up empirically, but it's the only solution that makes sense to me.

Hmmmmmmmmmmmm.

Red and Blue hats will have a significance, other than just colour preference.

If the Guinea pigs were Rats, I guessing that they would also have a genetically inbuilt preference, irrespective of peanut butter.

Though if Guinea Pigs were Rats, would that make Rats, Guinea Pigs.

Apologies.

That is example of inductive reasoning. Inductive reasoning always goes from specific to general. The theory is that because general is consisted of specifics, understanding many specifics leads to understanding general. However, your example is only 1 specific making conclusion about 99 others. At best, you could say "other people could share my preference too".

That is very unlikely.

Who is Will Paradox?

It is Free Will Paradox.

Will is the name given to a pair of conjoined twins, both of whom are doctors.

Why should he be freed?

Will Paradox is Anthony Paradigms half brother.

The term "will paradox" often refers to the apparent contradiction between free will and determinism. It's a philosophical debate about whether our choices are truly free or if they are predetermined by external factors or internal processes. This paradox arises from the seemingly conflicting ideas of human agency and the laws of nature.

Yes.

Thank you for the refresher course in philosophical terminology.

Hope it stays fresh as a philosophical terminology.

Well, the older one gets the more difficult it becomes to keep new data fresh...Less room in the fridge.

Though the older stuff remains stored and cool.

Use zip lock bags. They preserve food storage better.

My older stuff remains stored and cool.

You must keep them in your pant.

It's pants.

Yes, meat, especially sausages are best stored at about 4 degrees, in a sealed bag to avoid contaminating the passion fruit.

Always employ safe sacks.

How many do you have wear at a time?

What does PANT mean? This dictionary definitions page includes all the possible meanings, example usage and translations of the word PANT. A single leg of a pair of pants.

This really depends on the assumptions you make. One reasonable assumption could be that you are a member of the human race, so your choice is somewhat reflective of the general preference - with only one data point, that is the best you can do, to say that this choice is likely to be most common. Another assumption could be that there is something special about your thinking pattern, that it is not reflective of other people's thinking patterns - in which case you could argue that you should discard the single sample as not being drawn from the general distribution and make a random guess. You might also think of yourself as a contrarian, tending to go against the general consensus - and in that case you would guess that the color you picked is less common than the other one.

This is the problem of choosing the prior in the Bayesian statistics. How reflective do you think is your sample of the general distribution? If you believe that it is not reflective at all, then you should simply ignore it and start with the simplest model possible which is the uniform distribution (i.e. blue and red hats are equally likely to win out). And if you believe that it is reflective, whichever way, then a skewed prior is warranted. As to whether your belief is justified or not... well, that is a fundamental question of epistemology, far outside of the scope of this discussion.