Perceived Probability: what are the differences from regular statistical chance?

Igitur

Before I say anything, I will preface this by stating that I am new to the forum. While I have engaged in countless philosophical discussions before, I am not familiar with how OPs and replies are created/phrased on this forum particularly.

Anyway, to the point of the post:
I have been thinking a lot recently about the idea of "perceived probability" (I just made up that term, but it probably has been used before, possibly even to reference this idea). It is the idea that in real-world situations where chance is agreed on to be the decider of events due to lack of knowledge (like the order of a card deck after shuffling, ignoring the fact that it isn't actually random at all), while the chance to get a particular result may be a certain (likely lower) chance, the probability of getting any result that would result in the same reaction might be higher.

I have noticed that in some scenarios, this is accounted for, like how instead of just saying that the chance to get any particular 5-card poker hand is 0.0000384769292% (or 1 in 2,598,956), we group them in categories of hands. This represents this principle better.

However, in some other cases, it is ignored, especially with really rare occurrences (I had an example in my mind but I forgot about it before I got to making this post, so I'll just be general here). People tend to comment on how rare something is, often ignoring either other things that could have (but didn't happen) that would have had a similar effect or the number of instances where the thing could have happened but didn't. These things could be put in categories as well.

Following this train of thought, a way to work with all these other disregarded possible occurrences (and still provide an accurate representation of the probability according to this) could be to simply ignore the statistical chance of something happening that you weren't considering and only regard something as its statistical chance if you were thinking of it specifically. You would simply modify your perceived probability based on these factors.

It doesn't seem right that you just completely ignore the other occurrences, though. After all, the only difference is what the observer thought of them. This begs the question: why does it matter what we think about probabilities? Maybe it could help us understand the bias related to them regarding these conditions? There could also be other things that make a specific outcome significant, such as its actual effect (not the reaction of the observer). I would argue that there is little difference between outcomes if the effect on the observer and the reaction by the observer are the same.

This eventually leads to many philosophical questions relating to probability, which is a larger topic that I don't have the time or energy to share my complete thoughts on. I think I had more thoughts on this, but while writing this post forgot some of them.

I would like to see other people's thoughts on this (especially about what makes an outcome significant, and see if I can expand this idea to a more complete set of principles regarding my consideration of probability.

ToothyMaw

↪Igitur

Okay, so you are basically saying that people perceive probabilities based on how rare they perceive an occurrence to be when really the chance of getting a result that fits these perceptions is likely incongruous due to the fact that there are likely more possibilities for a given occurrence in a category than they understand there to be?

Igitur

↪ToothyMaw

Yeah, pretty much. The idea is that there are more unaccounted possibilities in either a category that is similarly rare, has the same effect, or cause the same reaction.

RogueAI

↪ToothyMaw

This sounds like epistemic probability (or maybe subjective probability?). For example, suppose I'm in a poker game with people I don't know. The dealer deals himself a royal flush. Well, any hand the dealer deals himself is fantastically improbable, but after seeing that, I'm pretty close to leaving the table. Suppose I stay and the dealer deals himself four of a kind. I'm probably walking away at that point. While it's possible two hands like that could show up innocently, it's vastly more probable the dealer gets two hands like that given the hypothesis "the dealer is cheating".

ToothyMaw

↪RogueAI

So the person playing cards is deceived by the apparent improbability of the dealer getting those two hands? I mean, the person playing cards could very well be right, and guessing that the dealer is cheating requires no evidence other than that it is an improbable outcome, which is in accordance with the knowledge that any specific hand the dealer deals themselves is incredibly improbable. I think Igitur is talking about perceptions of probabilities that are not accurate - specifically that do not take into account other things that could cause the given occurrence in question.

But epistemic probability is cool. :up:

RogueAI

↪ToothyMaw

Yeah, they can definitely be deceived. It's possible the dealer could innocently deal himself 20 royal flushes in a row, but everyone would have left the table long before then. In that case, they would have all come to the wrong conclusion.

"I think Igitur is talking about perceptions of probabilities that are not accurate - specifically that do not take into account other things that could cause the given occurrence in question"

OK, I was confused.

ToothyMaw

a way to work with all these other disregarded possible occurrences (and still provide an accurate representation of the probability according to this) could be to simply ignore the statistical chance of something happening that you weren't considering and only regard something as its statistical chance if you were thinking of it specifically. You would simply modify your perceived probability based on these factors. — Igitur

So instead of having a diminished idea of how rare it is for apples to fall on your head due to a perception that they may only fall from trees, you might consider specifically the rarity of instances in which an apple is dropped from a ladder onto your head and the instance in which it happens to fall onto your head from a tree. This respects the individual probabilities and also the greater probability of having an apple fall on your head.

This seems to require that probabilities are reducible merely by virtue of looking just a little harder at how one can reduce those probabilities of an occurrence into more specific parts - provided those distinct parts still result in that given occurrence. That is, for your view of the probabilities to be full. But that is probably not possible and would go beyond what can be perceived, I think.

edit: I mean that reducing the probabilities until they are no longer reducible is likely not possible

Mikie

Perceived probability is an interesting concept.

If you asked someone what the odds are of dying in an airplane or in a car, I imagine the majority would say the odds are higher in a plane. That’s the perception — and it’s wrong.

Ditto getting stuck by lightning. Turns out that your house getting hit is actually not that rare. Etc.

Probability is important. I feel like it’s the best we can do. But people’s perceptions will radically differ. It can be useful in gambling — like in poker — but otherwise it’s just irritating.

Igitur

↪ToothyMaw

totally agree
I made the points in the post because I was mostly referring to times when there are an innumerable (not too big, it would just take a lot of effort) amount of occurrences that could lead to the same result. These ideas are meant to cope with that.

ToothyMaw

I would like to see other people's thoughts on this (especially about what makes an outcome significant, and see if I can expand this idea to a more complete set of principles regarding my consideration of probability. — Igitur

I think part of what makes an outcome significant is whether or not it can be attached to a hypothesis, much like how

↪RogueAI

pointed out that the person playing cards could make a guess - that the dealer is cheating - based upon whether or not it would explain the rare occurrence of the dealer dealing themselves increasingly unlikely hands. This makes an unlikely occurrence a function of something that can indeed be verified. Otherwise, we are just talking abstract, mathematical probabilities and approximations of what is random that may not even be distinguishable in terms of a difference between reaction and effect, as you point out.

RogueAI

↪Igitur

Are you familiar with Bayesian probability calculus?

Igitur

↪RogueAI

Sounds familiar, but no. Probably knew at some point. Is Bayesian Probability where you estimate the probability of a hypothesis being true, or am I just mixing things up?

RogueAI

Sounds familiar, but no. Probably knew at some point. Is Bayesian Probability where you estimate the probability of a hypothesis being true, or am I just mixing things up? — Igitur

Someone can explain it better than me. Maybe ChatGpt.

Count Timothy von Icarus

In the poker example, you can think of it purely in terms of frequency. Dice might be even easier though. Suppose we want to know the chances of getting a 7 when rolling two dice.

Well, on the one hand, every roll for each die is independent, and there are 36 possible combinations here, so each would seem to occur with 1/36 probability.

Dice 1 Dice 2 Total
1 1 2
1 2 3

Etc.

But there are many more combinations that total 7 than 2. E.g. 3,4 - 4,3 - 5,2 - 2,5 - etc. (there is an interesting parallel here with low entropy states).

The grouping here depends on what question you want to answer. If the question is: "what are the chances that the first die is a 1 and the second die a 6?" the answer is different from "what are the chances I roll a 7?" With random variables, an outcome will be more common if there are more ways to produce it.

So for instance, Kobe Bryant having died relatively young was a lot more probable than him dying in a helicopter crash because there are many more way for that to occur than for him to specifically die in a helicopter crash.

I'm not sure if it's always a mistake to focus on the seemingly low probability of things happening in a certain way though. For example, even if there are many ways a friend could become a millionaire, I should still be surprised that she became one by winning the lottery. Or even if there were many ways for Tom Brady to win the Superbowl vs Atlanta, we should still be surprised that he could win down 3-28 at the end of the third quarter.

ToothyMaw

So for instance, Kobe Bryant having died relatively young was a lot more probable than him dying in a helicopter crash because there are many more way for that to occur than for him to specifically die in a helicopter crash.

I'm not sure if it's always a mistake to focus on the seemingly low probability of things happening in a certain way though. For example, even if there are many ways a friend could become a millionaire, I should still be surprised that she became one by winning the lottery. Or even if there were many ways for Tom Brady to win the Superbowl vs Atlanta, we should still be surprised that he could win down 3-28 at the end of the third quarter. — Count Timothy von Icarus

What you are doing in moving from the general to specific is precisely what

↪Igitur

prescribes to make sense of the fact that perceived probabilities are often times formed in terms of categories that omit many occurrences that might produce the same reactions - in these cases surprise. So, he is not saying that we shouldn't focus on low probabilities - I think - but rather, in fact, that we are sticking closer to reality in viewing each statistical possibility in specific terms, if possible. There are questions that might have more or less answers depending upon the variables, but that doesn't diminish the fact that the perceived probabilities are likely lower than what they should be if they represent reality closely.

If I'm misrepresenting him, he'll probably correct me.

Igitur

↪ToothyMaw

Pretty close on what I was trying to say. Think of this as more of an add-on, not a correction. It's better to have individual and perfect knowledge of all the probabilities, but since we often can't (or are too lazy to) we could (and do) group them into categories, based on the result of the occurrence actually happening, and we can also not consider rare things that happen that aren't significant as not truly rare based on the assumption that many other rare things that would have had the same effect could have happened but didn't. This obviously doesn't work for all situations, though.

ssu

This begs the question: why does it matter what we think about probabilities? — Igitur

The idea is that there are more unaccounted possibilities in either a category that is similarly rare, has the same effect, or cause the same reaction. — Igitur

Don't forget that people don't simply don't understand probabilities. Even if they know that the Casino always wins, people like to gamble. And how many understand the Monty Hall -problem the first time they hear it, especially if they are made to play the game without any knowledge of the famous example? To understand the connection of information to probabilities is hard, actually.

For example, how improbable it is to win in a lottery can be blurred from how many people do win the lottery. Here in Finland a lot of people play the local lottery, in which you have to get seven numbers correct from 40. To get seven correct has a probability of 1 to 18,6 million. But nearly every week or so someone wins it (even if there's just 5 million plus Finns) and typically only few weeks go without nobody getting seven correct.

fishfry

I have been thinking a lot recently about the idea of "perceived probability" — Igitur

Could you perhaps be thinking of the concept known as credence?

"Credence or degree of belief is a statistical term that expresses how much a person believes that a proposition is true. As an example, a reasonable person will believe with close to 50% credence that a fair coin will land on heads the next time it is flipped (minus the probability that the coin lands on its edge)."

Igitur

↪fishfry

Yeah, mostly. There is other stuff in the post, but credence is accurate. Not like the view of one particular unknown probability but how you consider occurrences (where you know the chance) when there are multiple times they could occur or multiple things that could happen.

fishfry

Yeah, mostly. There is other stuff in the post, but credence is accurate. Not like the view of one particular unknown probability but how you consider occurrences (where you know the chance) when there are multiple times they could occur or multiple things that could happen. — Igitur

Yes, it's a nice concept. As I understand it it's basically the same math as probability theory. But we are interpreting it differently. Instead of probability residing in the coins or dice, credence works in ourselves. It's a murky question to try to say what probability actually is, and why a coin or a dice should care. But credence is belief, and belief is not murky at all. I just ask myself what my degree of belief is, and that's what it is.

Credence makes life simpler, since we then don't have to think about what probability really means.

I did read your post and wasn't sure exactly what you were getting at, so my apologies if I missed the main point.

Perceived Probability: what are the differences from regular statistical chance?

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