The More The Merrier Paradox

X doesn't know whether O is real/not and that in probabilistic terms means that, insofar as X is concerned, O is as likely to be real as O is likely to not be real.

This is the same thing you said before and it's plainly false, so I'll ask again why you think it's true.

I place 98 red marbles and 2 blue marbles in an urn; then I blindfold you and have you select a marble from the urn.

Do you, before removing your blindfold, know what color marble you have selected? No. Do you know what color you've likely selected? Obviously.

First, repeatability in science is not about confirmation of results, it is to check if the results are irrefutable.

You cannot assign the probability of something being real, without first constructing some limitations.

Well, yeah. The point is not knowing whether P and not knowing anything at all about the likelihood of P are really obviously not the same thing

In essence the repeatability principle is that a single observation is dubious enough to require further corroboration as a confirmatory process.

The point is not knowing whether P and not knowing anything at all about the likelihood of P are really obviously not the same thing

Alright, then for both my urn and your urn, we'll say the sample space is { the marble I picked was red, the marble I picked was blue }, so in both cases the chances are 1 in 2 that you picked a red marble. Sound good?

I admit I haven't quite figured out the best way to describe or explain the fallacy here, but that it is a fallacy should be clear. Your conclusions make it clear something has gone wrong, don't they?

I certainly will.

X makes the observation.....
....A single observation just doesn't suffice....

we need to elicit the aid of Y and Z....
......."did you see that?" or "did you hear that?", etc.

assigning a probability value for O being real.

if I'm correct, there seems to be serious flaw with the repeatability principle

First, repeatability in science is not about confirmation of results, it is to check if the results are irrefutable.
— Philosophim

That's the same thing. If refuted then disconfirmed. If confirmed then not refuted.

There are two options: an observation is real or not real. Ergo, the probability it's real = 1/2 = 50% and the probability that it's not real = 1/2 = 50%

No, they really aren't. Let me give you an example. Lets say that some one sees the Loch Ness monster in the lake at a distance. Its really just a man in a submarine having some fun. But the first person invites another to stand where they are, and they too are convinced its the Loch Ness monster. Tons of people are invited, and everyone confirms it must be the Loch Ness monster, because that's what they want to see. Such repeatability is confirmation, but useless. Confirmation when someone is trying to refute a claim, like going down to the water for a closer inspection, is when it is useful.

Either I win it, or I don't. That does not mean I have a 50% chance to win or lose the lottery. We know this, because there are very known instances in which I would win, and many known instances in which I would lose.

It is possible it is real, or possible that it is not real. That does not mean it has a 50% probability of being real, or not real.

Better not, lest the gedankenexperiment immediately contract itself.

A single observation does suffice, at least for the determination that perception has been met with something

Even a mirage is real

For a mere observation, I would agree; the repeatability principle is irrelevant. For assigning a name to the observed, given lack of extant knowledge of it by X, Y, and Z, that would require some kind of three-way agreement. Or, they could all just call it what they want, and since there’s only three of them, probably wouldn’t hurt much. But let any one of the three, in turn, tell a forth, and the forth guy is gonna have some trouble.

Confirmation isn't useless. It is the lifeblood of the scientific method.

Suppose that you see something extraordinary, say E. you can't believe your eyes, You don't know if what you saw was real or not. What numerical value would you assign to E being real?

I'll link you an article from an a person who has a Phd in Astrophysics.

There is no numerical value to assign with that limited information.

Probability is all about working with limited information.

lottery

What do you do with cases in which all people see the same thing but only some of them see something real?

So FOR ME it might be useful to think that there is a 50% chance it is true or false, but it doesn't mean there is a 50% chance it is true or false.

You're right. Some people are more likely to hallucinate than others who, in turn, are more likely to observe the real. That means I have to calculate probabilities for each possible scenario.

However, in my defense, I'd like to point out that the variations are not so extreme as your numbers suggest. The Bell curve should be good enough to allay your concerns - most cluster around the mean.

What you're ignoring is the likelihood that O is real when X sees it, unreal when Y sees it, and real again when Z sees it, and so on. The more people you add, the greater number of possible events you ignore.

The bell curve isn't very relevant to my point.

However, remember that I'm only concerned about the principle of repeatability which is basically the belief that the probability of an observation being real increases with the number of observers.

While there might be a lot going on in between, I only have to consider the worst case scenaro (everyone [all 3, X, Y, and Z] observing something not real) and the best case scenario (everyone [all 3, X, Y, and Z] observing something real).

Then you should choose a mathematical model that's up to the task. An independent random variable with the sample space of {Real, Unreal] isn't it.

Not if you treat O as an independent random variable. If you do that the math forces you to consider those cases, lest the math be rendered useless.

You can ignore those cases of coure. Let me show you:

RRR - 12.5 %
RUU - 12.5 %
RUR - 12.5 %
RRU - 12.5 %
URR - 12.5 %
UUR - 12.5 %
URU - 12.5 %
UUU - 12.5 %

Turns into:

RRR - 12.5 %
RUU - 12.5 %
RUR - 12.5 %
RRU - 12.5 %
URR - 12.5 %
UUR - 12.5 %
URU - 12.5 %
UUU - 12.5 %

And your probability that O is real remains 50 %, because 12.5 % are 50 % of 25 %.

You're talking experimental probability and it's a fallback measure when theoretical probability can't be calculated.

In our case, theoretical probability can be calculated.

And I've already informed you that the probability for observation O being real can be broken down into three choices, mutually exclusive and jointly exhaustive:

Yes, and I have countered that by stating that doesn't work, and an alternative.

In other words, I've provided you choices that represent every possible value P(real) can assume. So, "that doesn't work" is essentially nonsense.

Ok, you're ignoring the discussion of theoretical probability, the cave with the bat scenario, and everything else I've put forward and simply keep repeating the same thing without addressing them. You have made your choice. Enjoy the discussion with others, there is nothing more to say at this point

What is the main issue here? Whether the observation O is real/not real, right? What model do you propose other than that which has to do with the probability of O being real/not? As far as I can tell, P(real) lies at the heart of the issue where P(A) means the probability of A. :chin:

You haven't quite made clear what "observation O is real/not real" means.

There are three observations: O(x, y, z). Variable O can have two values:

"sees unicorn"/"does not see unicorn".

We know the values of the variable. The input comes straight from our experience. So O is not a random variable. No probability. It's either "sees" or "doesn't see", and we get the values by asking.

No matter who sees the unicorn, they all flip a coin, and if the coin comes up heads they say the unicorn is there, and if the coin comes up tails they say it's not there. But they'll only accept that the unicorn is there by full consensus, so they keep flipping coins until it's all heads or tails. In that case the likelihood that the unicorn exists or doesn't exist, as per consensus, would be equal, but only because there are exactly 2 ways the game can end. With a different likelihood the probability changes according to how many constellations end the game, and how many of those constellations are dis/favourable.

For instance, if the probability that the observation O is real, say, 90% then the probability of O being real if all 3, X, Y, and Z observe O is 90% * 90% * 90* = 72.9% and the probability that O is not real = 27.1%.

First, if I observe x, that is presumptive evidence that x happened. There is no a priori reason to suppose that x did not happen.

Second, the purpose of repeatability in science is not to confirm or dispute what you observed, but to see if you have correctly identified the factors causing x. Perhaps x was caused by some extraneous factor you have not identified. If I can set up my experiment using all the factors you identified, and observe x, that is good evidence that you have correctly identified the relevant factors.

Third, there is no rational basis for assigning numbers to things we cannot count or measure. Among these innumerables is the "probability" subjectively assigned to beliefs, and the "utility" of acts and decisions. Bayesian probability is simply transvestite prejudice -- prejudice in mathematical garb. Putting lipstick on it does not make it rational.

You have hit the nail in the head. This is a serious problem.

Have you read "The Black Swan"? It's a notorious no-BS book regarding this exact subject.

We're not on the same page on this. The very idea of repeatability is to either confirm or disconfirm an observation.

There's no need to bring up the issue of causality because at the end of the day it's about an observation - whether it can be observed by different people in different settings.

What concerns us is whether a given observation is real or not. Either it's real or it's not. If one person makes an observation then the odds of that being real are 50:50.

And its interpretation. Perhaps you observed x because your electronics failed, not because of what you believed was the experimental arrangement. Perhaps your sample was contaminated or unrepresentative. I can think of many possible scenarios, none of which call your experience or veracity into question, only the adequacy of its description

Every observation of the same supposed type is a different token. None is exactly the same. You report, "I did x, and observed y." Someone else does x, but does not observe y. Does that mean that you lied? Or that y was a miracle? Or does it mean that factors not included in x lead to the observation of y? All are possible, but statistically, the last is most common.

On what basis are you calculating the probabilities?

All what you said boils down to the issue of whether a single individual's observation is real or not.

I have no clue whether it's likely to be real or unlikely to be real

If I assign a value greater than 50% to the probability that means I think it's likely but this contradicts my assertion that I'm uncertain

The only probability value that fits my epistemic state - uncertainty (not knowing whether likely/unlikely) - is 50%.

Not by my definition of "real." If your meter read 17, for whatever reason, you really observed 17.

Of course you do. Unless you have a sensory, neural or cognitive disorder, all the clues point to the fact that what you observed what was really there. As I said earlier, your use of "real" is non-standard.

Your subjective certainty is more likely to reflect your childhood experience than your observation. If you are only 50% sure that what you saw is real, that says your self-confidence has been harmed -- not that there is any question involving reality.

So the odds of a coin landing on edge is 50%.

1. Not everyone has picked up on it, but the "real" and "not real" thing is a bad framing right away. As Mww correctly pointed out, we know the observation is real, the question is just whether it points to some new phenomenon or just, say, noise in a cable or something.

2. The idea that if we have two options then those two options must have 50% probability is a logical fallacy. I can't seem to find the name of the fallacy right now, but it is a known, named fallacy. Probability does not work like that.

3. Multiplying the "50% chance of being real" is also wrong. The whole point of repeating the experiment is to raise our confidence level that it wasn't just experimental error. To the extent these numbers make any sense at all, the 50% needs to be updated after each positive result.

I beg to differ. When you observe something, say a reading on weighing scale that reads 12 kg, what's the checklist you have to go through before you come to the conclusion that what there is a mass that's 12 kg?

That raises a lot more questions than answers, friend.

It's being updated - probabilities are being multiplied. What other mathematical operation would you say is the correct method of updating to the final probability?

What wouldn't be on the checklist is the words "real" or "not real".

The question for me is whether you're interested in understanding this, or if the whole thread is just for you to proselytize. Numerous examples have been given as to why the number of alternatives has nothing to do with their probability. Ergo there is no reason to assign a probability of 50%.

It's not as simple as one operation; the actual calculation of a P value depends on the specifics of how much data is being collected, what the noise range is for that data and so on. But yes, as we gather more data our confidence in a proposition goes up.

Multiplying this number, as you've done, comes up with obviously absurd results. Imagine I am trying to figure out if you ate my cookie. If there are cookie crumbs on your shirt, I'm 80% confident you did it. If your fingerprints are on the cookie jar, 50%. But if I see both things, then by your logic, it's somehow less likely than either individual piece.
(and note, even if you quibble with the actual numbers, the point is, as long as they are less than 100% this will always be the case; multiplying them will decrease our confidence, by your logic.

Also consider a scenario where you observe a gold ingot on a table. Before you start measuring its weight, you must first determine whether the ingot is actually real or not, right? You couldn't measure the weight if it weren't real.

What you say implies that the probability has to be something other than 50%. Two possibilities - either less than 50% or more than 50% - make your choice and explain why.

If three people are involved, the probability that each one's observation being real is 50%. The probability that all three of them are observing something real is calculated thus: 50% * 50% * 50%

No; there is clearly something being weighed here, the observation is "real".
However, the proposition that I have N kilograms of gold needs further investigation to confirm.
Is the difference clear now?

The probability will depend on the specifics of what's being measured and how. It's something calculated, not something known apriori from the number of alternatives.

No it's not calculated like that. Can you respond to the argument I just made, refuting this (with the cookie example)

If there are cookie crumbs on your shirt, I'm 80% confident you did it. If your fingerprints are on the cookie jar, 50%. But if I see both things, then by your logic, it's somehow less likely than either individual piece.

Does that single measurement suffice in, say, writing a paper that's to be submitted in a peer-reviewed journal? I don't think so.

I'm mainly interested in the distinction between real and hallucination - this has priority over whatever may follow, right?

How confident are we that a certain observation is real or not? By the way, do you mean that you would assign a value other than 50% to the probability that a single observation is real? What are your reasons for that?

So the odds of a coin landing on edge is 50%. — Dfpolis

There is no third option between being real and not being real.

2. If all 3, X, Y, and Z observe O then the probability of O being real (call this R) = 50% * 50% * 50% = 12.5%

1. If all 3, X, Y, and Z observe O then the probability of O not being real (call this NR) = 50% * 50 * 50% = 12.5%

That is a totally different question than asking if the meter reading was real. The question of reality is ontological, that of what suffices for publication is methodological.

No, it does not have priority. The presumption is that unless you have a medical history of hallucinations, what you see is really there. Priority goes to relevant questions, not to vague and unsupported possibilities. In the first quotation above, you posed the standard of publication in a peer reviewed journal. No such journal has ever asked me to submit medical records showing I have no history of hallucination or mental illness.

We are morally certain that our careful observations are correct. Moral certitude means that we can rely on a proposition in good conscience. It does not mean that our belief in it is infallible.

I assign no numerical values to what cannot be counted or measured, because, strictly speaking, it is meaningless to do so. Of course, people do assign probability numbers to their beliefs. One might interpret such probabilities in terms of the odds of a fair bet, but such numbers are not a measure of the probability of a proposition being true, because there is no such probability. If the proposition is meaningful, by which I mean that it asserts some determinable fact, then it is either true or false relative to a determined context.

It depends on what you mean by "being real." Still, the existence of a third option is irrelevant to what I said.

Your claim is that "X is either y or not y" justifies assigning equal probabilities to y and not y. Since a flipped coin will either land balanced on its edge or not, then (by your logic) there is a 50% chance that it will end on edge. I do not see how you can escape this conclusion.

This is peculiar. Because the probability of reality of O is a subjective probability, therefore the mathematician has to consider the reality probability independent probability from each other.

Let me illustrate. Given a coin of heads and tails on the sides. Given that the coin is tossed, the probability of heads or tails in one toss are equal, at 50% each.

Now. X, Y, and Z each toss the coin once. You say that the probabily of tail is 12.5%, and the probability of heads is also 12.5% of any given ONE toss. That is simply absurd. The probability that the coin will land on heads (or else tails) in each one of the three times of the tosses, is 50% times three tosses, and averaged over three tosses.

If the observation decided to be true is 50-50 by each of X, Y, and Z, then the observation's probability is (50%+50%+50%)/3, just like in the coin toss.

There are two layers to observational data. First concerns its reality and the second concerns its correctness. For both, we need multiple observers

The probability calculations are the same for both and the error commited is identical in both cases.

So, if I'm hallucinating myself conducting a high-precision experiment with hallucinated equipment and hallucinated colleagues, I can publish my findings in a scientific journal?

There are two possibilities (real/not real) and either one is as likely as the other. 50% chance of being real and 50% chance being not real.

As I said, I do not use numbers that aren't counts or measurements to describe reality. So, I would not use subjective "probability." It is only a mathematical disguise for prejudice.

What are the odds of the flipped coin landing on edge?

What are the odds of the flipped coin landing on edge? — Dfpolis

This is a good question, you know, because I think it's happened for real but we should discuss this some other time as it's not relevant to my thesis as there are clearly only two options regarding any observation viz. is it real or is it not.

You need a brush-up course in probability theory.

I deflect that back to you

Now. X, Y, and Z each toss the coin once. You say that the probabily of tail is 12.5%, and the probability of heads is also 12.5% of any given ONE toss. That is simply absurd. The probability that the coin will land on heads (or else tails) in each one of the three times of the tosses, is 50% times three tosses, and averaged over three tosses.

If the observation decided to be true is 50-50 by each of X, Y, and Z, then the observation's probability is (50%+50%+50%)/3, just like in the coin toss

It is highly relevant as it relies on the same principle you use to assign a 50% probability to your alternatives. If we can have either A or not A, you say each has a 50% probability. So, since a flipped coin will either end balanced on edge or not, then the probability of its ending on edge is 50%

There is a simple statistical answer to the OP, which is that the procedure you use, multiplying the odds of discrete events to obtain the odds of a combination of them [ p(A&B&C) = p(A)*p(B)*p(C) ], only works when the events are independent from one another. In this case they are not: if I see a flower on a plant, the chances that my wife will see a flower on that plant are very high. If X sees O, the chances that Y sees O are very high. Etc.

If the probability of event B is affected by wether or not A happens, then the two events are not independent and you cannot just multiply the probabilities like you did. Another procedure applies, though covariance and correlations, more complicated.

As far as I can tell there's no edge (third option) between real and not real.

That is irrelevant to the way you assign probability numbers. Is your principle that "the truth of (A or not A) => P(A)=50% and P(not A)=50%", or not? If it is, then according to you, there is a 50% chance of a coin landing on edge. If not, all your claims about reality are baseless.

O is too vague

By stating only 2 possibilities (on edge or not)

A coin can land on edge or on a side. That is 2 possible outcomes.

There are two sides and one edge.

So you're saying there is a 33-1/3% chance of landing on edge?

Like you, I divided the number of possibilities into 100%

I would rather say that objectivity is an ideal which we can approach through repeatability (aka intersubjectivity) but never reach.

Several people sharing what each perceives subjectively = intersubjectivity. The principle of repeatability is basically saying that several people sharing what each perceives subjectively is a good way to approach tengentially the ideal of objectivity.

A Hobson's choice then.

That would be the wrong thing to do. Landing on a side is more likely.

This is not how probability calculus works.

One can tie as many dead horses to a carriage as one wants, it's not going to help pull the carriage. Scientific observers need to do much better than 50/50 for repetitions to work and increase experiment power. And if you set your risk of error to a more realistic 10%, then it works.

Ta-da! At long last! That is why your whole line of thinking is wrong.

You are absolutely right. Because there is no such thing as "probability calculus"

That's precisely the problem.

I am sorry you are uneducateable.

So agreement does happen on this site, once in a long while. That’s good news. :-)

A worthy challenge for an educator worth his salt, don't you think?

No one can put knowledge in a closed mind.