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. — god must be atheist

You need a brush-up course in probability theory.

To all those who're interested

I think we need to look at the issue differently. At this point I'd like to call on stage the concepts of relative probability and absolute probability. There's nothing complicated in these concepts - the former is a comparison between probabilities and the latter is a particular probability taken alone. As an example if I compare the probability of one person hitting a target and the probability of a different person hitting a target, it's relative probability but if I just look at each probability by itself it's absolute probability.

That out of the way, let's consider the scenario in the OP.

1. S = The probability that the observation O is real/not for each person (X, Y, and Z) = 50%

2. R= The probability that the observation O is real when all three (X, Y and Z) observe O = 50% * 50% * 50% = 12.5%

3. N = The probability that the observation O is not real when all three (X, Y, and Z) observer O = 50% * 50% * 50% = 12.5%

In terms of relative probability, N is less than S i.e. the probability that observation O is not real when all three make the observation is less than the probability that observation O is not real when only one of them make the observation. There's a significant, and desirable, drop in the probability of O not being real. In other words, having more observers causes the probability of the observation O not being real to fall considerably.

However, in terms of absolute probability, the probability of O being real even when all three observe O is still low, a pathetic 12.5%.

Please give it a read. It's disturbing but eye-opening.

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

We will have to agree to disagree on. I see neither reality nor correctness as being in question, only the adequacy of characterization and interpretation.

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

There are no justified calculations when the "data" used is not the result of counting or measurement. You still have not told me what your position is on the thesis that the probability of a flipped coin ending on edge is 50%. Your failure to respond shows that you are unwilling to fully consider my case.

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? — TheMadFool

It is not a question worthy of the time taken to consider it. Rational people do not waste time on irrelevant issues. If you really think that 50% of your experience is hallucination, please cease posting and seek medical help.

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. — TheMadFool

And so a 50% chance that flipped coins will wind up on their edge.

:ok: To be fair, let's hear your side of the story. How would you model the situation using probability.

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?

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? — 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.

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. — TheMadFool

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%.

You need a brush-up course in probability theory. — TheMadFool

I deflect that back to you, TMF. My description was flawless. Point out the mistake(s) in it if you please. Just making a general statement about my abilities is not an argument -- it's a judgment. You may have your reasons, so state them, please. I don't mind being judged, but I like to see the reason(s) behind it.

Or don't do it. I don't really care. You can go on your marry way, and spew (judgment withheld).

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.

I deflect that back to you — god must be atheist

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 — god must be atheist

This is not how probability calculus works.

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% — Dfpolis

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

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. — Olivier5

Good response! However, this would require that X observing O increase the likelihood of O being real when Y observes O and that, in turn, should increase the chances of O being real when Z observes O.

The probabilities would look like this (numbers arbitrary):

1. Probability of O being real when X observes it = 50%

2. Probability that O is real when Y observes it given that X observes it = 70% (greater than 50%)

3. Probability the O is real when Z observes it given that both X and Y observes O = 90% (greater than 50%)

Ergo,

4. The probability of O being real when all three X, Y, and Z observe O = 50% * 70% * 90% = 31.5% and the probability of O being not real = 1.5%

However, the problem with this is that it's a petitio principii. How can the first observation, if it's 50:50 that it's real, increase the probability that it's real on the second observation? To think that it does amounts to assuming the very thing that needs to be proven.

Remember, we need to prove that as the number of observers increase the probability of what's observed being real also increases. By positing that the probabilites are dependent you're in fact assuming the desired conclusion.

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

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.

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. — Dfpolis

As you rightly pointed out, if you flip a real coin the chance that it'll land on its edge is not zero. The edge of a coin is part of the probability space of coin flips - it's the third possibility.

Let me be clear on this score:

1. Heads = the observation is real
2. Tails = the observation is not real
3. Edge = ?????[what should be written here?]

A few additional issues:

- O is too vague. Certain phenomena are more subjective than others. Like if it's a change in the lighting (O="the lights went off") the probability that X will correctly notice O is very high, like 0.9999. If O is about something more subjective like, say, the beauty of a woman (O="A beautiful woman entered the room") then X may agree or disagree that this happened, and repetition of observers may not bring any certainty because the beauty of a woman is a matter of taste.

So give an example of O, ideally not too subjective, so that a realist probability of noticing it can be at least imagined.

- What you ought to compute is the odds of all three observer being wrong at the same time (not noticing O when O actually happens) because replication is to control for the faillability of individual observers.

Eg O=the lights went off

Prob(X doesn't notice)=0.001
Idem for the other guys.

Leaving aside that dependency between observations that I was speaking about sooner for ease of calculus sake, and using your procedure, the prob that all 3 fail to notice O=1 in a billion.

That is not the point. I can take your experience and state multiple possibilities: (1) The observation was properly reported, (2) There was interference from an unknown source, (3) you have sensory problems, (4) you have mental problems,.etc. So, if I come up with 4 possibilities, does that make each one have P=25%? And does that change when I think of a 5th possibly, so it suddenly changes to 20%? Of course not.

You chose to state your problem so that there were only 2 possibilities. I did the same. By stating only 2 possibilities (on edge or not), I did exactly what you did and applied the same principle you applied. Doing so shows the absurdity of your principle.

O is too vague — Olivier5

You've gone past a checkpoint without completimg the necessary formalities. The first and foremost concern is whether an observation is real or not. Until you establish that everything that follows is of questionable value. In your examples, you need to first find out whether the woman or the lights are real or not and the only approved method for doing that is to have as many observers as possible and therein lies the rub.

By stating only 2 possibilities (on edge or not) — Dfpolis

So a coin can't land heads or tails then? :chin:

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

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

There are two sides and one edge.

Well, the truth is that replication of observation is not generally considered a good way to increase certainty in arts. Just because they all love Beyonce does not force me or anyone to recognize she's a great artist. What people generally conclude after hours of debate (usually during their teens) on the Beatles vs the Stones, or any other artist which one debater likes and the other not, is that art is more deeply subjective than a COVID test. So repetition of observation doesn't work on all topics.

What you are really trying to refute (or play about refuting) is the idea that to duplicate observations is a good way to reduce incertainty (or increase certainty) in sciences, not in arts or beauty tastes.

Therefore you are already pre-defining events in your premise, having already postulated a certain type of generally agreeable event (perhaps unconsciously but you still did exclude art).

And you have already assumed something else: that it is a kind of event that observers can perceive unlike, say, a neutrino passing by. So let's agree about a more specific example, a narrower type of perceivable objective events.

Like elephants for instance (I love elephants). It doesn't need to be one specific elephant like Dumbo. We can remain more general than that.

There are two sides and one edge. — TheMadFool

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

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

I don't know the probability values for the outcomes. How did you get that number?

I'm mainly concerned about objectivity and how there's the principle of repeatability that lies at its foundation.

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

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

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

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

I would rather say that objectivity is an ideal which we can approach through repeatability (aka intersubjectivity) but never reach. — Olivier5

Intersubjectivity? :chin:

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.

In my understanding, observation is followed by conjecture which is then subjected to attempts to refute it. The value of the conjecture (not the observation) depends on its ability to stand up to being refuted. However, a 'good' conjecture is not one that cannot be refuted but cannot be tested. I can conjecture that there is an invisible dragon in my garage, but unless I can provide ways for others to try to refute that, then it has little value as a conjecture.

So, back to the original point at the start, X observes O, and makes a hypothesis about O (the conjecture). (this is often the 'aha' or 'I wonder' moment in science), and sets about finding ways to show to Y and Z that they are not hallucinating by expressing ways that Y and Z might be able to test the hypothesis. My statistics skills are rusty, but I suspect this is a different statistical process.

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. — Olivier5

A Hobson's choice then.

The issue is about observations, whether they're real or not. Hypothesizing comes much later on. If one must talk of hypothesis then that an observation is real counts as one but the method of verification is, unfortunately, identical and thus susceptible to the same problem. It's like buying 3 identical burgers from the same outlet; if one isn't good, the others aren't likely to be good too.