What force controls probability?

[69dodge]

If the value of a dollar to you is sufficiently small, and the value of possibly winning several million is sufficiently large, buying a lottery ticket is extremely rational.

Is there any way to determine the relative values to someone of a definite dollar and of a small chance at winning a million dollars, besides just seeing if they play the lottery? I don't see any. And if there isn't any, you're basically saying that anyone who plays the lottery is rational by definition.

I'm not sure what "rational" means exactly, or what it ought to mean, but defining it as synonymous with "anything that anyone decides to do" seems pretty pointless.

 

[LawnOven]

Change the dollar amounts to Win = 4 x your entire net worth, and Lose = your entire net worth, and I suspect most of us would pass.

Unless you are like me, and have a negative net worth.

I would definately play that game.

 

[69dodge]

You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way.

If you divide the number of heads by the number of tails, that ratio will gradually approach 1 as you keep flipping the coin. But if you subtract the number of tails from the number of heads, that difference will not approach 0. There will be lots of excess heads or tails at the end too, not only along the way. But not so many, compared to the total number of flips, that the ratio will be far from 1.

But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

The separate coin flips don't organize themselves. Nothing prevents the coin from landing heads up every time. Every sequence of heads and tails is just as likely as every other sequence. There are simply so many more sequences that are roughly half heads and half tails than there are sequences of any other ratio, so it makes sense that the sequence you get will probably be one of the many half-and-half ones rather than, say, the single all-heads one.

 

[ond_magiker]

The idea of behind a "force" causing the 50/50 heads or tails landings is a misconception of a what is really just a mathematical model of the coin toss. In reality the coin simply does what it does - except that it can only land one of two ways - heads or tails... which gives you the "50/50" model used to help interpret the outcome, roughly, before you make a toss; it does not force the outcome however.

Take for example a game of roulette at the casino: you have roughly a 50/50 "chance" that the ball will land on either RED or BLACK (excluding the GREEN zeros). Let's assume your friend joined one of the tables before you came in the casino and has had a chance to already see 3 of the results and lets say all three were BLACK... in his mind, according to the 50/50 "chance model," the next hit is more likely be a RED than a BLACK, but for you, who has just joined the table now the chances are 50/50 even. Does this change the past 3 hits on the board? No, of course not. Does it affect the next hit? The answer is of course, no. Probability is a mathematical concept so it does not 'affect' reality. Quantum mechanical probability is based on certain physical calculations which are made prior to an outcome which is not the same thing because on the roulette wheel and the coin toss there are no real useful calculations made before the toss and therefore: no real accurate prediction can be made on what will come 'out' since you don't know what is going 'in'. Hope that helps.

I don't quite follow. Are you saying it's correct of my friend to believe the next outcome is more probable to be red than black? If so, I can understand him, as many people believe this, but they are of course totally wrong.

 

[drkitten]

Is there any way to determine the relative values to someone of a definite dollar and of a small chance at winning a million dollars, besides just seeing if they play the lottery?

Ask them?

A person who claims not to want money, but then plays the lottery anyway, would arguably be acting irrationally. (Unless there were some social benefit gained from playing the lottery -- "Oh, I just do it because I like to flirt with the cute ticket-seller.....")

 

[drkitten]

I think your own qualifiers make it a relevant question. For example "the thought that they might win" and "relatively nominal sum": that implies the assumption that they are accurately making just the type of calculations I was talking about.

It does not. The amount of psychological "lift" you get from the hope may not depend on the accuracy of the calculation -- or even on the existence of a calculation.

 

[Jorghnassen]

Funny how rational and irrational (also what is "common sense" and what isn't) aren't so clear cut .

 

[Dave1001]

Funny how rational and irrational (also what is "common sense" and what isn't) aren't so clear cut .

Yeah, I think most of us knew that going in. But I think a good short hand for rational is what maximizes the agent's odds of persistance as an agent. Because if it ceases to persist as an agent, it ceases to be a factor in future interactions. Sort of like the agents in the tit-for-tat game, and what drives persistance in natural selection environments.

 

[Dave1001]

It does not. The amount of psychological "lift" you get from the hope may not depend on the accuracy of the calculation -- or even on the existence of a calculation.

Well, I think this is just a difference in first principles and definitions of terms. Sort of like if you defined a prime number to be "multiples of two" and we're defining prime numbers to be "integers which are only divisible by 1 and themselves". We'd similarly end up arguing on parallel tracks.


It seems for your chosen definition rational is completely a function of an agent's action in any context. Why is the action rational? Because the agent did it. Is it rational to to pay a psychic $1000 to hear them tell you what their dead spouse wants you to do? Yes, because of the psychological lift you get from hearing their communication. Is it rational to tithe 10% of your gross income to an evangelical church? Yes, because of the psychological lift knowing that you're going to heaven. I won't say that it's a meaningless approach to ascertaining rationality. I just think it's a particular definition divorced from the analysis others of us are using. Sort of like if you chose to define rational as "whatever will give the agent the least hope". That's not a definition you're using, but I think it's just as arbitrarily different from ours.

I think the definition for rational choice we're using is reducible to that which most likely perpetuates the persistance of the rational agent. Hence the choice which leads to more resources to maximize persistance is more rational than the choice that reduces such resources. Thus, not maximizing returns from $1 invested is not the most rational choice. I think this is the same measure used in the Tit-For-Tat game and implied in most discussions about what is or is not rational. Although not generally spelled out in this level of detail (though I'm sure 100 more footnotes could be written), I think this is the default definition. Rather than "the rational choice is that which provides the most anticipatory happiness" or "the rational choice is that which provides the least anticipatory happiness".

 

[drkitten]

It seems for your chosen definition rational is completely a function of an agent's action in any context.

No.

Why is the action rational?

In broad terms, because it achieves a goal that the agent has (at reasonable cost).

Is it rational to to pay a psychic $1000 to hear them tell you what their dead spouse wants you to do?

Does it make you feel better? If so, then it's no less rational to pay a psychic $1000 to make you feel better than it is to pay $1000 for tickets to a sold-out show.

I think the definition for rational choice we're using is reducible to that which most likely perpetuates the persistance of the rational agent. Hence the choice which leads to more resources to maximize persistance is more rational than the choice that reduces such resources. Thus, not maximizing returns from $1 invested is not the most rational choice.

If you accept "returns" to be an extremely general concept, including things that we don't typically think of as financial, then, yes. But maximizing "returns" would then include things like the happiness you get from thinking about your possible lottery winnings, a happiness that does not seem to be dependent on expected value.

If you define "returns" to be purely financial, you just defined the entire entertainment industry out of existence, since going to a film costs you money and returns you nothing.

In presenting his development of game theory, Von Neumann and Morgenstern found it necessary to make the simplifying assumptions that all "returns" can be quantified and compared on a uniform scale. Even they weren't foolish enough to assume that this scale is a purely financial one.

 

[NobbyNobbs]

There is no force that acts on the coin to prevent it coming up heads a billion times in a row. That result is not prohibited, just extremely unlikely. So unlikely that we would question the "fairness" of such a coin or the toss.

Nothing "makes the predicted results happen". The landings do not "organize themselves". If they did then the Gambler's Fallacy would be true...

A coin toss is sufficiently complex that the result is random and either outcome has a probability of 0.5 every time the coin is tossed. The coin doesn't "know" about the previous tosses.

It is the randomness that causes the observed result. The upward force and induced spin rate varies slightly for each toss. The air currents are slightly different each time, etc. It is conceivable that someone could practice a particular flipping technique and acheive enough consistency to skew the results one way, but that wouldn't be a random event...

Another way to see it is that we know it is a random process precicely because the measured outcome, over a large number of trials, is 50/50. Any other result would be a strong indication that something non-random is happening... Then, and only then, does it make sense to seek a force acting on the coin (or other cause).

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

Ok, so I've been lazy and haven't read the whole thread, but I had to respond to this post. It seems to me that you're saying you get the results you do because the process is random, and you can prove the process is random because of the results that you get.

This is a circular argument. Did I read something wrong?

 

[Schneibster]

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen. ...

But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails? ...

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row? ...

The conversation seems to me to have gotten a bit far afield.

The question here, and please correct me if I've misunderstood you, seems to be, "what characteristic of the universe forces probabilistic predictions to come out correct?"

The answer appears to me to lie behind the fact that it is an inherent characteristic of the universe that when a process (that is, a sequence of operations or events with a defined beginning and ending) has alternative potential results (endings), and the process can be repeated, there will be a potential for each alternative to occur at each repeated trial of the process. However, in each trial, only one of the alternatives will be observed (unless you are into alternative universes, and even then, the "you" that you will continue to think of as "you" will observe only one of them in any one universe). The details of the process (objects involved, forces that affect those objects, particular states chosen as the "beginning" and "ending" of the process) will determine not only the number and type of alternatives, but also how likely each alternative is with respect to the (presumably) unity probability that there will be some result. (Note that if this is not a unity probability, then you cannot clearly define an "ending" state, and discussion of probability would be moot.)

Now, note that we've invoked objects, forces, and states; clearly, we are discussing physics here. Thus, the process is governed by physical laws, which are, by and large, and as far as we have been able to observe, essentially immutable over both space and time (that is, over a long enough series of trials, I'll get the same number of heads and tails today as I will tomorrow, and I'll get the same number at home as I will at the bar). This has exceptions, but we know about most of those, too (for example, if my coin is brass on one side and iron on the other, and I flip it over a magnet, it will alter the probabilities).

So basically, what I'm saying is that the fact that such probability calculations work so well is a consequence of the fact that we live in a universe in which physical law determines the outcome of the overwhelming majority of, if not all, processes, and in which physical law is essentially immutable. This is borne out by the fact that we seem to be able to assign such probabilities to the behavior of the smallest constituents of matter/mass/material and force/energy/influence, and when we observe the behavior of these constituents, we never observe behavior in violation of these probabilities; when we do, we go looking for the new law that governs this unexpected behavior, modifying our earlier understanding.

This is a kind of determinism, but it is not philosophical determinism; at the quantum level, we can predict the probability that a process will attain various alternative states extremely accurately, but we cannot predict which alternative any particular trial will result in. Just as we cannot predict whether the coin will come up heads or tails, but we can predict that (absent some physical force that we are not aware of) it will come up heads half the time and tails the other half.

This appears to me, in other words, to be the result of two fundamental characteristics of the universe that exist a priori, that is, without any underlying "machinery" or "cause:"
1. The behavior of objects, systems, and processes is governed by immutable physical laws; and
2. These laws specify the probability that various fundamental processes will result in various alternatives.

Rather a long answer for what is actually a rather deep question, IMHO. Hope it was worth your while to read.

 

[Hellbound]

...Rather a long answer for what is actually a rather deep question, IMHO. Hope it was worth your while to read.

Yeah, what he said.

That's what I was trying to get at earlier, only mine wasn't as smart, or clear, or readable, or, you know, good.

 

[Schneibster]

Thanks!

 

[Notrump]

There Is No Force - Only Math

There is no “force” of probability. It is a purely mathematical concept.

Let’s allow coin flips as a good representative for a wide variety of probabilistic events. With coin flips we are conceivably dealing with a deterministic process. But measuring the conditions and calculating the result of even a single flip is far beyond our capabilities. So we resort to the laws of probability, which are purely mathematical. Other than quantum mechanics (and some might argue even then), we only relate probabilistic laws to the physical world when actual measurements or calculations are difficult or impossible.

Assuming unbiased conditions, then according to the laws or probability, no matter what has been the result of previous flips, the next one is equally likely to be heads or tails. That also means that if after 100 flips, 60 heads occurred and 40 tails, either type is equally likely to show up the majority of the time in the next 100. Interestingly, if the result were 50-50 in the second 100, then the average number of heads per flip would decline from 0.60 after 100 flips to 0.55 after 200. If the result were 54-46 in favor of heads in the second 100, then the average number of heads per flip would decline from 0.60 after 100 flips to 0.57 after 200, despite a majority of heads during the second 100.

So in the long run the average for each type will likely approach 0.50, even if the absolute difference between the number of occurrences of each type remained nearly unchanged or slowly increased. Thus “reversion to the mean” does not mean that an event, which had been occurring less frequently than predictions, will then start outpacing predictions. Instead it means that the overall average will likely revert nearer to the predictions.

"Likely" is the key word. In actuality, anything can happen. But by employing the mathematical laws of probability, we can often make reasonable decisions and preparations for otherwise uncertain future events.

Again, it’s purely math. There's no “force” of probability.

 

[born]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet.

How about you factor in the "tosser". Each of us have a certain degree of subconscious reflex action. If that same person keeps flipping the same coin, with their usual style of movement and spontanious force level, there should end up being some sort of pattern.

 

[lenny]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play....

chaos keeps going; each coin toss stops.

poincare' considered both types of systems about 100 years ago; hardly pseudoscience (overhyped in public no doubt, but strong mathematical core.)

 

[lenny]

How about you factor in the "tosser". Each of us have a certain degree of subconscious reflex action. If that same person keeps flipping the same coin, with their usual style of movement and spontanious force level, there should end up being some sort of pattern.

i do not know of an experiment testing individuals; however there was an experiment some time ago which, grouping many people together, came up with ~51% chance that a fair toss by a normal person (no magicians!) would land with the same side up facing up as was up when it was tossed...

(i can look for the reference if anyone wants it)

 

[Tarot_Is_A_Card_Game!]

Bingo!

There is no “force” of probability. It is a purely mathematical concept.

I was just going to post the same thing, but you beat me to it!

 

[fuelair]

Nothing drives probability. That is a meaningless concept. Probability is simply a mathematical statement of observed occurences. Actually, if things did not work out according to the mathematics there would be a need for an explanation. (The odds that two things that are able to happen randomly mean they will happen equally over a large number of opportunities. If they do not, they are not happening randomly and and explanation is in order)