101% probability

[luckyme]

As a non-mathematical poster, I’m hoping for an epiphany here.

Event A - chance of it occurring small but greater than 0.
Causal events cA1 thru cA100 – total chance of them being the cause of A = 100%

Event A occurs – the chance that cA1 thru cA100 caused it increases to -- ??

I struggle to get above 100% in these situations.

I also can’t grasp how the mere actual occurance of A changes the chances of any specific cause since we had assigned them probabilities based on A occurring. A’s occurring is a ho-hum event as far as cA1 thur cA100 go.

PLEASE don’t get ahead of me on this, I’m confused enough. Stay with my abstract statement, no examples, and just point out, with explanation, the flaw in my approach above.

There is another step for me once I’m convinced my foundational understanding is right or wrong.

thanks, luckyme

[chezlaw]

Your initial situation is:

if event A happens then the chance that cA1 thru cA100 caused A is 1.

If you learn that Event A happened then nothing about the probabilities of cA1 thru cA100 being the cause of A changes.

It may now be more likely that each of cA1,.., cA100 happened but that's because A may be evidence that one of the causes happened.

chez

[soon2bepro]

I don't see how chances increase in any way when A occurs.

[madnak]

Methinks you're misunderstanding. Is this in relation to David's post about Biblical accuracy and miracles and conspiracies? Well, you don't want examples. So.

If the probability of event A happening is 0.02, and the probability of event B happening that causes A is 0.2, then there's a paradox. Because B entails A, if the probability of B is 0.2, the probability of A must be at least 0.2. Whenever B happens, so does A, so A is at least as likely to happen as B.

Here's where I think you're getting confused. The scenario you're describing is as follows, if I'm not mistaken: If A happens, A has a cause (one and only one). There are 100 possible causes of A, call them cA1 through cA100. Because A will have one and only one cause, and these are all the causes A can have, the probability of one of them being the cause of A is 100%. Edit - I'm also assuming that if any cA happens, A must also happen. That makes it simpler.

Your error here is in assuming A from the start. Remember, if A doesn't happen, neither do cA1 through cA100. They can only happen if A happens. So if there's a 20% probability that A happens, and there's a 100% probability that a cA is the cause of A, then there's a (20%)(100%) = (20%) chance that a cA will occur. It's impossible for cA1 + cA2 + cA3 + ... + cA100 to be greater than 20%, because every cA implies A, so obviously cA can't be more probably than A.

What you're saying is that all the cAs added together represent 100% of the probability of A. You're not saying there's a 100% chance of them happening - there's only a 20% chance of them happening. Since the probability of any cA happening is the same as the probability of A happening (when A happens, some cA happens, and vice versa), if you increase the probability of A happening you increase the sum total probability of all the cAs happening.

I think I could make this super-clear using examples /images/graemlins/frown.gif

[luckyme]

[ QUOTE ]
Your initial situation is:

if event A happens then the chance that cA1 thru cA100 caused A is 1.

If you learn that Event A happened then nothing about the probabilities of cA1 thru cA100 being the cause of A changes.
It may now be more likely that each of cA1,.., cA100 happened but that's because A may be evidence that one of the causes happened.
chez

[/ QUOTE ]

thanks chez, but does the bold part not go against my premise ... I assumed A could happen so it's happening changes nothing about my assignment of probability to cA1 to cA100.
I suspect you mean .. some specific event B thru X that occured with A or just prior or post it that adds weight to one or more cA's at the expense of other cA's ?? or something else ?

thanks, luckyme

[luckyme]

[ QUOTE ]
What you're saying is that all the cAs added together represent 100% of the probability of A. You're not saying there's a 100% chance of them happening - there's only a 20% chance of them happening. Since the probability of any cA happening is the same as the probability of A happening (when A happens, some cA happens, and vice versa), if you increase the probability of A happening you increase the sum total probability of all the cAs happening.

I think I could make this super-clear using examples

[/ QUOTE ]

You may be saying what I'm saying. I'll rephrase.
Event A has one or more possible causes. We assign each of them a probability of causing A. Their total probability of that = 1. The chance of A happening can be .001 to .99999 or more.

Event A merely occuring does nothing to the underlying causal probablities ??

thanks, both for no examples and not getting ahead of me. luckyme

[chezlaw]

[ QUOTE ]
I think I could make this super-clear using examples

[/ QUOTE ]
How about poker. Suppose you have the 4th nuts, how can you lose?

100% of the time that you lose its caused by your opponant having the first, second or third nuts but the probability of them having any of those hands may be very low.

Once you lose the probability of them having each of those hands increases (assuming you dont get to see the exact hand).

chez

[FortunaMaximus]

It's a weighted ratio and not a cumulative, I think.

I'll echo the no-example annoyance, but it's a nice challenge.

[chezlaw]

[ QUOTE ]
[ QUOTE ]
Your initial situation is:

if event A happens then the chance that cA1 thru cA100 caused A is 1.

If you learn that Event A happened then nothing about the probabilities of cA1 thru cA100 being the cause of A changes.
It may now be more likely that each of cA1,.., cA100 happened but that's because A may be evidence that one of the causes happened.
chez

[/ QUOTE ]

thanks chez, but does the bold part not go against my premise ... I assumed A could happen so it's happening changes nothing about my assignment of probability to cA1 to cA100.
I suspect you mean .. some specific event B thru X that occured with A or just prior or post it that adds weight to one or more cA's at the expense of other cA's ?? or something else ?

thanks, luckyme

[/ QUOTE ]
hopefully the poker example makes it clearer.

chez

[madnak]

I'm using an example because this is convoluted.

Let's say John and Jim are in a room with a big red button. In another room is a light bulb.

The light bulb can turn on in only one of two ways - either Jim presses the button, or John presses the button. Jim is three times as likely to press the button as John. Therefore, for every time the light turns on, there's a 75% chance Jim pressed the button and a 25% chance John pressed the button. We'll call Jim J1 and John J2. Notice that J1 and J2 here add up to 100%. Every time the button is pressed, the light goes on.

Now let's say there's a 20% chance the light will turn on. What does that tell us?

Well, it means that 80% of the time, the light will stay off. This means that 80% of the time neither Jim nor John will press the button. The other 20% of the time, someone will press the button. We know that Jim is three times more likely to press the button than John, and since the button is pressed 20% of the time, that means Jim will press the button 75% of that 20% of the time and John will press the button 25% of that 20% of the time.

In other words, there are three things that can happen - Jim can press the button, John can press the button, or nobody can press the button. We have the following probabilities:

Nobody presses the button: 80%
Jim presses the button: 15% (75%*20%)
John presses the button: 5% (25%*20%)

We know that 80% of the time nobody presses the button because the light only turns on 20% of the time. For the rest of the time, Jim will press the button 3 times more than John.

What happens if the light turns on 60% of the time? Now we know that 40% of the time, nobody presses the button. The other 60% of the time, either John or Jim presses the button. Jim will press it three times more often than John, so now the probabilities are as follows:

Nobody: 40%
Jim: 45%
John: 15%

Compare the two scenarios. J1 and J2 tripled! And the only reason that happened is because we increased the chance of the light turning on. This is how increasing A can change the probability of cA1 and cA2. (But never over 100%)

[luckyme]

[ QUOTE ]
[ QUOTE ]
I think I could make this super-clear using examples

[/ QUOTE ]
How about poker. Suppose you have the 4th nuts, how can you lose?

100% of the time that you lose its caused by your opponant having the first, second or third nuts but the probability of them having any of those hands may be very low.

Once you lose the probability of them having each of those hands increases (assuming you dont get to see the exact hand).

chez

[/ QUOTE ]

OK. That's enough... you owe me a pint !!

1st nuts out against you - 20%
2nd nuts out against you - 30%
3rd nuts out against you - 50%
( of the times that you lose)

They annouce - "You Lose" and toss the cards in the bin. what changed in the above %'s.

my claim is nothing.

luckyme

[chezlaw]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I think I could make this super-clear using examples

[/ QUOTE ]
How about poker. Suppose you have the 4th nuts, how can you lose?

100% of the time that you lose its caused by your opponant having the first, second or third nuts but the probability of them having any of those hands may be very low.

Once you lose the probability of them having each of those hands increases (assuming you dont get to see the exact hand).

chez

[/ QUOTE ]

OK. That's enough... you owe me a pint !!

1st nuts out against you - 20%
2nd nuts out against you - 30%
3rd nuts out against you - 50%
( of the times that you lose)

They annouce - "You Lose" and toss the cards in the bin. what changed in the above %'s.

my claim is nothing.

luckyme

[/ QUOTE ]
??? you agree with what I said and then demand a pint - no fair.

Nothing about the probabilities of each cause given that you lose changes just by finding that you lose.

but given that you have lost its now a lot more likely that they have each of those hands because now they cannot have the 675th nuts.


not even a pint of budweiser for this attempt

chez

[madnak]

Well, they have to have one of the top three nuts now, which they didn't before. Probability of (N1 or N2 or N3) has gone from x<=1 to x=1. But that is really complicated. Ill-considered example.

[FortunaMaximus]

[ QUOTE ]
I think I could make this super-clear using examples

[/ QUOTE ]

That deserves the pint, not the point for the pint. /images/graemlins/tongue.gif

[chezlaw]

[ QUOTE ]
Well, they have to have one of the top three nuts now, which they didn't before. Probability of (N1 or N2 or N3) has gone from x<=1 to x=1. But that is really complicated. Ill-considered example.

[/ QUOTE ]
seems like such a simple example. /images/graemlins/crazy.gif

chez

[luckyme]

[ QUOTE ]
Now let's say there's a 20% chance the light will turn on. What does that tell us?

[/ QUOTE ]

My position is an analysis based on -- or starts at ...
"Of the times the light turns on"
Event A has occured, it's a given.
You're switching levels in a sense, stepping back to a bigger picture.

My first question really is as simple as it sounds, I just need to get it cleared and agreed before I can move on. ( you can see it does cause some confusion).

thanks, luckyme

[luckyme]

[ QUOTE ]
??? you agree with what I said and then demand a pint - no fair.

[/ QUOTE ]

that was for using an example ( they so often bog down a discussion). And you'll see it doesn't fit that well for my next step -

In the next step we have an Event A that has endless competing claims for it's cause but no evidence connecting them. We don't have a good basis for assigning which one is the actual cause of A ( unlike in chez example).

The probablity that cA1-cA100 in total caused A is still 1. When A occurs it is still 1. Unless event B or more occurs that adds clarification, we are still in the same boat. The mere occurance of A gives us no basis for changing the weighting of cA1-cA100. They'll still total 1 and they're still 'unkown' quantities.

Don't get ahead of me.

As long as the chance for A was non-zero, nothing changes in my estimation of cA1-cA100 chance of being the cause of A just by it occuring.

I think this is as simple as my 1st question, but again, I may be missing something and I want to confirmed or shot down. Then I'll see if it applies to another step.

Sorry for the kludgy way I lay it out..I'm not a mathematician.

thanks, luckyme

[chezlaw]

[ QUOTE ]
[ QUOTE ]
??? you agree with what I said and then demand a pint - no fair.

[/ QUOTE ]

that was for using an example ( they so often bog down a discussion). And you'll see it doesn't fit that well for my next step -

In the next step we have an Event A that has endless competing claims for it's cause but no evidence connecting them. We don't have a good basis for assigning which one is the actual cause of A ( unlike in chez example).

The probablity that cA1-cA100 in total caused A is still 1. When A occurs it is still 1. Unless event B or more occurs that adds clarification, we are still in the same boat. The mere occurance of A gives us no basis for changing the weighting of cA1-cA100. They'll still total 1 and they're still 'unkown' quantities.

Don't get ahead of me.

As long as the chance for A was non-zero, nothing changes in my estimation of cA1-cA100 chance of being the cause of A just by it occuring.

I think this is as simple as my 1st question, but again, I may be missing something and I want to confirmed or shot down. Then I'll see if it applies to another step.

Sorry for the kludgy way I lay it out..I'm not a mathematician.

thanks, luckyme

[/ QUOTE ]
Sounds exactly the same, nothing in my example relied on being able to assign the probabilities.

You're still starting with conditional probabilities given A happens and then saying that doesn't change if A happens.

That's clearly true but its hard to see where you are puzzled. Clearly the relative probabilities of each cause doesn't change unless there's additional information other than just A happening.

I assume you're heading to some point about DS's post but I don't think anyones making an error that is denying the obvious truth of the claim here.

chez

[madnak]

So you're saying when A happens then cA1 through cA100 add up to 1. And then you're asking if that changes when A happens? I'm not sure I understand. Haven't you already assumed that A happens, as a given?

Or are you saying, "for every A there's a 100% chance it was caused by cA1...cA100," and then asking whether that changes if an A happens? Of course it wouldn't if you set it up that way.

What are you confused about, and what do you mean about >100% probability?

[luckyme]

[ QUOTE ]
What are you confused about, and what do you mean about >100% probability?

[/ QUOTE ]

I'm not confused at my initial approaches, that's the scary part. What's confusing is that when I apply them to some situations on here, I end up in serious disagreement with respected posters. I'm likely going wrong somewhere in the process ...

So, I'm retracing my steps. Chez seems to agree that even in the case of conflicting causal claims that are of the nature of excluding other possibilities then the occurance of event A does not change the original probalility that a specific one was correct.

To use your lightbulb example ( shuddddder...). The light may or may not go on when you walk into the room. Your friends have theories/claims of cause -
Hortense claims his brother jim is turning it on.
Heathcliff claims his brother John is. etc.

At step 2, I'm merely clarifying that the fact the light came on doesn't assist us in deciding whether Hortense is right or not. We would need more evidence, Event B or more, to make progress in that decision.

You seem to prefer examples, I'll dig up the most recent one that captures what I'm trying to get clarified and use it in step 3. Unless you see a problem with step 2.

thanks, luckyme

[Mickey Brausch]

This thread belongs in the Probability forum.

[ QUOTE ]
Event A - chance of it occurring small but greater than 0.
Causal events cA1 thru cA100 – total chance of them being the cause of A = 100%
<font color="white">. </font>
Event A occurs – the chance that cA1 thru cA100 caused it increases to -- ??
<font color="white">. </font>
I struggle to get above 100% in these situations.

[/ QUOTE ]Why would you go above 100% ? I think you are confusing the probability estimates before the fact, with the "probabilities" after the fact. (After the fact, there are no probabilities, as such. Sh*t happened.)

After your event A happened, the potential causes cA1 thru cA100 "collapsed" to the specific cause that brought about event A.

If this could be repeated, by the way, and without prior outcomes affecting the future, you'd again have a legitimate set of causes cA1 to cA100 and a potential event A, etc.

Mickey Brausch

[FortunaMaximus]

A variation of Schrodinger's cat? Only as the subject, not the observer?

[chezlaw]

[ QUOTE ]
This thread belongs in the Probability forum.

[ QUOTE ]
Event A - chance of it occurring small but greater than 0.
Causal events cA1 thru cA100 – total chance of them being the cause of A = 100%
<font color="white">. </font>
Event A occurs – the chance that cA1 thru cA100 caused it increases to -- ??
<font color="white">. </font>
I struggle to get above 100% in these situations.

[/ QUOTE ]Why would you go above 100% ? I think you are confusing the probability estimates before the fact, with the "probabilities" after the fact. (After the fact, there are no probabilities, as such. Sh*t happened.)

After your event A happened, the potential causes cA1 thru cA100 "collapsed" to the specific cause that brought about event A.

If this could be repeated, by the way, and without prior outcomes affecting the future, you'd again have a legitimate set of causes cA1 to cA100 and a potential event A, etc.

Mickey Brausch

[/ QUOTE ]
I think this is meant to be about missing information not before/after the fact.

Though if you like then next time you want to assign a probability to god existing we could just agree its after the fact so probabilities don't exist /images/graemlins/wink.gif

chez

[David Sklansky]

Does the following math make sense to you?

There is a 90% chance that no miracle ever happened.

There is a 6% chance that Christianity is true.

Assumming the two above premises, if a miracle is shown to have occurred, there is now a 60% chance that Christianity is true.

[FortunaMaximus]

[ QUOTE ]
Does the following math make sense to you?

There is a 90% chance that no miracle ever happened.

There is a 6% chance that Christianity is true.

Assumming the two above premises, if a miracle is shown to have occurred, there is now a 60% chance that Christianity is true.

[/ QUOTE ]

Without needing to think about it, yeah.

Wonder about lucky though.

[luckyme]

[ QUOTE ]
Does the following math make sense to you?

There is a 90% chance that no miracle ever happened.

There is a 6% chance that Christianity is true.

Assumming the two above premises, if a miracle is shown to have occurred, there is now a 60% chance that Christianity is true.

[/ QUOTE ]

I'll try it. There are two possibilities. Event A never occurred - 90%. Event A did occur - 10%. Of that 10%, xtrianity being true ( and because it contains miracles) occupies 6% and other miracle causing stuff occupies 4%.

Yep. All causal 100% seems accounted for ( granting the premises and not quibbling over numbers).

I phone a mathguy and announce ... "A biblical strength miracle has occured". Nothing changes. xtrianity is still at 60% of the 'posible causes of miracles'. Not 50 and not 70.

If that seems ok, I can go to the next layer.

thanks, luckyme

[madnak]

Yes, it's 60% of the possible miracles, but it's still only 6% likely in general.

If Hortense predicts the light will go on and that the light going on was caused by Jim, then if the light goes on Hortense is more likely to be correct. Because at that point we can throw out all the possibilities in which the light doesn't go on (all of which are contrary to Hortense's prediction).

It doesn't increase the chance of Hortense being right relative to Heathcliff, though.