Long Term Reification

[luckyme]

I'd like to wander through 'long-term'.

We create a concept called 'long-term expectation' to help us visualize some probability situations. It has no existance and can't influence outcomes of any single situaton or a series of them.

When a situation occurs that has several potential outcomes ( it's hard to think of ones that don't fit that description), each outcome has some probability of being the actual result. Whether we're looking at a unique situation or one that we run into everyday, the probability of the various outcomes are independant of that.

The question - does that statement " the long-term doesn't apply" have a meaning in probability calculations?
I've thought it never applies ( since it not something that exists therefore can't influence anything), just as historical outcomes don't apply.
a) a true coin has flipped 10 heads in a row. The 11th toss has a 50-50 chance of being heads.
b) I'm offered to bet a large amount on the results of tossing a weird-looking irregular multi-faceted rock, each face being numbered. The rock will be smashed after the toss. The probability of any face coming up can be calculated by a super computer. The fact there will be no long-term results for this rock toss, does not make the situation any different than the coin one. ??

Am I missing something? 'Long-Term' never applies to current outcome probability?

thanks, luckyme

[Copernicus]

I would rephrase your original premise as: "long-term expectation" (in the context of the likelihood of an occurrence, not the value of the occurence) and "probability" are equivalent representations of the same concept.

Their equivalence, of course, can only be demonstrated through "long-term" experiments.

Your proposal that the long-term doesnt exist is equivalent to recogntition of the law of large numbers.

A single trial has negligible impact on the law of large numbers, which looks at the limit as the number of trials approaches infinity, and to that extent the long-term doesnt exist from the perspective of that single trial.

[luckyme]

[ QUOTE ]
Your proposal that the long-term doesnt exist is equivalent to recogntition of the law of large numbers.

A single trial has negligible impact on the law of large numbers, which looks at the limit as the number of trials approaches infinity, and to that extent the long-term doesnt exist from the perspective of that single trial.

[/ QUOTE ]

hmmmm... I think I'm going farther than that, and pushing on the other end of the rope.

Neither has any effect on the other. The LoLN is not an entity that can affect an event nor be affected by an event. 1,000 trials don't affect the LoLN either, nor did it affect their outcomes, nor will it affect the next.

I've ran across the "long-term doesn't apply" enough times to know it does affect how people make a decision when the situation they're facing is rare or unique. I've even capitalized on their view. Here, in a philosophy forum, seems a good place to look for the best way of explaining that the long-term never applies, it never affects an event. The outcomes of an event have probabilities of occuring ... period, even if the LoLN is repealed while we sleep, even if it's a unique situation.

Perhaps another way -- we don't need to know if it's a recurring or common situation in order to calculate the probability of various outcomes. We only need to know the variables involved. ??

'long-term' is a different issue altogether.

thanks for the comments, luckyme

[chezlaw]

For pure arithmetic ev The long term expectation is just another way of looking at the same thing.

People get confused by situations where the EV is an amount they cannot possibly get. Long terrm expectations transform the EV into an amount they can get.

In real subjective EV's the expected number of times the experiment will be repeated is vital.

chez

[madnak]

I agree that "the long-term doesn't apply" is typically misused. I think utility is what people are actually referring to in these situations. The idea that it's foolish to take a +EV action just because you won't have a large number of trials makes no sense. But due to utility, an action that would have a positive expectation over a large number of trials might have a negative expectation over a small number of trials.

For example, if I can pay $1,000,000 to flip a coin to win $11,000,000 under the circumstances in KnickNut3's thread (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=5356204&an=0&page=0#Post 5356204), there's no way I would take that deal over 1 trial. My life would be destroyed by debt 50% of the time. It would be -EV because the utility of winning $11M is actually less than the utility of losing $1M.

But if I can take the bet 10 times, now I have only a 1/1024 chance of losing money. I'm very likely to win at least 2 million bucks. That is a deal I can make. And with 100 trials, my risk of ruin is negligible.

So in this sense "there is no long run." But that's because of changing utility, not changing probability.

[luckyme]

[ QUOTE ]
So in this sense "there is no long run." But that's because of changing utility, not changing probability.

[/ QUOTE ]

That seems to capture what I'd digging for.

[ QUOTE ]
But due to utility, an action that would have a positive expectation over a large number of trials might have a negative expectation over a small number of trials.

[/ QUOTE ]

I'm not sure I follow that. Are you referring to a 1 in a million lottery that pays $1M but is only charging 50c for each unique ticket? So if you buy 10 tickets you 'figure to lose', but you're in a +EV situation each time you buy.

I understand the Utility aspect of KnickNuts wager, but you are referring to expectation, which seems + to me, long or short. I'm not clear how multiple negative expectations will add up to a positive by repeating, or ...??

thanks, luckyme

[madnak]

I'm just talking about the KnickNuts wager. Fewer trials mean a greater risk of ruin (that's why we need bankrolls).

Er, that was unclear.

In a situation like KnickNut's, there's a higher risk of ruin. But in general it's just that with fewer trials you're more likely to end up down. You have more variance. That's why you need a bankroll. So you can afford a large enough number of trials to eventually come out on top even if variance causes you to lose in the short run.

If losing has greater negative utility than winning has positive utility, then the number of trials can influence the correct choice. The lower the number of trials, the greater your chance of losing.

[guesswest]

I think you're possibly overthinking this lucky - 'long term doesn't apply' is just an expression, I don't think anyone's using it literally. I don't think anyone's suggesting there is no quantifiable expectation involved, regardless of the number of trials.

Shifting utility is most certainly an issue, but the primary issue when people dismiss the long-term and turn down a +EV bet is just exposure - they're using that expression to communicate they won't take small +EV on a massive bet because they don't want to take on that much risk. Obviously, the more times you know you can take the same +EV bet the greater the chance that your variance will synch up with your expectation, so the lower the risk.

[luckyme]

[ QUOTE ]
'long term doesn't apply' is just an expression, I don't think anyone's using it literally

[/ QUOTE ]

Either way, I'm putting forward a contrary view.
a)They say it and mean it. - My claim is that it's a waste of good air because the long term is not a factor in our probability calcs, no need to point it out.
b) They say it and don't mean it. - see above..and below from my op...

[ QUOTE ]
The question - does that statement " the long-term doesn't apply" have a meaning in probability calculations?

[/ QUOTE ]

Long-term outcomes are derived from our probability calculations, not the other way around. There are factors that influence probability of outcomes .. the number of sides on the die, how true they are. The number of cases on a stage, who the accounting firm is. "Long-term" is not a factor it's merely one way of laying out the results.

It seems circular to now take one form of the outcome of our prob calcs and use the term "they apply or they don't apply" when referring to the actual calculation.

( EV is just adding a arbitrary $, or happiness or comfort value to the probability calcs, so it would seem that the 'long-term' EV can't affect the present EV calculation either.. but since it's secondary to probability I wasn't addressing it from that aspect. I see chez has a comment on EV and I'll raise some questions there).

Is there a time when I'm calculating probability that I need to put 'long-term' as one of the factors that apply? If not, why do people mention it at all?

thanks for the help, luckyme

[luckyme]

[ QUOTE ]
In real subjective EV's the expected number of times the experiment will be repeated is vital.

[/ QUOTE ]

I'm not clear on your claim so I need to probe a bit.
since EV is derived by adding a V factor to the calculated probability, and that isn't dependant on the number of trials, it seems we'd need to construct some very special circumstances to make the number of trials an issue, vital or otherwise. let's see...

The vital factor in subjective V would seem to be what I think of the position I'll be in at the end of any trial. So, I may be comfortable agreeing to bet on '6' on the die at 6 to 1 ( yummy), if they roll 1000 times before we settle at $10,000 a bet, I may not be willing to settle after each bet ( I may only have a 30,000 bankroll).

But that is apples and oranges. It's not a repeat of the same trial it's two separate trials under separate conditions. hmmmm.

ok, maybe stated this way -- if the 'expected number of times the experiment will be repeated' then what you have done is create a different event consisting of X repeated units. "I did a 5 mile walk this week" is not the same as "I walked 1 mile 5 times this week".

Obviously I'm not getting your point, chez... back to you. thanks, luckyme

[Copernicus]

[ QUOTE ]
[ QUOTE ]
'long term doesn't apply' is just an expression, I don't think anyone's using it literally

[/ QUOTE ]

Either way, I'm putting forward a contrary view.
a)They say it and mean it. - My claim is that it's a waste of good air because the long term is not a factor in our probability calcs, no need to point it out.
b) They say it and don't mean it. - see above..and below from my op...

[ QUOTE ]
The question - does that statement " the long-term doesn't apply" have a meaning in probability calculations?

[/ QUOTE ]

Long-term outcomes are derived from our probability calculations, not the other way around. There are factors that influence probability of outcomes .. the number of sides on the die, how true they are. The number of cases on a stage, who the accounting firm is. "Long-term" is not a factor it's merely one way of laying out the results.

It seems circular to now take one form of the outcome of our prob calcs and use the term "they apply or they don't apply" when referring to the actual calculation.

( EV is just adding a arbitrary $, or happiness or comfort value to the probability calcs, so it would seem that the 'long-term' EV can't affect the present EV calculation either.. but since it's secondary to probability I wasn't addressing it from that aspect. I see chez has a comment on EV and I'll raise some questions there).

Is there a time when I'm calculating probability that I need to put 'long-term' as one of the factors that apply? If not, why do people mention it at all?

thanks for the help, luckyme

[/ QUOTE ]

I guess im still not getting your point. If you dont need to mention "long term" in one context, you dont need to mention "short term" in the other...they are different representations of the same probability.

Saying "I have a 1/6 chance of rolling 7 when I roll two die" and "If I roll two die 6 million times, the expected number of 7's will be 1 million" or "the sample mean from n trials of rolling two die as n approaches infinity is 7" are all the same thing. There are short, long and infinite expressions that are interchangeable.

One may be more helpful in describing a given experiment, but none are any more relevant than the other for any experiment.

[chezlaw]

[ QUOTE ]
I'm not clear on your claim so I need to probe a bit.
since EV is derived by adding a V factor to the calculated probability, and that isn't dependant on the number of trials, it seems we'd need to construct some very special circumstances to make the number of trials an issue, vital or otherwise. let's see...

[/ QUOTE ]
An example of what I mean is insurance. Unless it's priced wrong, insurance is always bad from an arithmetic ev point of view.

From a subjective point of view it depends how often the insuranced event is likely to happen.

It makes sense for your average bod to insure their car against theft as their car gets stolen infrequently and its a real pain. The subjective value of reducing the risk is high enough to overcome the negative arithmetic ev.

If you own 2000 cars then it makes much less sense to insure them against theft. Thefts will be common but cause much less hassle - now the subjective value of reducing the risk may not be enough to overcome the negative arithmetic ev.

chez

[Copernicus]

[ QUOTE ]
[ QUOTE ]
I'm not clear on your claim so I need to probe a bit.
since EV is derived by adding a V factor to the calculated probability, and that isn't dependant on the number of trials, it seems we'd need to construct some very special circumstances to make the number of trials an issue, vital or otherwise. let's see...

[/ QUOTE ]
An example of what I mean is insurance. Unless it's priced wrong, insurance is always bad from an arithmetic ev point of view.

From a subjective point of view it depends how often the insuranced event is likely to happen.

It makes sense for your average bod to insure their car against theft as their car gets stolen infrequently and its a real pain. The subjective value of reducing the risk is high enough to overcome the negative arithmetic ev.

If you own 2000 cars then it makes much less sense to insure them against theft. Thefts will be common but cause much less hassle - now the subjective value of reducing the risk may not be enough to overcome the negative arithmetic ev.

chez

[/ QUOTE ]

What if all 2000 are stolen by Nicolas Cage and a crew of hot women in 60 seconds?

jk of course, but Im not sure that having 2000 cars makes insuring them less "subjectively valuable". It depends on whether the exposure of the 2000 cars to theft is less than 2000 times the exposure of 1 car. [Putting aside the fact that if you can afford 2000 cars you can probably afford to replace them if they are stolen].

Insuring them might become more aritmetically -EV if you take measures to prevent theft that are more practical with a large number of cars that dont correspondingly reduce your premium. For example hiring an armed guard may be very practical for 2000 cars, but not so for 1 car. Exposure to theft is then greatly reduced, but I dont know of any actuarial adjustments that would be made for the presence of a guard.

[luckyme]

[ QUOTE ]
I guess im still not getting your point. If you dont need to mention "long term" in one context, you dont need to mention "short term" in the other...they are different representations of the same probability.

[/ QUOTE ]

Actually, perhaps you do get my point, but that depends on what you mean by short-term. I've been probing about why people make a special effort to state in certain unique or rare probability events that "the long-term doesn't apply". As you've expressed, the long-term is just a special way of visualizing probability. You're stating that the reverse is also true, and if you look at the 'short-term' as ' a long-term of one trial' then that seems valid.

I don't think "there is a 1/6 chance of a 3" refers to a trial of 1, for example. I don't see probability that way but more like the schrodinger's cat situation. A true die has a 1/6 chance of rolling a 3, before anyone ever thought of odds. Probability is a property of the die, as in, " a True die will roll a 3, 1/6 of the time", even if it's never rolled. "A cubic die has an equal area on all sides" ( that's one reason it's a true die).

Why I think we may still be on different pages is because I never need to ask "how many trials" and in that sense "short-term of one" doesn't even apply. When we say "1/6 chance of rolling a 3" we are not referring to a series of 6 trials ( that would be the long-term view) we are talking about it in a non-concrete way.

The probability exists – we apply it to the number of trials we are considering, from 1 to infinity. There is no need to state “I’m not thinking of it in infinite trials this time” or “The expected outcome of 300 trials doesn’t matter this time” or … anything. We don’t have to list out the trial setting we are not working in at the moment.

So what is it that people think they are 'not applying' when they say "the long-term doesn't apply" ? I've phrased it as "it never applies" since it's an arbitrary extension of the basic probability, you may say "it always applies" because we can any multipliers we want to the basic form. x=y is the same as 10x=10y.

so why is “the long-term doesn’t apply” ever typed out?

Obviously, I’ve op’d this very poorly, thanks for trying to work thru it,
luckyme