Is retrospective decision-making valid?

[ledwix]

Suppose a risk is associated with an event. The event has probability A > 0 of being extremely successful and making your life awesome. The event has probability B = (1 - A) of being a failure and making your life considerably worse. Now suppose that A is much, much greater than B. There is almost no chance that the event is going to turn out bad, and when you ask people for advice, you get resounding encouragement. From this position in time, absolutely everyone agrees that you should carry out the event due to its high chance of success. Now with this encouragement, you carry out the event, but you find that the section B of the sample space actually occurs, and so your life becomes much worse.

Retrospectively, you did something that made your life much worse. Does that mean you shouldn't have done it and that B was actually 100%? Or, given that the initial probabilities were actually correct, and that there is just no way to determine the result of a single iteration of an event unless 100% or 0% is the probability of the event, should you have actually done it still?

Also, I'm not asking if retrospective decision-making is useful. It can't possibly be useful if the initial probabilities were actually correct. Once you make a decision with good knowledge of the chances of its success, there is no way to go back and change things once you know the outcome. Instead, I'm asking if it's valid, i.e. should you have actually done it?

[Patashu]

saying that the probability of any event that's already happened is 100% (or conversely 0%) is a useless distinction to make and ignores the point of what probability is. moreover, probability is not something that actually exists (barring quantum physics) - what we have are probability models that use information about prior events to produce a model that is probabilistically accurate for future events.
while these probabilities can be changed and even turned into certainties by the addition of new evidence and the adjustment of the probability model, taking an event on it being probabilistically likely to be good for you and then finding it's not isn't a failing of the model - it's exactly what the model predicted could happen, after all. at most it could be a failing of gathering more evidence before making the decision, if more evidence can be gathered

[Vendetta21]

Retrospective decision-making is valid when you're confronted with Newcomb-like problems, but when you reconcile retrospective decision-making with probabilistic decision making you instead get timeless decision theory.

[Vendetta21]

So what I'm saying is you should make all you decisions in a fashion that is time-neutral.

[MrRubix]

EDIT: Eh let me type something more descriptive, h/o

You're technically answering your own question. When you say "much better" or "much worse" you refer to utility, which is the end-product of the benefit/cost duality that results from the probabilities on the margin.

For instance, I could say event X has a 50% chance of turning out favorably and a 50% chance of turning out unfavorably (say the price moment of a commodity), but I can use options to limit my downside, etc.

But let's assume we take all of this into account. We take into account all information -- all hedge strategies -- all outcomes, etc. All we know, given what we DO know, is that P(Good)=.99 and P(Bad)=.01, let's say (further modeled with a 100-sided die, for instance).

The only thing we know, here, within our encompassing model, is that 99 times out of 100, we're going to end up better off, and 1 time out 100, we're going to end up worse off as a result of our "black swan." Our alternative is to not "play into the game at all" if we value our current position enough such that the probability of B, albeit low, is not something we want to risk. There are some traders, for example, who take on events such that they ensure they will never lose more than X dollars. They may limit their upside, but as humans are are far more sensitive to a loss of X than a gain of X in terms of marginal utility.

The question then becomes "Are we willing to risk this bad event happening?" The answer is typically "yes." We take risks every day. Even when we cross the street, we have a relatively high rate of survival and a relatively low rate of having a crazy driver clock out of nowhere and run you over. There's a certain point in our human psyche -- our utility interpretations -- that allow us to dictate the terms of how much risk we're willing to handle in exchange for reward.

There is no way to argue that "We should have chosen differently" -- that is only with the bittersweet gift of hindsight. If A and B already include all known information, you can perform the event multiple times in order to adjust the probabilities (much like how we might adjust the probabilities of die rolls over time based on what we extrapolate from our histogram). Alternatively, we can try to infer probabilities by understanding the system's information more clearly and accurately.

Either way, it only makes sense for us to say "A and B were actually something else" when we've gained information. That gained information can be in a variety of forms, but ultimately, nobody is safeguarded against things we simply don't have information for.

[devonin]

Also, it's just a faulty premise after B(Bad) happens to say "So retrospectively the chance of B happening wasn't actually .01 but instead 1.0"

I mean, yes, that is what happened, so if your system was claiming that it was 0.0 then the system was faulty, but you've only made the choice one time. If you had some method by which to go back and reproduce the same choice in the same conditions, chances remain .99 that (Good) will still be the outcome of the decision.

[MrRubix]

The whole point of probability is to model what we *don't* know on the *margin*. Anything that occurs is sunk.

[MrRubix]

Originally Posted by Vendetta21

Retrospective decision-making is valid when you're confronted with Newcomb-like problems, but when you reconcile retrospective decision-making with probabilistic decision making you instead get timeless decision theory.

Retrospective decision-making isn't really retrospective when we're talking about Newcomb-like problems (unless we invoke a variety of fairly nonsensical assumptions when it comes to our world -- at least, compared to causal decision models) -- the problem there is typically a conflation of the language used to describe what's going on.

It's all part of the same canon -- stuff like Zeno's Paradox, the Envelope Paradox, Newcomb's Paradox, Monty Hall Paradox, Einstein-Podolsky-Rosen Paradox, Schrodinger's cat paradox, Birthday paradox, etc... they are all not really paradoxes. They may seem paradoxical if you apply certain models/languages to them that put different bits of information at odds against each other, but really the problem is that the models aren't being leveraged properly with respect to decision making/causality standalone.

[MrRubix]

Originally Posted by Vendetta21

So what I'm saying is you should make all you decisions in a fashion that is time-neutral.

*Risk-neutral

Check out something like http://en.wikipedia.org/wiki/Rationa...tral_valuation

In this case substitute u and d for something favorable and unfavorable

[Vendetta21]

Originally Posted by MrRubix

*Risk-neutral

i was actually just making a bad joke
http://singinst.org/upload/TDT-v01o.pdf

[MrRubix]

Oh, I see XD

[ledwix]

So, what you guys are mainly saying is that if you cross the street on a regular day and get run over by a car coming around a corner at 90 mph, it was still a good idea given the knowledge that there was almost no chance that it would happen? This is the view that I hold, but how come so few people hold it? A pure misunderstanding of probability? I find that most people I talk to tend to believe that good decisions are defined in terms of good results. An NFL coach makes a very gutsy decision out of desperation, it succeeds, and commentators laud him for being a genius. If the decision fails, they talk about how poor a decision it was. This type of deterministic logic seems to be used everywhere.

[MrRubix]

Ledwix: Yes. There are some risks that are low, unavoidable, and high-impact. We can demonstratively show with statistics and utility models why it's typically a good idea to insure against these risks whenever possible.

Risks come in different forms though -- systematic/market (undiversifiable risk) and idiosyncratic/specific risk (diversifiable risk). For instance, I can insure against a low-probability high-impact event of, say, my servers all going down at once if I place them all in different areas. So if a power outage nukes one server, it won't nuke the others. I lower my risk by spreading out into environments that are affected by unrelated variables in some way. Similarly, instead of investing X dollars in one company, I might invest X/10 dollars in 10 companies. That way if one company goes belly-up, I don't lose everything.

But then there is systematic risk -- the stuff that screws everyone. It's risk you can't avoid through diversification. You can't gain insurance from anyone because they're just as exposed as you are to the underlying risk. Luckily, not everyone agrees about the direction that the risk will move. You can only try to beat systematic risk by being hedged. For example, consider a jet fuel futures market. It's relatively illiquid -- so if something awful happens, it hurts everyone. The only way you can limit how badly you are hurt is if you are hedged -- meaning that someone, at some point, made a bet with you and entered into a contract where you were guaranteed a limited downside because they assumed your risk. Of course, the more systematic the risk, the harder it is to hedge yourself perfectly (resulting in costly hedges).

Of course, the upside is greater with systematic risks because, obviously, they're riskier. Therefore you are compensated more if you exposed yourself to a risky situation that happened to move favorably.

Taking your point about the NFL coach, it's due to a massive misunderstanding of statistics. We laud people as being geniuses when they are lucky when they could have just as easily been unlucky. Sometimes geniuses fail, too, and sometimes idiots get lucky. It's always easy, in hindsight, to say "I got rich off Company X because I always knew their stock would go up" without considering the comparably more numerous cases where people lost out betting the other direction or in lower magnitudes even though nobody had better information -- it was simply getting lucky off a bet. It's a frequent case of confirmation bias. If we get a few thousand people in a room, all rolling dice, a few of them are going to get multiple 6's in a row by pure chance alone. Does this make them skilled? Not necessarily. The hard part is knowing what's luck and what's skill aimed at maximizing the chances.

Consider that dice example as being an analogy for an infinitely large number of events being performed constantly all around us. Black swans occur all the time -- but in forms that are not meaningful to us.

Sometimes good decisions turn out badly and there's nothing we could have done better. The depressing thing about higher-level finance, for instance, is that you come to realize how much of it is really just a betting game. The guys who crunch their numbers better than the other guys in terms of assessing probabilities are the ones who win the most bets because they know how much to risk, how to hedge, where to expose themselves, who to hire, how to pay them, how to handle their downsides and bottom lines, what technology needs to be employed, etc.

In short, a good decision takes into account not only the expectation of an action's result, but the inherent variance -- as well as the number of times you plan to perform this action.

[MrRubix]

Check out the following when you get a chance:
-The Trillion Dollar Bet
-Fooled by Randomness by Nicholas Taleb

In particular, the stories about the darts, Nero vs. John, the Black Scholes model, the implications of Monte Carlo simulation, and trading compensations are very interesting. If you can't be bothered to watch/read those, I'll explain if you want.

[Cavernio]

"So, what you guys are mainly saying is that if you cross the street on a regular day and get run over by a car coming around a corner at 90 mph, it was still a good idea given the knowledge that there was almost no chance that it would happen? This is the view that I hold, but how come so few people hold it? A pure misunderstanding of probability? I find that most people I talk to tend to believe that good decisions are defined in terms of good results. An NFL coach makes a very gutsy decision out of desperation, it succeeds, and commentators laud him for being a genius. If the decision fails, they talk about how poor a decision it was. This type of deterministic logic seems to be used everywhere."

But this is not necessarily bad, because we might not have a very good model for predicting what the probabilities ARE. Something like crossing the street, we probably have a pretty good one. Something like choosing the strat to win a sports game? A lot more up in the air. I basically see the question not as 'Are the chances good' but 'Is the model good'. The world we live in is not static, and constantly readjusting our model is called learning.
Furthermore, its not just numbers we have to pay attention to when making a decision, its the consequences as well. If you decide to cross an apparently deserted highway that is usually not busy at all, only to find that you get hit by that car coming around the corner, because you thought you only have a 1% chance of getting hit, you were still pretty ****ing stupid, because a 1% chance of being hit is high when you're taking your life into your hands unnecessarily. People are known to put a lot more weight on experiences that've happened recently than to look at the entire picture, and I hear all the time that this is dumb and that they shouldn't put more weight on the most recent negative experience, they're ignoring the numbers, they don't understand statistics, etc. BUT, evolutionarily, acting on situations with putting more emphasis on recent events allows an organism to change their model quickly if they need to, and that probably meant the difference between life and death for many animals, from encountering a new predator to learning that a specific patch of food you've eaten at for years has suddenly become poisonous. Its certainly very useful for when you don't understand a situation fully. Now, as humans, we can mix intelligent thought into this, and it rarely happens that we don't have some understanding of why something happens one time versus another. But retrospective decision-making doesn't just involve saying 'I guess I shouldn't have done that', it involves thinking about what just happened and trying to pull information that you may not have used to your advantage before the decision. Even in something like playing poker, if you go all-in because statistically you figure you're more likely to win, but you loose, and you then tell yourself afterwards that you made a bad play, you might realize or toy with the idea that something the other player did was a tell, and that you were wrong that time. (When people say 'I shouldn't have done that', I think they really mean 'Next time I shouldn't do that', or would correct themselves upon thinking about what they're saying.)
People are still dumb when they decide to use the most recent events on situations that are purely random though, like because you lost a coin flip 10 times in a row you're due for a win. But situations like those are very, very few IRL.