We live in an uncertain and complex world, yet we continually have to make decisions in the present with uncertain future outcomes. Indeed, we should be on the look-out for "black swans" - low-probability high-impact events. To study, or not to study? To invest, or not to invest? To marry, or not to marry? While uncertainty makes decision-making difficult, it does at least make life exciting! If the entire future was known in advance, there would never be an element of surprise. Whether a good future or a bad future, it would be a known future. In this course we consider many useful tools to deal with uncertainty and help us to make informed (and hence better) decisions - essential skills for a lifetime of good decision-making. Key topics include quantifying uncertainty with probability, descriptive statistics, point and interval estimation of means and proportions, the basics of hypothesis testing, and a selection of multivariate applications of key terms and concepts seen throughout the course.
1.2 Decision Making Under Uncertainty
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Из курса от партнера University of London
Probability and Statistics: To p or not to p?
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Dealing with Uncertainty and Complexity in a Chaotic World
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Dr James AbdeyAssistant Professorial Lecturer, LSE
University of London
[MUSIC]
In this section,
I'd like us to consider decision making under uncertainty in a little more detail.
So in the previous recording we played a game, the Monty Hall Problem.
And whereby, you had to try and find that sports car.
Now, that was a great example of decision making under uncertainty because at
the time you had to make the choice about which door to choose, you did not know for
sure where the sports car was.
True, I perhaps reduced the number of possibilities for you.
You originally began with three doors, and
my opening of door B reduced the possible options down to two, namely doors A and C.
But quite rightly you played to the probabilities of what one hopes and
selected door C at the final stage of the game
which gave you twice the chance of winning than sticking with door A.
Now, in that iteration of the game, you were simply unlucky.
You experienced bad luck because the sports car was behind door A all along.
However, we shouldn't consider this as just like a one-shot game.
But if we played this game multiple times,
then as an optimal strategy it would always pay to switch door.
Because in the long run, by having the strategy of switching, you
would be winning on average twice as often as if you stuck with your original choice.
So I don't promise you success in your decision making every single time.
Uncertainty exists, and we can never know for
sure what's going to happen in the future.
We'll never have the luxury of having that
crystal ball to know exactly what's going to happen.
Of course, with the benefit of hindsight,
it makes decision making very straightforward.
Once you know what was behind each of those three doors,
choosing where the sports car was would be a rivially easy thing to do.
But of course, in life we never have that benefit of hindsight.
So here, I'd just like us to consider a few examples of decision making
under uncertainty, which typically affects all of us at various stages in our lives.
For example, to study or not to study.
Well, what's the purpose of an education?
If we consider, for example, going to university and studying for
a degree, what is the purpose of that?
Well, I admit, different people may choose to go to university for different reasons.
For some, it may simply be for this sort of intellectual stimulation.
Maybe they have just a passion for a particular discipline and
want to pursue it further.
But I'm guessing the majority of people will pursue a degree
in order to enhance their job prospects.
So, possession of a degree would not guarantee you a job at the end of it.
There aren't really any certainties in life other perhaps than maybe death,
taxes, and in my case a computer crashes, as well.
So the possession of that degree or
certificate isn't a guarantee of a well-paid job at the end of it.
Or we could, though,
consider this as perhaps increasing your chances of success.
Namely, if you are a degree holder, you are increasing your probability of going
on to have, lets say, a successful career, if we decide to consider your
lifetime earnings as your sort of metric of success.
Of course, there will be some unemployed graduates out there in the world.
Just as there will be some, or many, employed non-graduates.
But if we consider in the long run pursuing an education, i.
e., opting to study versus not to study,
in the long run that tends to be for the benefit of people.
So other than to study or not to study, let's consider maybe a monetary example.
To invest or not to invest?
Should you buy a particular stock of a particular company?
Well, of course, we cannot know with certainty today whether the shared price
performance of a particular stock is going to be upwards or downwards.
But if we consider some very skilled investors, a natural example
would be a Warren Buffet, I'm speculating that the doesn't have perfect foresight.
And when he's made numerous investments over maybe 50,
60 years of investing, occasionally he's perhaps called it wrong.
He's made an investment where that investment ended up losing money.
Because, of course, he doesn't have that crystal ball and
he cannot know with certainty which stocks are going to perform very strongly.
However, we uphold him as a great example of an investor, an investment guru really,
the Sage of Omaha, we don't hold it against him that he may get
it wrong on occasions because he wins far more often than he loses.
You've only got to consider the performance of Berkshire-Hathaway
over many decades, and
I think we are all pretty much convinced of his investor skill.
So to invest or not to invest?
Looking at the data and trying to come up with probabilistic assessments about which
companies are more likely to perform better than others, and
that could guide our investment decisions.
Other examples.
To marry or not to marry?
Arguably one of the perhaps the largest or
greatest decisions we have to make in our lives.
Now, of course, when two people enter into that marriage contract,
they cannot know for sure whether they will go on and live happily ever after.
I like to think most marriages tend to be successful.
Indeed, I'm fairly a recent spouse, and I'm optimistic
that I made the right choice and it will go on and be a long and happy marriage.
But as we know some marriages will end in divorce.
Sometimes amicably, sometimes less amicably.
However, with the benefit of hindsight, yes, you could argue those two individuals
should never have got married in the first place.
But I would suppose at the time that they did get married they thought,
based on the available information, it was the best course of action to pursue.
So we can never guarantee success, but
hopefully we tend to get things right far more often then we get them wrong.
Now, I mentioned that, really, there are very few certainties in life other than
perhaps death and taxes as two main examples.
So I may be just a little bit morbid for a moment,
but I think it's one worth considering, and that's the one of life expectancy.
I know that one day I will die.
What I do not know is when that event is going to occur.
Now, we talk about life expectancy.
That doesn't tell you exactly how long you have left to live,
it's simply an expectation.
Now, my personal goal, I'm trying to live to 100, that's my target.
Only time will tell whether I actually, I'm able to achieve that goal.
Now, I can look around and see that, today, we have more people becoming
centenarians, turning to that age of 100, than ever before in history.
We have perhaps a larger population than previously.
But we also have access to much better health care than we did decades and
centuries ago.
So more and more people are able to make it to 100.
Now, I consider myself to be in reasonably good health, and
I'd like to think there's a reasonable probability that I will reach 100.
But of course, I cannot know this for sure.
So when I make decisions about my life, it's clearly based
around my personal life expectancy, how long I expect to continue to live.
If I thought I only have, let's say, six months left to live, then clearly
that's going to affect what I decide to do in the remaining six months of my life.
There are clearly lots of things I'd like to do I haven't done yet.
For example, many countries I've never visited.
And if I think I only have six months left to achieve this,
then I'm going to do that traveling within those next six months.
Well, I'm going to be a little bit optimistic and
hope I will make it to be 100, which means I've got decades
left to undertake all the things I would like to in my life.
Indeed, retirement planning, saving for a pension.
Now, this is something I think everyone should be doing,
although there are some figures in the UK which said that there was a significant
proportion over 40 who actually haven't made any personal pension plans yet.
And indeed, the clock is very much ticking for those individuals.
But I think it does pay to be very long-termist.
So in my pension provision, I have to consider certain parameters.
Namely, when I would like to retire.
So how many years should I be saving for this pension?
How much money I should be investing in a pension on a monthly basis.
Now, of course, this is going to be affected by what kind of lifestyle
I'd like to achieve in retirement.
If I'd like to travel around the world, let's say, first class on airlines,
and stay in five-star hotels, then clearly I'm going to need quite a lot of
money to achieve quite a luxurious lifestyle.
And hence, that would affect my decisions today about how much to save
each month into a pension fund.
Another parameter to consider would be the return
that the pension fund is likely to generate.
If I effectively hand over my pension savings each month to a fund manager,
then he or she will be investing it, perhaps in stocks,
bonds, perhaps a wide ranging portfolio, and
one could perhaps expect a particular return to be achieved on those funds.
And of course, depending on how successful I think that pension fund is going to be,
that's also going to affect when I would be financially in a position
to be able to afford to retire, as well as how much money I should be investing or
saving for my pension on a monthly basis.
So things such as that, and to marry or not to marry, how much to save for
a pension,
these are decisions typically many of us will have to make during our lives.
Unfortunately, we have this inherent uncertainty we have to deal with.
So the best we can do is form our expectations of the future.
For example, in that Monty Hall problem,
you had an expectation of winning the sports car.
If you switched to door C, the expectation was that probability of two-thirds
that you would win the car, and hence you played to those probabilities.
Now, you were unlikely in that one instance.
And, indeed, bad luck can affect all of us.
But so, too, can good luck.
But if we do play to the probabilities, I can't guarantee you success, but
we can be confident that we will win far more often than we lose.
[MUSIC]
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