Class:
Informatics, Computing, and the Future
Instructor:
Dan Berleant
Transcriber:
Brooke Yu
Date:
Tuesday, February 05, 2013
Professor: Did anybody no get a copy? so take a look. It's on the Delphi method. You have the data. You just need to process it.
Professor: Alright, so any questions on this
homework? What do you do or
something?
Male
Student: Do we just chart out our
readings from our question?
Professor: Yeah.
You'll end up with a graph that will probably look something like
this. This is the median.... This is the 75% mark, 25% mark. You could put a bar or something to indicate
the low and high estimates
This is the
middle 50%. Okay?
You know,
this sort of presumes you can divide the data into 4 equal sized sets of data,
right? But unless the amount of data
points you had is not divisible by 4, you'll have to adjust, so some of these
will be between two data points
If you have a
in even number of data, then the median is the between the two middle
numbers. You can kind of figure out how
to do that.
Question
number 4 gets back to the term project, but also to sort of what we want to get
out of this course. It guides you to
think about the problems the course wants you to look at.
Any other
questions?
Alright. So it'll be due in a week. And we're actually done covering the Delphi
method, so we'll go onto something else today.
By the way, does anyone not have their Delphi method data? Did you all get yours? Anybody not have their data yet? Great.
I should point out that this only has to be done on the second
iteration. You don't have to do it
twice.
Last time we
looked at prediction markets, which is another way to predict the future. Today we'll look at it in a little more
detail- this concept of prediction markets.
Okay? So, you know, the Delphi method was one way
of getting crowd source predictions. The
problem with that is if you're wrong, it doesn't matter. You think if people sort of have to put money
on what they're guessing or estimating, then they'll do a more careful job of
it, and that's what prediction markets are about. It's about buying and selling predictions so
people will try harder to get it right.
So that's
what prediction markets are all about.
The word market, by analogy, is like the stock market.
So people
make predictions all the time. They
don't always do it in prediction market, but people are always making
predictions. I guess what I want to do
with point number 2 is establish that making predictions is sort of an
intrinsic human activity that could help explain why we are the way we
are.
Like, it
could explain why we're the smartest species on the planet because of the need
to make predictions.
Let's look at
the kinds of predictions people make.
Everyone makes them. So
predictions people make and are better than animals at.
Well, people
think about people's reactions, which is a prediction. It's a very human activity to do.
Okay? The ability to predict the effect of your act
on others is useful. If you can predict
how people will react, you can gauge your actions accordingly
In a highly
social species like humans, it's important to figure out how people will react
so you can work and operate effectively within a social context.
In order to
do that, in order to really predict reactions, you need a theory of mind, which
means you need a model in your mind of other people's minds. When you think "how will they
React" is sort of simulating their mind in your mind.
A dog might
be able to figure out how you're going to react to some degree, but they don't
do a very good job of this. They don't
simulate other minds in their mind, which is what we do all the time
You know,
when I'm making up a homework, I think "well, if I state this problem this
way, how are the students go to interpret it?
Will they understand it?
Alright?" At the same time,
you as student wonder when you're doing an assignment "is he a tough
grader? An easy grader? Do they really want That?"
This is why
people sort of don't know how to do assignments that well until they learn what
the professor really wants. Or tests,
you know? I don't give tests very often,
but it's the same deal. Unless it's
multiple choice, you might wonder if the professor will grade higher if you use
certain words.
So people
have the capacity to have a theory of mind where they can model other people's
minds in their own minds. This may not
sound like prediction markets, but we'll get there.
Basically,
when you're a member of a social group- like dolphins too- they seem to do this
sort of thing too. You're in a game
theory scenario. This is where two
parties are adversarial. One will win
and the other won't. In real life the
person with the better theory of mind ends up ahead of the game. There's a whole academic field called game
theory where you analyze and try to understand how things work in competitive
situations.
Well, turns
out that this need to have a theory of mind and to compete in a social setting
is likely to be one of the causes of human brain size. Humans have pretty large brains. Well, not that big. This is 2 feet wide. Humans have, not the biggest brains on the
planet, but among the biggest.
You know,
look at the ratio of body size to brain size, humans are basically the
biggest.
The concept
here is that populations in a social setting tend to compete in various ways,
and that causes bigger brains to develop or to be selected for.
This is an
outline of a human brain.
This, on the
other hand, is a chimp brain. They're
pretty big, but not nearly as big as a human's.
They have
that wrinkling too, but it's greater in humans.
We have more wrinkles on our brains, showing we have more surface area
folded to fit into the skull.
Chimps are
smart, but not as smart as humans.
Okay? So this is called the social competition
theory of the development of the human brain
So there are
different theories about why the human brain is big. Many researchers favor this idea though.
We're never
going to prove absolutely because we don't have time machines, but we can think
about it.
Okay, so
anyway, where I'm going is that this need to predict and the difficulty of
predicting explains intelligence.
So what is it
we need to predict?
So somebody-
what is it we need to predict? If our
need to predict explains why we're so smart, what is it that we need to
predict?
Male
Student: Weather.
Professor: Okay, if you're a farmer and in ancient times
when you could starve if the crops failed, you might need to predict
weather. What else might we need to
predict? I think we can generate a
couple more before we go on.
Anything?
What did I
mention up around the ceiling?
Something we
need to predict....
Okay, how
about I give you a hint? Social
competition. Is that enough of a
hint? What do we need to predict?
Remember I
said something about having a theory of mind?
And they think some animals have it?
Why do we need a theory of mind? What
does it help us predict?
So what you
can understand what other people are going to do. You have an internal theory of how people's
minds are working. How could that help
you?
Male
Student: So you could predict if another
country is going to try and kill you
Professor: Right or if the caveman in the other cave is
going to hit you with a rock.
Professor: Or, you know, if the tribe only has ten rocks
available and 11 people, you don't want to be the person that doesn't get a
rock.
So the theory
goes that humans are humans because we need to predict in order to compete with
other humans in a social setting.
You know,
elephants are pretty smart and they travel in groups. Porpoises travel in groups too, as well as
chimps. Deer- well, deer can travel in
groups, but they're not very smart.
But of
course, in addition to the social competition theory of the human brain, other
predictions are important. Like the
weather. Someone mentioned that. The country puts a lot of money into making
highly sophisticated weather forecasts.
This is a
picture from Portugal. It's a picture of
a weather pattern. Sun is setting,
lights are on the in the village. I
don't know what's going to happen, but it looks like rain.
Here's
something. A waterspout is a tornado
over the water. A tornado can draw water
up into the funnel. You can see the
spiral on the surface of the water that's how much wind is down there. You know, water's very heavy. It doesn't take that long for a waterspout to
lose its energy. It's amazing it can do
it a all.
Indeed, the
national weather service is a large government agency that is computer
oriented- they have a lot of computers used to predict the weather
scientifically.
A lot of
money goes into predicting the weather because it's so important
economically. We know the weather man
isn't perfect, but it's a lot better than it was. Now they have predictions that go up to 10
days all because of computers.
So weather
prediction uses computers. The Delphi
method doesn't. I think I'd be better
off going to weather.gov than asking you guys what the weather will be.
I'm sure
weather.com uses government information to post that.
There may be
companies that do it too, but not your local TV station.
Okay, so
there's other forms of group wisdom besides the Delphi method. For example, sports betting. People like to do that often.
And, you
know, you should be able to determine what the odds are that a team is going to
win a game based on large numbers of people betting. In fact, groups that kind of serve as a
clearing house for sports bets will issue odds that they'll sell bets for, and
sometimes those are picked up by the media.
The reason
that's even news at all is because it's an estimate of the actual
probability. That's just the kind of-
that's exactly what a prediction market is except it has a few different
wrinkles. It's getting a bunch of people
to make bets on what they think will happen and they use money so they'll get
good estimates.
Here's
another example. This is from last
year's class.
So last year
in this class, I asked "will the average global temperature for 2012 be
the highest ever recorded." There
was a company selling those predictions.
Remember,
there were predictions- if it turned out to be the highest ever recorded, you'd
get $10. If you said no, you'd get
$0. If you thought it was going to
happen, you'd buy. If you were even more
confident, you'd buy a prediction for $9.
If it didn't happen, you'd lose $10.
You'd have to be sure to buy such a prediction.
So it turns
out last year at this time, you could have bought a yes vote for $2.50. Ultimately, you would have lost your
$250.
Turns out
2012 was the 9th hottest year on record.
So it was hot, but not the hottest, so you would have lost your
$2.50.
Per share,
right? If you bought 10 shares, you
would have lost $25.
This
assessment came out just a couple of weeks ago.
[Teacher
reading: [On board.]
Professor: This is a pretty cool map. It shows the difference between 2012's
temperatures and the average temperatures at various locations around the
globe. You can see it's colder down here
in Antarctica. You can see the farther
north you get, the greater the anomaly.
It's a lot
warmer than one would have expected on average.
Okay. So why am I going on about last year instead
of this year? Well, because the company
that offered those bets where people could buy those predictions for $2.50. That company has problems. The company was called intrade.com.
Turns out the
company was basically barred from business in the US.
It was done
in November- not long ago.
Professor: Basically, they forced intrade to not do
business in the US. A few months later
it turns out the intrade is still in existence, but it's a much smaller
entity. This morning when I checked to
see if you could buy or sell predictions on the same question for 2013, you
couldn't.
So it's a
much smaller operation because most of its business was in the US, even though
it's an Irish company.
Anyway, the
person writing this article was pretty upset about it, not because they wanted
to make bets, but because it's... let's see.
Well, first
he claims it's harmless, but, you know, the US already allows other forms of
gambling.
The problem
is that prediction markets work. They
give good information about the real probabilities about future events. And so by preventing people from using them,
they're removing a tool that people can use to predict the future.
You could
look at the prediction market and see the odds to figure out a good
estimate. We can't do that anymore in
the US with intrade. They lost most of
their customers.
So according
to this author, by making prediction markets illegal, [Teacher reading: [On
board.]
So this
person who wrote this article was very much against this. They think prediction markets should be
allowed.
So the
company did not go out of business.
We'll look at it in a minute.
Fewer
predictions that you can buy and sell, fewer people making predictions. I didn't try one myself, but I'm sure if I
did it'd say I had an IP address in the US.
Male
Student: You could just change your IP
address.
Professor: Yeah, but the feds might come knocking on my
door. The company had its share of bad
luck. The founder of the company died at
42 before this happened. He died....
climbing mount Everest.
He was within
50 yards of the summit of Mt. Everest.
He was clearly a risk taker and he started a company then tried to climb
mount Everest. That's very
dangerous. If you want to try, it's
really expensive to do, and a significant fraction of people who try don't make
it.
Meanwhile, he
has a child who will grow up knowing his dad tried Mt. Everest and didn't make
it. Okay, let's see what all the
excitement is about and to go intrade to see what it's like.
If you look
at the home page, it looks like it always did, but it has fewer predictions you
can buy and sell. Let's look at
some.
Markets- Here are scientific markets. They used.
Have dozens, but now there's only 5.
[Teacher
reading: [On board.]
Here are some
related to ET life.
Here's one
about physics. There's some activity-
people are betting on these, but it's not nearly as many as there used to
be. There used to be several dozens of
scientific things.
Politics-
well, since Americans can't use this site anymore, there's less of a focus on
American politics. There's some, but
Italian politics rates pretty high on this list, but I don't follow Italy's
politics.
Construction
and engineering. Three of them.
Will the
world trade center be re-opened by the last day of December 2013. That's looking pretty good right now. So you could buy a prediction for $8, and if
it happens, you'd get $10.
I was looking
at this earlier. A lot of these markets
have few people buying and selling, so the prices are pretty erratic.
Okay. We can look at a few more in detail if we
have time at the end of class.
Okay, so at
intrade, every prediction is worth $10 or $0.
Why do you think a prediction contract or the price of a prediction will
tend to get closer to $10 or $0 as the prediction gets closer to
happening?
Why do you
think?
Male
Student: Because there's a certainty of
it happening or not happening?
Professor: Right, so things become more certain the cosier
it gets. So if you're betting on whether
the year will be the hottest year on record, you don't know much in January,
but you know more in December. So the
price of the contract will get closer to $10 or $0 if the evidence shows it's
likely or not.
How about
this one. Could the price of a
prediction get high and then end up low or vice versa?
Male
Student: I think if they came out with
new support for a prediction, you know, for or against it, it could skyrocket
up or fall down
Professor: You know, let's suppose you could buy a
prediction for $1. That means, people
only thing there's a 10% chance. If it
seems more likely, the price will go up.
I followed
intrade in the last election. That
happened a lot, you know? When people
thought one candidate was ahead, the price of the prediction they would win
would be high. Then it might drop as the
ratings dropped.
So yeah,
could a price get high and end up low?
Yes.
Sports have
always been something people wanted to bet on.
You know,
what's the difference between sports betting and buying a prediction? Nothing.
It's the same kind of thing.
It's hard to
throw a ball up that high. I'm not a big
tennis fan, but my wife is, so I see some of it.
So sports
betting has a long history because people want to predict games and win
bets.
You can
imagine the ideal bookmakers. An honest
bookmaker will offer odds to a sporting event that results in equal payoff for
the bookmaker, regardless of outcome. So
the bookmaker would set the odds they're willing to buy and sell debts such
that the number of people who bet for one team vs. the other, when the
bookmaker takes the money from the people who got it wrong and gives it to the
people who got it right, they'll end up even.
How do real
bookmakers differ from that?
Male
Student: It's not equal.
Professor: Right.
Does anyone know how to a roulette wheel works? How does the house get a cut of the roulette?
Male
Student: I've never bet in my life.
Professor: How many different outcomes are there? Like 32?
Then there's an extra one for the house.
So there are 33 outcomes instead of 32, but if it lands on a 5 and you
bet 5, you get 32 times what you bet.
So Vegas is
the same way. They skew the payoffs and
so on so they get money and make a profit.
Or if you had
a system that was fair in that sense, then the true odds according to the group
wisdom would come out the odds that would result.
Okay? Here's another example- political
predictions. Election season- media,
ordinary people, etc. predict what's going to happen. Remember the last election- it was nonstop on
the news
Polling,
trend analysis, analyzing demographics, etc.
Everyone has
a different opinion, and that's why you could imagine instead of asking
individuals using groups.
Polls aren't
bad. They often work, but they don't
work well in the last election.
Prediction markets have been claimed to do better because you're not
just asking people on the phone. You're
getting people to put money on who they think is going to win and people are
more careful with their judgment.
Predictions
markets are perfect on this front either.
Let's look at the last election.
Okay. This is going back to November. Here it is.
Okay, so this
is from last November. The person who
wrote this blog was kind of famous at the election for predicting everything so
well. Here, he's talking about how
predictions markets did. He's talking
about intrade because it was legal back then.
So a lot of people had good data.
In the last
election, it was a legal company, and it turns out that in intrade, the trades
for romney were more favorable than in other markets.
So there's
some questions about why intrade or why one prediction company would- the crowd
source wisdom there would differ from other places.
Romney was
given a 30% by intrade, but a 15% chance by another company.
So why would
that be? Why would one prediction market
get another result from another?
Here are some
possibilities. How can these be
skewed?
Male
Student: You could take down the
server.
Professor: Okay, can anyone think of a non-computer
related way to make it give the wrong answers in essence?
Well, let's
suppose you decide "I don't care whether I make money or not. I just want to make the price of the
prediction go up." Then you could
just go and buy lots of predictions. You
don't care if you make money. It's like
stocks- you drive the price up. If you
drive the price up, maybe the media will talk about it.
Maybe they'll
think the candidate will be more likely to win, so maybe you do that to get
publicity for your candidate.
I you do it
for reasons other than trying to maximize your financial position, even for
other reasons, then you'll distort the predictions because the prices will
change in response to what you're doing, but you're not trying to make
money. So in that sense, you're
manipulating the prices. Another thing
that can skew results is if people buy predictions, not because they're trying
to manipulate, but for other reasons.
Let's suppose
there are two sports teams, and you really want.... we'll call them team cool
and team uncool. You really want team
cool to win. You'd think you'd bet on
team cool, right?
That might
not be the right thing to do. Perhaps
the right thing to do would be to bet on team uncool, because then if team cool
wins, then you're happy to lose $5. If
they lose, you'll make $5, and you'll only be a little sad they lost.
So that's one
reason why you bet against the team you want to win. If they win, you're happy. If they lose, you make money but you're not
too unhappy.
So that's not
irrational at all. You might just want
to try to control the amount of drama in your life. You don't want to be too upset if they
lose. Or maybe you want more drama and
so you bet on your favorite team. If
they win, you're happy and you make money.
But if they lose, you're sad and you lose money.
The minimum
drama approach would be to bet the amount of money a win is worth to you. Then there's no drama at all. You don't really care.
But in any
case, people can do that and there's no reason why they wouldn't do it in an
election.
So it's irrational
in the sense that it's not specifically geared to making money. It's buying bets for another reason, so it
skews the price of the predictions, and you get bad predictions.
These are
reasons why putting money on your bets is not always a perfect way to get the
crowd source wisdom.
Any
comments? Thoughts? Questions?
Okay, well,
buying and selling predictions is kind of like the stock market. Economists look at the stock market because
it's a leading economic indicator. Who
knows what that it? The opposite of
leading and lagging.
Male
Student: What shows the future, kind of
Professor: Exactly.
Leading refers to showing the future.
So economists like leading indicators because some obscure price of
something that they feel is a leading indicator goes up, that means they think
the economy will go up.
That's why
they like leading indicators. The stock
market can be a leading indicator, so the stock market is kind of a prediction
market. People buy stocks today because
they think the stocks will go up more tomorrow or next year, and normally they
go up if the company is doing better. So
people buy stocks because they think the company will do better and make more
money next year.
So the stock
market is something of a leading indicator.
Okay. Well, you know, prediction markets are kind
of... an abstract concept. If you were
to imagine a way to use group- to collect wisdom from a group, you know, you
might come up with a Delphi method. You
ask people and get an average. That sort
of makes sense.
But you
probably wouldn't come up with a prediction market, because it's a little
abstract. It's clever and hard to dream
up.
So you
probably wouldn't come up with a prediction market, so that's why it's sort of
a modern concept.
The earliest
design for prediction markets appeared in a science fiction story from
1975. He called it a Delphi Pool. It was related to the Delphi method but he
added money to it.
Making people
use money makes people bet more carefully, and presumably better. Here's an example of how this was
applied.
This happened
a few years ago. There was an attempt to
make a prediction market for terrorist attacks.
So why have a
prediction for that? Why buy and sell
these predictions?
Can anyone
imagine why they'd want to have a prediction market for that?
Male
Student: Like they predicted if it would
happen?
Professor: Yeah, people would make predictions on that
Male
Student: People bet on anything.
Male
Student: And if you bet then do it, you
win.
Professor: Exactly.
That's exactly what people were hoping.
They thought that if terrorists wanted to make money, then the few
people who knew about the attack would go and bet that it was going to happen
so they could make money. The people who
designed this prediction market would hope that if there was a spike in a
prediction, that'd be an indicator something would happen.
Male
Student: That's just kind of creating
something you're trying to stop.
Professor: That's right.
So it's sort of an incentive to terrorists to do it. So you might think "what the heck is the
US government Doing?" Seems like a
crazy idea, doesn't it? Does it sound
like a crazy idea?
Male
Student: I don't know. Might be a government cover up for 9/11.
Male
Student: Did it pay out or
anything?
Professor: Well, here's what happened. They set this up a number of years ago. It was called PAM, but I forgot what that
was- policy analysis market. It wasn't
just for terrorist action they just wanted to sneak those in there
Anyway, a
couple of senators found out about it, so they canceled the program, and a
program director at DARPA had to resign.
When these
things get politicized, you can imagine how politicians act
Somebody has
a role, so the program director who permitted it to be set up had to
resign. To answer your question, from
what I could see, it's not clear if any terrorism predictions were ever
actually traded.
But it's a
clever idea, but it does seem to encourage ideas.
Male
Student: I would feel bad if I bet on a
town getting attacked and then it got attacked.
Male
Student: You'd feel a little convicted
about it.
Professor: Let's see where we are. We can look at some more predictions if we
have time. I'm in a bit of a quandary. I had homework before for people to go on
intrade and to pretend they had $100 and see if they would make money pretend
on their predictions, but now. I mean, I may still do that, but intrade just
doesn't have as much available, and I can't ask you to put money on it because
it's illegal now.
Intrade
wouldn't even take your bets unless you changed your IP address.
Male
Student: Make a paypal account from
another country.
Male
Student: So the whole thing's not
legal?
Professor: Well, I guess it's legal in Europe.
Male
Student: I just thought it was certain
type of predictions.
Professor: I don't know the details. I think it was always in the illegal grey
area because gambling. Anyone know
anything about the legality of online gambling?
Male
Student: I don't really have money to
gamble away, so no I don't.
Male
Student: I know there's always a lot of
places popping up that do online gambling illegally. If they just put them in inconspicuous places
and get caught, they just move them.
They do that a lot where I'm from.
Professor: The whole thing is pretty shady.
Professor: Anyway, intrade used to be legit. I don't know about that other site. I don't know if we should try to do this or
not. Mostly, the thing is that they
don't have as great a selection of bets as they used to. What do you think. What to try it? They have some bets- excuse me, predictions.
Or should I
try to redesign the homework?
Male
Student: Maybe something a little less
sketchy.
Professor: Well, it's not illegal to pretend.
Professor: Well, what do you think? How many people want to do it? How many people don't want to do it?
Male
Student: I'll do it.
Male
Student: I'll do it.
Professor: The concept of a prediction market is a good
one. It is a way to predict, and as that
one writer said, it's unfortunate intrade is not allowed to operate in the US because
it reduces our ability to tell the future and you can make better decisions if
you know the future. I wanted to try one
more thing. We spent some time doing the
Delphi method predictions. I thought we
could try the Delphi method and then try to pretend we're putting money
it. Let's just do it.
So here is a
question. Will a live person land on
Mars by 2024? Okay?
This is a
little different from the Delphi method.
We're just asking yes or no. Not
a date. So any comments about why you
vote one way or another on this?
Anyone
remember what the Mars one organization is?
Female
Student: Aren't they supposed to go in
2023?
Professor: Yes.
Male
Student: Didn't they shut down the whole
NASA thing?
Professor: Well, NASA hasn't sent anyone out since the
1960s.
Male
Student: I thought Obama cut their funding.
Male
Student: They ended the space shuttle
program.
Professor: There's an international space station, but I
don't know what the status on that is.
In my life, it's always been an argument. People have always argued over the cost of
the space program and feeding poor people or something. It's an argument that's not going to go
away. Going to Mars is a cultural
activity and it costs a lot of money and people have to want to do it. When budget crunches happen, those kinds of
questions come up. So there's nothing
new about it. That argument has been
around for a long time.
So they're
always cutting the budget then they add to it, then cut it again.
So any other
comments about whether or not a live human will land on mars by 2024? Think to yourself right now. Don't tell anybody just yet. We'll have a vote. I'll ask for all the yes's and all the no's.
Alright, how
any vote yes?
How many
people vote no?
In the delphi
method, we'd talk about it. But now
we're going to do something different.
I'm going to ask you to think deeply about ... let's see. How can I state this?
If you're
right, you're going to get $5,000. You
have to wait a few years, but you'll get $5,000 if you're right.
And if you're
wrong, you get $0
So think
really carefully now. Think about
this. And then we'll revote to see if
anyone changes their mind. Now, pretend
it'll really happen. I'll give you a
minute to think about that.
Think about
that $5,000
Okay. Let's try again. How many people vote yes?
How many
people vote no?
Okay, so when
$5,000 are at stake, people do it differently.
You can see why the delphi method gives a different estimate than a
prediction market. People say prediction
markets are better because you care more about your answer.
Okay. We have 5 minutes left, and I think we should
look at a couple of other sites.
By the way,
UK football means soccer.
Casino,
poker, horse racing. Let's take a look
at sports in general.
Well,
American football. We can do that.
Should have
done this before the last super bowl.
So this
is.... oh, do these countries play American style football?
Male Student:
I'm going to say no.
Professor: Anyway, it looks to me like betfair is a
sports betting company. It's a
prediction market for sports.
Predictwise.com.
Nope. That's just an explanation.
Looks like
intrade and betfair are the two big ones.
Let's look at intrade one more time and then we'll adjourn. Anyone want to pick one of these?
Male
Student: Politics.
Professor: Let's see what's going on there. Anyone into Italian politics? Australian?
UK?
Male
Student: I'm not into American
politics.
Professor: Alright, let's see about Italian
politics. Which party will win
2016. Oh, here's some US stuff.
Okay, so will
democratic party retain the US Senate in 2014?
It looks like the current.... I guess this is 0 to 100, so the current
estimate is at 63% that democrats would retain the Senate. So it's a 2/3 change the democrats will
retain the Senate.
The house of
representatives in 2014, they have an 87% chance of that. You can buy a bet- actually, you can't, but
it would be $8.30
Male
Student: You could go to hidemyass.com
Professor: Haha, okay.
I won't require you to use it in homework 4. Alright, so anyway, that's prediction
markets.
Think about
them next time you bet on sports and we'll go into something else nex
time.
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