Exploring gambles reveals foundational difficulty behind economic theory (and a solution)

February 2, 2016
Parallel worlds branching into the future, with reality selecting one trajectory through the space of possibilities. Credit: Peters and Gell-Mann

In the wake of the financial crisis, many started questioning different aspects of the economic formalism.

This included Ole Peters, a Fellow at the London Mathematical Laboratory in the U.K., as well as an external professor at the Santa Fe Institute in New Mexico, and Murray Gell-Mann, a physicist who was awarded the 1969 Nobel Prize in physics for his contributions to the theory of elementary particles by introducing quarks, and is now a Distinguished Fellow at the Santa Fe Institute. They found it particularly curious that a field so central to how we live together as a society seems so unsure about so many of its key questions.

So they asked: Might there be a foundational difficulty underlying our current ? Is there some hidden assumption, possibly hundreds of years old, behind not one but many of the current scientific problems in economic theory? Such a foundational problem could have far-reaching practical consequences because economic theory informs economic policy.

As they report in the journal Chaos, from AIP Publishing, the story that emerged is a fascinating example of scientific history, of how human understanding evolves, gets stuck, gets unstuck, branches, and so on.

"We found, for instance, that Daniel Bernoulli made an inconspicuous but consequential error in 1738 that was corrected by Laplace in 1814, but reintroduced by Menger in 1934," said Peters. "This is one factor that held back the development of our perspective."

The key concepts of time and randomness are at the heart of their work. "Questions of an economic nature stood at the beginning of formal thinking about randomness in the 17th century," he explained. "These are all relatively young concepts—there's nothing in Euclid about probability theory." Think of it simply in terms of: Should I bet money in a game of dice? How much should I pay for an insurance contract? What would be a fair price for a life annuity?

"All of these questions have something to do with randomness, and the way to deal with them in the 17th century was to imagine parallel worlds representing everything that could happen," Gell-Mann said. "To assess the value of some uncertain venture, an average is taken across those parallel worlds."

This concept was only challenged in the mid-19th century when randomness was used formally in a different context—physics. "Here, the following perspective arose: to assess some uncertain venture, ask yourself how it will affect you in one world only—namely the one in which you live—across time," Gell-Mann continued.

"The first perspective—considering all parallel worlds—is the one adopted by mainstream economics," explained Gell-Mann. "The second perspective—what happens in our world across time—is the one we explore and that hasn't been fully appreciated in economics so far."

The real impact of this second perspective comes from acknowledging the omission of the key concept of time from previous treatments. "We have some 350 years of economic theory involving randomness in one way only—by considering parallel worlds," said Peters. "What happens when we switch perspectives is astonishing. Many of the open key problems in economic theory have an elegant solution within our framework."

In terms of applications for their work, its key concept can be used "to derive an entire economic formalism," said Peters. In their article, Peters and Gell-Mann explore the evaluation of a gamble. For example, is this gamble better than that gamble? This is the fundamental problem in economics. And from a conceptually different solution there follows a complete new formalism.

They put it to the test after their friend Ken Arrow—an economist who was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972—suggested applying the technique to insurance contracts. "Does our perspective predict or explain the existence of a large insurance market? It does—unlike general competitive equilibrium theory, which is the current dominant formalism," Peters said.

And so a different meaning of risk emerges—taking too much risk is not only psychologically uncomfortable but also leads to real dollar losses. "Good risk management really drives performance over time," Peters added. "This is important in the current rethinking of risk controls and financial market infrastructure."

This concept reaches far beyond this realm and into all major branches of economics. "It turns out that the difference between how individual wealth behaves across parallel worlds and how it behaves over time quantifies how wealth inequality changes," explained Peters. "It also enables refining the notion of efficient markets and solving the equity premium puzzle."

One historically important application is the solution of the 303-year-old St. Petersburg paradox, which involves a gamble played by flipping a coin until it comes up tails and the total number of flips, n, determines the prize, which equals $2 to the nth power. "The expected prize diverges—it doesn't exist," Peters elaborated. "This gamble, suggested by Nicholas Bernoulli, can be viewed as the first rebellion against the dominance of the expectation value—that average across parallel worlds—that was established in the second half of the 17th century."

What's the next step for their work? "We're very keen to develop fully the implications for welfare economics and questions of economic inequality. This is a sensitive subject that needs to be dealt with carefully, including empirical work," noted Peters. "Much is being done behind the scenes—since this is a conceptually different way of doing things, communication is a challenge, and our work has been difficult to publish in mainstream economics journals."

Their results described in Chaos are easily generalized, which is necessary to reinterpret the full formalism. But it "may not add very much in practical terms, and it gets a little technical." So that's a future "to-do item" for Peters and Gell-Mann.

"Our Chaos paper is a recipe for approaching a wide range of problems," said Peters. "So we're now going through the entire formalism with our collaborators to see where else our perspective is useful."

Explore further: After a half century, the exotic pentaquark particle is found

More information: "Evaluating gambles using dynamics," by Ole Peters and Murray Gell-Mann, Chaos, Feb. 2, 2016. DOI: 10.1063/1.4940236 , http://arxiv.org/abs/1405.0585

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LifeBasedLogic
Feb 02, 2016
This comment has been removed by a moderator.
Gigel
4 / 5 (8) Feb 03, 2016
Life is most important in life.

It's hard to see what you are telling. Stop using circular statements.
Mike_Massen
3 / 5 (6) Feb 03, 2016
LifeBasedLogic says
Life is most important in life
What does that mean ?

Surely if when looking at key details, ALL life, observed here on Earth, is indisputably based on amino acid structures, the relationships are purely chemical energy interchange under brutal & every present process of "Natural Selection"

All life = amines, which arise from Ammonia/Water/CO2 & reflect early Earth's atmosphere where chemical reactions for production of all life's components are everywhere AND subject to energy differentials all the time by non-random processes re chemical bonding creating meta-stable structures & very easily too

ie. Formamide arose easily on early Earth & with heat & lightning, after only a few hours it leads always to Guanine, one of our DNA bases, with other bases similarly generated Eg lightning & metal salt catalysis.

Nature proves its pattern as Brutal extension of "Eat & bet Eaten" all the time !

Can LifeBasedLogic articulate his position well ?
julianpenrod
1.6 / 5 (5) Feb 03, 2016
A fundamental problem with "economics" is the claim that finances throughout the world behave like a system behaving with laws in response to random events, not arbitrarily driven. Workers are paid by bosses, bosses get the money from the presidents, presidents answer to board members, companies depend on money from banks and stock holders, banks depend in rules in government and their owners. A constant hierarchy in power. But, in any finite population, there is a highest level. Those are the New World Order. They share in a single pot of money, all the material wealth that isn't bolted down. They no longer worry about which money is whose, they all share in it. And they manipulate events and how money flows to the less rich.
Uncle Ira
3.2 / 5 (9) Feb 03, 2016
Exactly. Life is most important in life. Any thing claiming to be a legitimate theory of anything must concede that point or it is not a legitimate second perspective; it can't be true.

David-Skippy. Aren't you suspended from school for disrupting the classes? Knock it off couyon and stay off the school yard until you have served out your time. (And you get demoted two grades when you get back for being so stupid by wearing your silly looking pointy cap while trying to sneak back in early.)

Thank you Murray Gell-Mann


Don't thank him, he can't help you. He is the physics PHD doctor, not the kind that treats mental conditions.
Phys1
3.9 / 5 (7) Feb 03, 2016
"Is there some hidden assumption, possibly hundreds of years old, behind not one but many of the current scientific problems in economic theory?"

"The second perspective—what happens in our world across time—is the one we explore and that hasn't been fully appreciated in economics so far."

Exactly. Life is most important in life. Any thing claiming to be a legitimate theory of anything must concede that point or it is not a legitimate second perspective; it can't be true.

Thank you Murray Gell-Mann

DavidW, or is it BartV, you ole religious freak, is that you ?
I add your new alias to my list without delay!
___
Presently ignoring:
Benni bschott plasmarevenge cantdrive45 gkam kaiserderden antigoracle Seeker2 promile swordsman viko_mx DavidW BartV bluehigh baudrunner Solon hyperfuzzy julianpenrod emaalouf theprocessionist wduckss Old_C_Code Bigbangcon katesisco jimbraumcos indio007 LifeBasedLogic
This list is updated continuously.
gkam
1.7 / 5 (6) Feb 03, 2016
Me, too, Phys?

How are you going to get educated?
Uncle Ira
2.7 / 5 (9) Feb 03, 2016
Me, too, Phys?

That is a silly question.

How are you going to get educated?

Well choot me where I stand Cher, you say something about your self I agree with. I have learned a lot by watching peoples correct all your blurts and blahs. If glam-Skippy makes a technical comment instead of a bumper sticker slogan' you can learn a lot if you wait a minute or two for one of the Real-Technical-Smart-Skippys to come along and help him with where he went wrong.
LifeBasedLogic
Feb 03, 2016
This comment has been removed by a moderator.
LifeBasedLogic
Feb 03, 2016
This comment has been removed by a moderator.
LifeBasedLogic
Feb 03, 2016
This comment has been removed by a moderator.
Vietvet
3.7 / 5 (9) Feb 03, 2016
@LifeBasedLogic aka DavidW

I see you escaped the asylum and are off the meds.
bschott
1.7 / 5 (6) Feb 04, 2016
@LifeBasedLogic aka DavidW

I see you escaped the asylum and are off the meds.


Did you run out due to self upping of the doses and need a quick fix?
pepe2907
5 / 5 (1) Feb 06, 2016
I see bullying somebody to became "new normal" even in a scientific forum. Which is a pity.

LBL, although from an individual's perspective that one's individual life is highly valuable the quite cruel truth is that in general the value of individual life from the perspective of a set of humans is not so high. Because everybody /in a "large enough" set or society/ is relatively easily replaceable /and our high adaptability as species helps to that/ and from biological point of view the "price" of replacing life with another one lowers with increasing of number of individuals in a /finite/ set, lowering the number of lives which are necessary to be replaced in that set compared to it's reproduction capacity, and probably as it may sound somehow paradoxical - general survivability of the individuals in that set. Struct. spec. educat. time to edu. etc rise it.
And the "price" /!/ in society is set according to that theor. calculable amount /cause money are a thing of society after all/
Phys1
4.3 / 5 (6) Feb 06, 2016
@pepe
It is against the guidelines to feed the trolls.
pepe2907
5 / 5 (1) Feb 06, 2016
Well, excuse me, as an accidental observer I don't see him as a troll, I pretty much see you as trolls. Please excuse me again, my mistake ... perhaps.
Anyway, I see usually cleaning the mess with terms used /as with value versus price for example - because your life may present a "value" for you, but life insurance for it comes at a "price", and as much as I understand things, insurance market operates with prices, not values, except the specific risk-to-price value, allowing them to stay profitable taking risk of paying to your heirs specific sum in the case you lose your life/ is a better way to deal with trolls /and sometimes with authors too/, and taking less time and effort too.
Captain Stumpy
4 / 5 (4) Feb 18, 2016
as an accidental observer ... my mistake ... perhaps
pepe
you see a singular event and didn't actually see the whole

to understand you would have to first research the typical post of said user by reviewing his past posts here:
https://sciencex....c/?v=act

then you would have to continue to read his other sock-puppet:
https://sciencex....W/?v=act

you can also note with a little research that the person (he gives his name) also has been kicked out of most moderated sites for the exact same thing: the circular trolling/spamming argument of "Life is most important in life" regurgitated ad infinitum

thus his posts are intentional baiting to justify (to himself) his fanatical pontification which is nothing more than repeating "Life is most important in life"

a jiggling mass of illogical confusion with a prolific desire to proselytize and share his delusion

kinda like a gummi bear on crack in an earthquake

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