Is that lotto ticket worth two dollars? Should I take out an extra insurance policy? Simple gambles extend through all major branches of economic theory. And, according to a new paper by SFI’s Ole Peters and Murray Gell-Mann, we’ve been wrongly conceptualizing them for some 350 years.
The paper, which appears in the journal Chaos, presents two approaches for evaluating gambles—expectation values and time averages. The expectation-value approach imagines all possibilities and averages across them in a linear additive way. In the words of 17th century mathematician Christiaan Huygens,: “if anyone should put 3 shillings in one hand without telling me which, and 7 in the other, and give me choice of either of them; I say, it is the same thing as if he should give me 5 shillings.” The time-average perspective imagines that a gamble is played repeatedly and computes what happens over time. Unless the repetition is additive, the two perspectives give different answers.
"The first perspective—considering all parallel worlds—is the one adopted by mainstream economics," explains 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."
Instead of looking at how individuals optimize wealth across parallel worlds, the time-based perspective considers how they optimize wealth as time passes. "What happens when we switch perspectives is astonishing. Many of the open key problems in economic theory have an elegant solution within our framework,” Peters says.
The Chaos paper illustrates the different approaches through a gamble. Toss a coin; if heads shows your wealth is multiplied by 1.5, if tails shows it’s multiplied by 0.6. Keep repeating the gamble. While the expectation value (the average across all possible worlds) grows exponentially, your wealth in any one reality will decay exponentially over time.
Because evaluating simple gambles is at the heart of the field, the time perspective can inform 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," Peters says. "It also enables refining the notion of efficient markets and solving the equity premium puzzle."
Read the article on Phys.org (February 2, 2016)
Read the paper in the journal Chaos (February 2, 2016)