Wednesday, May 1, 2013

Gibbs Free Happiness

Money can't buy happiness. Or can it?

Richard Easterlin found in 1974 (the so-called Easterlin Paradox) that once basic needs are met (around US$70,000 today in the developed world), happiness does not increase with income.

A new study by University of Michigan economists Justin Wolfers and Betsey Stevenson demonstrates that this hypothesis is not supported by data. It seems we are unsatiably-greedy beings after all.

Perhaps these two can be reconciled (in what I will glibly call Gibbs Free Happiness) using a thermodynamic analog, namely Gibbs Free Energy:
G(p,T) = H − T S = U + WT S
  • U is the internal energy
  • W is work exerted on the environment
  • T is the temperature
  • S is the entropy
  • H is the enthalpy
If you did not study physics, look these up later. For now, I will supply my own definitions:

Total happiness is like enthalpy H, the total amount of happiness accumulated up to now. This is what I infer that the study measured. This is itself composed of:
  • Invested happiness is like internal energy. This is the non-liquid happiness for being in a non-shareable state that consumed finite resources or opportunites and is not easy to get in or out of: having gone to college, having a career in one's field of interest, owning a home, having children.
  • Altruism is like work W, easily spent in small amounts or given away (in the form of helping others out financially, doing favors for, etc.) and easily received, reversibly without friction loss.
Opportunity, i.e. the number of distinct dimensions with accessible ways of spending your happiness (more precisely, the logarithm of the total number of distinct combinations of ways of investing all your happiness) is the analog of entropy S. Opportunity, naturally, goes up with income.

Risk tolerance, the conversion factor from opportunity to happiness, is the analog of temperature T. Our sensitivity to risk in undertaking self-satisfaction depends on our environment. When in equilibrium with a world of abundant happiness, T is high and one opportunity is as good as another: small-risk/small-reward vs. big-risk/big-reward have the same long-term payoff, and we can afford to float risk, to be wrong in the short term. Conversely, in a world of few opportunities, low hanging fruit that are easily achieved are more valuable than reach for the sky ventures that have a low payoff, because with few chances to convert money to happiness, we just can't afford to be wrong.

So what? It turns out that in physics, lots of things tend to saturate through this very mechanism. Electrons left over after atoms take their fill conduct freely as electricity. So is it Gibbs Free Happiness that saturates around $70K?

My hypothesis is that it does, that this study is consistent with Easterlin's original observations, that the "free happiness" -- that excess happiness that can be freely given away without noticeable adverse impact to oneself in a zero-sum world -- wanders away so easily precisely because we have little capacity to make us of it ourselves.

In other words, if you can't use excess happiness, just gibbs it away! Others won't be sorry.

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