Storytelling Science

The Mathematics of Happiness

Amitabha Mukerjee


News items earlier this week reported on a scientific paper with the unusual title: "Money, sex and happiness". The paper related levels of happiness to factors such as money, marriage, and frequency of sex.

In the West, rational scientific knowledge has achieved such a dominance that intuitive knowledge is not considered real anymore. Contrastingly, India celebrates the importance of the intuitive - when the Upanishads discusses higher and a lower knowledge, the sciences are definitely in the "lower" category.

While science has done much to explain how the world works, it has been limited to "well-posed" problems, where the observations are repeatable; larger, more important questions, such as the purpose of existence, or how to achieve happiness, have remained outside the pale of science. Admitting this, Einstein said: "One thing I have learned in a long life: All our science measured against reality is primitive and childlike, and yet it is the most precious thing we have."

So does this new attempt by science to measure happiness constitute an important step in this grand debate?

Although the new paper garnered attention because of its focus on sexual behaviour, the results are very similar to earlier work by the same authors. The basic idea is to apply statistical tools originally developed in econometrics to measure the dependence of one's perceived happiness to factors such as marriage, money, or sex. Based on the simple model explained below, you can answer questions like: how valuable is a "marriage" in one's life - how does it compare, for example, with a job that pays twice the salary?

This burgeoning field has been dubbed as "happiness economics" in the media. The basic idea is to take large nationwide surveys with data on income and marriage status, together with qualitative questions such as "do you feel you are playing an useful part in things?" or even self-reported assessment of "level of happiness". Then one constructs an utility model for happiness:

level-of-happiness = function (income, marriage-status, health, ... )

where variables like income may be actual values (standard model), or a ratio (comparison model). The ratio model works better but you need to supply a reference value for each variable.

Now, assuming that the function is "linear", you can write the function as.

Happiness = c1 income + c2 marriage-status + c3 x health . . .

where c1, c2, c3 etc are the "coefficients" of these "life-event" factors. What is "c1"? If you plot the responses of happiness against income (factor1), you get a "cloud of points. If you fit a straight line through the middle of these points, then c1 is the slope of this line - i.e. if income rises by 1 unit, happiness goes up by c1.

Fitting a line through a cloud of data points.
Many would disagree with the very principle of linearity - for example, a fundamental principle in economics, the law of diminishing returns, says that as your earn more, the same increased income will result in a smaller rise in happiness. Also, even if you look at the cloud of data in a plot like the figure, you can see that the straight line is at best a very poor approximation. However, in the absence of other models, one can start with a linear model.

Now, the main idea behind this work, in the words of Clark and Oswald (2002), is to "use the relative coefficients of income and life events ... to calculate a monetary 'compensating amount' for each kind of life event."

What this means is that coefficients like c1 and c2 determine how much an increase in factor1 would compensate for an unit loss in factor2. For example, if suddenly your spouse were to die, how much more must you earn to maintain the same level of happiness? The answer is easy to get if you believe the linear equation above - if your marriage status goes from 1 to 0, then your loss in happiness is -c2. So income must rise by (c2 c1) to maintain the same happiness. The economists then make the claim that losing a spouse is equal to (c2/c1) amount of annual income, which for the US and the UK, works out to around Rs. 40-50 lakhs per year. A more important factor for happiness is health - going from excellent to fair is the same as losing Rs. 2 crores per year. While these numbers are for affluent western societies, for middle class India, one may lower them by a factor of five to ten perhaps.

While these results are best tentative, they do provide insight into the many ways in which statistical methods are changing the social sciences. But do they mean that science can answer the larger questions of life? There is a hint on this in one of the other results in the study: religious people are happier and live longer than rational scientific atheists like me!

So I am afraid that for a very long time, these questions will remain the grist of more intuitive fields like religion.