Sunday, November 08, 2015

Change matters more than absolutes: (or ‘The unexpected virtues of incrementalism’)

Kahnemann and Tversky’s seminal paper on prospect theory had several path breaking insights. One in particular stayed with me because of its highly non-intuitive nature. Stated with an example, it is as follows: Say A’s net worth is Rs. 150 lakh and B’s net worth is Rs. 20 lakh, we are used to believing that A is happier than B or in economics jargon, A’s utility level is higher than B’s. (For the purpose of this argument, I am ignoring the claims of there being more to life than money. That is because this idea transcends money – you can very easily replace net worth in the above example with “units of being at peace” or “ounces of respect from fellow human beings” or some such measure of whatever you hold to be more relevant to happiness than money.)

Prospect theory does not make a prediction of this sort (A being happier than B). It is silent on who has higher utility. If pushed, the proponent of prospect theory states, “the data provided is insufficient. What was A’s and B’s net worth yesterday?”

Let us make it interesting. Say A moved from Rs. 200 lakh yesterday to Rs. 150 lakh today and B moved from Rs. 15 lakh yesterday to Rs. 20 lakh today. Now prospect theory would predict that B is happier than A. Most readers would think, “Well, this is obvious! Especially given the new information.” Stated in the whole detail, this later change of stance seems logical. However, this does not prevent almost everyone from offering the response in the first step above when the changes in net worth were not known and only current levels were known. Perhaps, in absence of the change information, we assume no change. That is fair but what is noteworthy is that we do offer an answer – which suggests that most of us think absolute levels are the predominant drivers of utility (or happiness) and while change matters, it matters only so much. It is an erroneous assumption. This is where prospect theory makes a non-trivial contribution to our understanding of ourselves.

We human beings are tuned to notice changes and contrasts. An extreme example of this is the Ganzfeld effect where the subject is exposed to undifferentiated and strictly uniform field of color for a long period of time such that the subject stops perceiving the color altogether (and even hallucinates). Our sense of color is really speaking a sense of distinction in stimuli. Take away the distinction and the brain slowly settles down into ignoring the color entirely. Most of our day-to-day judgments operate with the help of contrasts. We are highly sensitive to changes. Equally importantly, we are quite insensitive to absolute levels.

Combining these two connected ideas (high sensitivity to changes and low sensitivity to absolute levels), one can attempt to create an optimal path for maximizing utility (or happiness!) over the course of a single human life. No prizes for guessing that this path would advocate thorough incrementalism. To put the matter a bit more mathematically, we are used to thinking (in a manner ignorant of prospect theory’s observations) that the overall happiness of a person in the whole life – at least in its material aspects – is some sort of ‘area under the curve’ of material wellbeing. Hence if A moved from net worth of say Rs. 150 lakh to Rs. 200 lakh to Rs. 125 lakh to Rs. 175 lakh again over four decades of working life, each of these states lasting for say a decade each, we would calculate (implicitly) overall happiness over the four decades as 10*(150+200+125+175) = 6500 lakh-years for A. Likewise B with networth movement of say 10 lakh to 15 lakh to 40 lakh to 100 lakh over the same four decades would prompt us to suggest her overall happiness to be 10 * (10+15+40+100) = 1650 lakh-years. Clearly in this case A’s life was nearly 4 times as happy as B’s.

A prospect theory-informed first-cut attempt at the mathematics of these two individuals would work differently. Assuming A and B inherited their starting wealth the first decade has no utility value. Thereafter, A goes as follows: 10* ((200-150) + (125-200) + (175-125)) = 10* (50 – 75 + 50) = 10 * 25 = 250 delta-lakh-years. (Pardon the units, the actual units do not matter for the sake of this argument since our intent is to merely compare the two individuals.) B’s path is a bit rosier: 10 * ((15-10) + (40-15) + (100-40) ) = 10 * (5 + 25 + 60) = 10 * 90 = 900. It turns out B is nearly 4 times as happy as A.

Which prediction is closer to observed instances? I am inclined to think that it’s the latter. Clearly the above first-cut mathematics is way too simple. In real life, the absolute levels of material wellbeing matter too, all the more so in crises and in enabling risk-taking. However, it suffices to say that the dependence of happiness on change in the level of these drivers is of far more importance than we generally acknowledge.

There is another observation – and this is not from prospect theory. It is simply based on observing human beings. The capacity for happiness of every human being is finite. This means, we may have to modify our equations to put an upper limit of some sorts on happiness units in each time period, even after making it dependent on change. Beyond a threshold, a bigger increase in a happiness-inducing input (money, fame, love, peace etc) does not add to happiness. So if the change in wellbeing is beyond a threshold, the happiness from that change would max out and not increase further with the size of the change (for that period). In other words, it might be better to postpone that extra increase to the next time period if possible.

To make the mathematics a bit more explicit, I would state the following.
Before prospect theory, happiness over life of t_max years would be as follows:

Where L is the level of material wellbeing (or level of fame or level of self-actualization)
This prevalent but naïve hypothesis would suggest that a billionaire is 1000 times happier than a millionaire. Or to switch to fame as a source of happiness, the person adored by 1 million people is 100,000 times happier than a person adored by say 10 individuals.
After prospect theory the equation is nuanced as follows:
Where DeltaL/Delta_t is the discrete change in level of material wellbeing (whatever driver of happiness you choose – money, fame etc) across two successive time periods and Delta_max corresponds to the maximum change in wellbeing upto which humans are happiness-sensitive to the change.

To get a bit less mathematical and bit more lyrical, it is more happiness-inducing to get to the summit of life using the long-winding steps than using the helicopter (if one is available). It may seem tempting to prefer the helicopter so that one can quickly get to the summit which can then be enjoyed for longer – rather than wasting time on the steps. However, our dual hypotheses above (prospect theory and finite capacity for happiness) predict that the one-time happiness of getting to the summit is likely to be overshadowed by the cumulative happiness of the multi-step path. Also, the summit itself is likely to lose its ability to induce more happiness over a short period of time (because there would be no increase from there on).

Is there a real life implication of this thought? Maybe! To put it simply, if one has the flexibility of organizing the improvements in one’s drivers of wellbeing, it is optimal to organize them into a gradual increase mode than to maximize the jump. Also, since absolute levels of happiness-drivers matter much less than we are used to thinking of, the hurry to maximize absolute levels is probably suboptimal use of our limited resources (time, energy, bandwidth, goodwill etc). Presumably, this could inform some decisions related to trade-offs in career decisions, location preferences or social standing pursuits.