Wednesday, September 23, 2015

Counterfactuals, What If , Turing Machines and Oh My


"If she had said yes things would have certainly been different" - my dear readers I  caught your attention, didn't I? Well what can I say sentence like these really act like a bait to fish in public these days as attention deficit is running wild. Anyway without digressing further  into my personal romantic escaped which I may tell you totally sucks, lets jump into the subject of today's disquisition.  Look at the first question again, i can guarantee that almost everyone of us sometimes or other have pondered a hypothetical world  that differs from reality that we live in. Call it wishful thinking, fantasy , cynicism whatever you may as I welcome you to the world of "Counterfactuals".

Counterfactuals are in general  a hypothetical scenario that would have occurred had certain conditions prevailing at the given time were different. Now why is this important? It is important because it is the main foundation on the basis of which we carry out any debate that can range from policy prescription to economic decision to personal choices.  Determining the counterfactuals is essential as it helps to identify whether the decision we made had actual impact on the outcome or not, especially for assessing the situation that involves the  pre-post scenario. For instance let's say local government has introduced a scheme or awareness program for promoting girl education. Now let's say after the intervention literacy rate among girls ticked up. Now as usual politicians will tout the achievement and general public will also buy into it. But while comparing the scenario before intervention and after intervention we miss-out one crucial counterfactual and that is what would have happened if there were no intervention? Would the literacy rate have remained same or would it have been different? What would be your answer? Take a break have a Kitkat and think again for second. In general people would opine that without intervention the situation would have been same as before. But here is the catch, on doing so we may have overlooked the fact that perhaps the girl's literacy rate was already rising in the first place, that is  even before intervention started. If so then it simply implies that policy intervention had no effect what so ever instead it simply reinforced the eventual outcome.


The best example of not considering counterfactuals comes from Fredric Bastiat under celebrated phenomena that all Austrian School economist love to cite called "Broken Glass Fallacy". According to which once a ruffian kid broke the window of a baker with a brickbat. The crowd gathered and at first wanted to punish the kid. But a wise guy argued, since the kid broke the window now glazier will get the job to repair it. The money he earned will be then spent for cobbler to mend his shoe. The cobbler will then buy meat from the butcher who in turn will buy a bread from baker. So the same money that would have remained idle with baker would now circulate and make every one better off by increased wealth. In surface this appears too good to be true, but if you look at the undercurrent you'll find that had the glass window not been broken in the first place then baker might have put it in bank which would have lent out to others, thus stream rolling all the asserted economic activities. So you see breaking things to create wealth is not a good idea at all. Otherwise we should simply bomb our cities so that there will be more demand for repairs and unemployment goes down. Sounds stupid isn't it.

The question now arise is why counterfactuals invariably appears in worldly affair? Perhaps the answer is in quantum physics according to which world we live in happens because of chance. Out of infinite possibility as a result of particle wave duality there is only one reality in which we live. So there are always several possibilities and only one outcome. One may downplay impact of counterfactual like great Morpheus did in Matrix Reloaded "what happened, happened and couldn't have happened any other way" ( aside: isn't it ironic that the both Matrix sequel sucked big time and couldn't have happened any other way"). But when our decisions are forward looking that notion of ignoring counterfactuals will be a Pollyanna thinking.

Now at this point you must be thinking  if counterfactuals are something that haven't occurred at all then how to determine their effect in first place? How to properly quantify them ? Is there any standard tools to measure it? unfortunately the answer is no. Especially in research methodology there is something called Randomized Control Trial that segregates the control and intervention variable to produce ceteris paribus condition so as to isolate the effect of intervention only . But again choice of control variable itself is presumptuous putting dent to entire argument. Meanwhile perusal of any standard text book on Capital Budgeting provides you with tool such as Decision tree, What If and Scenario Analysis. These are all based on Bayesian Analysis and Prior Probabilities which entails degree of risk under certain apriori conditions. But they again miserably fail to account for counterfactuals as it is  less about risk and more of the domain of uncertainty.  Besides this of course in economics there are some concepts called Opportunity cost and Excess Profit  that do give some hope. but alas, how far do they gauge  in actuality is in itself a counterfactual.

So what else then. Some might say- "Hey let's build Ultracomputers that can crunch Yottabyte of data ( mind you that will make a Big Data a girly number) and sort out all the possible outcomes from all the possible counterfactuals". Tempting as  it may sound but it is not tenable either. The reason is something called Church Turing Thesis which says only those mathematical problem that can be solved by Turing machine is computable. But as counterfactuals generate infinite possibility it cannot be solved by Turing machine and hence is not computable at all. So no matter how fast or how large machine you built still the solutions will elude you. Of course there is possibility of it being solved using Hypercomputers but till this date as Mathematician Martin Davis asserted, it is still a technological  myth akin to elephant graveyard. Therefore with utter disappointment we have to throw towel and say we give up. There is no way we can determine all possible outcome and determine the correct path. So whatever happens, happens for good. Kind of solace isn't it? Reminds me of grape was sour adage.


Anyway to sum up if tomorrow someone asks you why are you still single or why you are so indecisive in your career, job or personal life. Just tell them you are weighing in on Counterfactuals. And if they give you puzzled look just suggest them to read this essay. I will definitely owe you one.