Our debt to Kenneth Arrow: From the Impossibility Theorem to Learning by Doing in the world of business

One of most celebrated Economists and thinkers of our times, Kenneth Arrow died two days back. The world of business owes him so much that we cannot possibly make a complete list any which way we try.

I will take only a few examples from his papers that got him the Nobel Prize, those that have ramifications in the world of business. He was the youngest economist to receive the Nobel at the age of 51 in the year 1972.

I will first take his Impossibility Theorem, the one that has made him so famous but it has remained the less explored item in the world of business. It deals with the rank preference of individuals and whether these ranked preferences could actually lead to the society’s ranked preference that would satisfy certain conditions.

The easiest to understand is the voting system for candidates or parties. If A is preferred over B and B is preferred over C, then does it lead to the conclusion that A is preferred over C? Supposing we reverse the order and start with whether C is preferred over A? What happens to the sum total of these preferences for the society to arrive at the best candidate?

It could well be that chocolate is preferred over vanilla and vanilla is preferred over butterscotch, but butterscotch could well be preferred over chocolate. Now if you have many customers queuing up for ice-creams with these kinds of preferences could you possibly aggregate them for the entire group? Would that aggregation be efficient?

The arbitrariness of the societal preference to choose based on this ranked preference system raises the doubt that much would depend on the way the orders are selected. Arrow’s Theorem proves by the way that, “when voters have three or more distinct alternatives (options), no ranked order voting system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a pre-specified set of criteria, like pareto efficiency or non-dictatorship.”

Think of the applications of this in the field of business. Every business plan is not one unique plan; it has an alternate plan with which it is competing. So it could well be the ranked preference question:

A>B>C or B>C>A or C>B>A etc

If each manager is asked to vote given these ranked preferences, the organization wide ranking would never be pareto efficient.

The arbitrary nature of the best selected plan in business is never in doubt, going by Arrow’s Impossibility Theorem; it tells you that you could be wrong in aggregating ranked preferences of individuals or groups.

The same pervades the entire edifice of surveys conducted where individuals are asked to rank their preferences and a simple aggregation rule is used to get to the organization wide ranking of preferences.

All that you must keep in mind is that the aggregation result could be very arbitrary.

The easiest example I can go back to is the choice of ice-creams or the choice of different add-ons to different food items. It could well be that chocolate is preferred over vanilla and vanilla is preferred over butterscotch, but butterscotch could well be preferred over chocolate.

If you add frills like sprinkles or crashed nuts or other sweeties, it could actually complicate the situation with the problems of ‘No-Association’.

The next time you run any survey which ranks the preferences of individuals to get to the organization wide ranking, remember that the plain aggregation could be very arbitrary to get to any conclusion.

I would think that a lot of data that gets analyzed about the buying behavior of individuals in a store misses to get to a logical conclusion given that we face the same challenges of aggregation.

Let me now move to the theory of Learning by Doing, which epitomizes Toyota’s production system and many other endogenous growth systems that the world had seen. Arrow believed and proved that investment in human capital and innovation is the fundamental driver of economic growth and it is not external influences that had driven growth but mostly internal growth drivers like the firm’s ability to cut cost or produce more with the same resource endowments.

This in other words means that the positive spillover effect of innovation drives growth.  This would also lead to the conclusion that competition, that drives innovation will be an essential part of endogenous growth. This has implications for new product development that would create new usage patterns or habits that did not exist before.

Could we take this to the new product launches of our times that created new habits of people that so far never existed? Think of Snapchat or the Instagrams or the LinkedIn of our times and we would see this unfolding. All this had nothing to do with the endogenous growth theory that anchored on savings rate or the rate of technological growth.

If companies have to grow, it need not be true that getting into new markets with the same product offerings could be the only way. You could grow by simply taking out costs and get to the same output with a fraction of the earlier inputs. The return to capital could be your milestone, which even with much higher revenues you may not be able to achieve.

So for the world of business, Arrow leaves us with more questions than answers. His magnum opus on limits of markets, tells us that buyers and sellers exchange only incomplete information. Markets could fail with this incomplete nature of information, like the ones between medical insurers and the patient-clients or the ones between used car salesman and the buyer of the used car.

Arrow leaves us with the wisdom that markets are actually never complete, it is in this incompleteness that some will prosper and some will not.