Unwise by One third: The fallacy of self-correction

Bandwagon behavior, and coupled to it the ‘free-rider’ problem has wide scale ramifications from equity and derivatives trading to public accountability in capital raising and deployment and in many other areas including the simple experiment of finding the best candidate for a job amongst a large number of applicants. The behavior in most bourses as the opening bell is sounded till the closing has similarities that can be attributed partially to the effects of information asymmetry or sometimes to potential difficulty to actually get a mathematical solution to a complex problem where unknowns are either large or a simplistic linear model may not be the right fit to get as close to the reality as possible. Relying on availability heuristic or copying the behavior of others is the more ‘sensible’ response, which may not be the more rational one. The engines through which these actions get guided or influenced is a more recent study where market participants could actually be incentivized to act on signals of others rather than actively seek information for a more personal inquiry. Inquisitorial journey into areas where timely information and perfect information could be rarity further compounds this problem plaguing financial markets in particular.

As David Brooks would say it, in “this buffered world of private choices”, decisions are taken more sequentially than in an integrated manner, although it may seem otherwise. From planning decisions, in absence of perfect on-line up to date information, where availability heuristic is the basis of taking a view, to the more venerable corporate planning for the long term, sequential processes lead to decision making where decisions taken by others and priori probabilities of the correctness of these decisions have a bearing on the posterior probabilities and on the decisions thereof.

In a world that is more oriented towards marketing a product or an idea or a value proposition, we have the same incidence of sequential decision processes driving results. The launch of a successful product in a test market is a pre-condition for its subsequent success, the idea behind any political move must be tested positively in carefully chosen segment of the population, to be of any significance going forward.

To draw the first customers to a product or a service is the fundamental driver towards success of that product launch and a positive response can only catch on if that is carefully nurtured with the right interventions. One person’s decision is no more cocooned and sequestered in a world that is far more networked than before and sequentially as people exercise their choices on products, ideas and mandates, we have the incidence of what is summarized as ‘bandwagon effects’, or what is called the effect of ‘information cascades’. From one man who his bent on his instincts (he is more likely to over-estimate his positivism when he is keen to buy while could under-estimate his negativism when he wants to reject) to a herd who rely on instincts of others, we have a market phenomenon which cannot be called a self-correcting mechanism anymore; thus when bubbles start to inflate it is mostly unnoticed or when credit is extended the inflection point is never fully understood as there is no self-correcting force in play. Similarly when too much credit is taken out of the market, it is never known when too much has already happened as every bank watches the other in deciding on the next course.

Abhijit Banerjee in his seminal paper in 1992, titled, “A Simple Model of Herd Behavior”, introduced the topic of ‘everyone doing what everyone else is doing although private information suggests doing something quite different’. His simple model brought to the fore the disastrous consequence of such an eventuality, “In equilibrium we find the reduction of informativeness be so severe that in an ex ante welfare sense society may actually be better off by constraining some of the people to use only their own information.” The Nash equilibrium that creates the most efficient solution is itself based on sequential acceptance of other’s choices which are themselves based on choices exercised prior to theirs, which may or may not be based on rationale. Lack of informativeness in the final outcome is a very pretentious denouement of the bandwagon effect.

Taking this case forward we have a few more inter-connected issues that get surfaced. The signals that influence a decision are not free, nor can they be sometimes priced correctly or traded that have no externalities involved. This makes modeling more difficult and most experiments have simplified this problem.

Asch in his experiments in the period 1951 to 1956, (he used a number of confederates and one single participant, where the participant was the last to respond when the responses of the confederates were known) which led to the Asch paradigm and later his variations led to the same result that “participants conformed to the majority group (confederate) in about one-third of all critical trials”, regardless of what the participant’s individual responses or preferences were.

In the seminal article by Robert Schiller in March 2008, ‘How a bubble stayed under the radar’, which came out in New York Times, he took examples from the work by  Bikhchandani, S., Hirshleifer, D., and Welch. I, where the effect of prior and posterior probabilities explain how a sequential decision making works.

Easley David shows how this works in this brilliant example taken from his paper, ‘Networks, Crowds and Markets: Reasoning about a highly connected world’:

“A person’s signal telling them to accept is denoted as “H” (a high signal, where high signifies he should accept), and a signal telling them not to accept is “L” (a low signal). The model assumes that when the correct decision is to accept, individuals will be more likely to see an “H”, and conversely, when the correct decision is to reject, individuals are more likely to see an “L” signal. This is essentially a conditional probability – the probability of “H” when the correct action is to accept, or P[H|A]. Similarly P[L|R] is the probability that an agent gets an “L” signal when the correct action is reject. If these likelihoods are represented by q, then q > 0.5. This is summarized in the table below.[1]

Agent Signal	True Probability State
	Reject	Accept
L	q	1-q
H	1-q	q

The first agent determines whether or not to accept solely based on his own signal. As the model assumes that all agents act rationally, the action (accept or reject) the agent feels is more likely is the action he will choose to take. This decision can be explained usingBayes rule:

If the agent receives an “H” signal, then the likelihood of accepting is obtained by calculating P[A|H]. The equation says that, by virtue of the fact that q > 0.5, the first agent, acting only on his private signal, will always increase his estimate of p with an “H” signal. Similarly, it can be shown that an agent will always decrease his expectation of p when he receives a low signal. Recalling that, if the value, “V”, of accepting is equal to the value of rejecting, then an agent will accept if he believes p >0.5, and reject otherwise. Because this agent started out with the assumption that both accepting and rejecting are equally viable options (p = 0.5), the observation of an “H” signal will allow him to conclude that accepting is the rational choice.

The second agent then considers both the first agent’s decision and his own signal, again in a rational fashion. In general, the nth agent considers the decisions of the previous n-1 agents, and his own signal. He makes a decision based on Bayesian reasoning to determine the most rational choice.

Where “a” is the number of accepts in the previous set plus the agent’s own signal, and “b” is the number of rejects. Thus, a + b = n. The decision is based on how the value on the right hand side of the equation compares with p.”

This is summarized by Robert Schiller as: “In other words, more than one-third of the time, rational individuals, each given information that is 60 percent accurate, will reach the wrong collective conclusion.”

Collective conclusion of the market based on sequential reasoning, where informativeness is itself scarce and on a shaky ground leads to the general argument that when the market as a whole could be taking an irrational decision, the chances of that being deciphered and acted on by an individual participant is remote. When market itself is one third unwise, as individual participants respond seeing the response of others as in the Asch experiment, the self-correcting principle of the market falls flat, or at least the mathematical fallacy is no more on a shaky ground.

This leads us to the conclusion that bubbles can only burst when the crisis is full blown, when the collective conclusion leads to this denouement where the Nash Equilibrium shifts; the collapse of a paradigm only needs one small nudge against a mountain of wisdom that is more unwise.

 

Procyon Mukherjee

25^th July 2013