Using the Random Walk Hypothesis to Explain Personality Volatility

Some time ago, Blackcat raised the issue of people who have personality preferences that are split down the middle—say a preference that is so close to its alternative that it makes saying one is definitively X quite meaningless. Generally, when theories lack the capacity to explain and predict phenomena that exist outside its circle of conditions, either a new theory is adopted or an existing theory is expanded on and/or updated to accommodate the “new” goings-on. Various ideas were put forth. One was that preferences on the margin ought to have a category of their own. Others were put forth still more. Given this, and my curiosity in regards to people with personalities that change, we need a mathematical principle for explaining this phenomenon. My thesis is that personality volatility is to a great extent explainable by the Random Walk Hypothesis.

The Random Walk—sometimes called “the drunkard’s walk”—is based on the idea of a drunkard in a narrow corridor that can only lurch forward and backward. In order for his movements to be considered random, three conditions must be met: (1) He has to be equally likely to lurch forward as backward. (2) He has to lurch forward by exactly the same distance he lurches backward. (3) He has to lurch once every constant time interval. In effect, one can think about this geometrically with the aid of a probability distribution bell curve with the drunkard’s highest probability at his current position, and declining probabilities the further forward and backward from that point.

I begin with the supposition that all things of nature follow rules. Nowhere is there any irregularity. Rules can be deterministic and probabilistic depending on the frame of reference and what is being measured. If one flips a coin, the side it will land on is based on a probability. Yet, an extensive case study of a coin flip that is caught on camera and slowed down can demonstrate that given how the coin was tossed and the external conditions one can calculate that it was determined by physical laws. We conclude that the one does not exclude the other; the important thing is that each system is consistent.

If all things of nature follow rules, then personality, which is part of nature, would also have to follow rules. Just as the coin toss can be looked at from a physics perspective and a probability point of view, so too can personality variation be looked at from the one and many others. In effect, this essay argues that many volatile personalities that fluctuate can for all purposes of probabilities be explained by the Random Walk Hypothesis.

If one is on the margin of perceiving and judging, as many are, then at any given time one is equally likely to have an instance of judging as one is likely to have an instance of perceiving. Thus, the best indicator of whether one will be more inclined to judge or perceive tomorrow, is whether one judged or perceived today. This must be the case given the probability distribution curve where the highest probability of one’s future state is one’s current state. The further away the less probable. Yet, if people do indeed consistently test on the line--say between a preference of perceiving and judging--then over the long-run we should expect to see corrections. (I.e. if one has had 9 instances of judging in a row, but is on the line between judging and perceiving, then over the long-run this should correct quite naturally since the line is the rule, and fluctuations from one side to the other and back are only temporary and stochastic).

We may also apply the Random Walk principle to a conversation between two people with very similar personalities. Indeed, if we take a case of two INTPs, then how the conversation plays out may be understood by applying the Random Walk principle. Random Walk tells us that one INTP is just as likely to talk as the other. Further, if talking at T1, then this is the best indicator that there will be talk at T2. This can explain, for instance, why once INTPs of similar minds start talking, they can go on for hours. But if a silence ensues, then Random Walk tells us that if silence at T15, then the highest probability is silence at T16, and the conversation may never restart or reach its previous level.

In summary, we have concluded that personality volatility and interactions between similar minds may be understood by applying the Random Walk principle. It is true that Random Walk is stochastic, while the application of other scientific laws will show that phenomena manifests in a way that is more deterministic than probabilistic. However, I have argued that the one does not exclude the other, and that the utility of each depends on what is being measured and what angle one is approaching a given phenomenon from. This small essay has given one such approach—namely, the Random Walk principle. This prinicple can help one assign probabilities to the future states of volatile personalities.