Antisocials Are Inevitable

A utopia, in which everyone is a cooperating member of society, cannot exist (at least not for long). Why? Because it is unstable. If everyone plays by the rules, all it takes is one individual to break the rules, gain an advantage over others, and attract more people to break the rules.

Short of utopia, is there something else we can aspire to as a society? Indeed. We can dissuade antisocial behavior. Behaviors can be shaped by incentives. The specific incentives in a society lead to a particular balance of behaviors. That particular mix is not what is optimal for everyone. But it is a stable equilibrium. Equilibrium means that if society is in that state, it will remain in that state unless something changes. Stable means that if society’s composition deviates from the equilibrium, it’s in the interest of some people to change their behaviors (for better or for worse), gain personal advantage and drive society back towards that stable equilibrium. So society’s long term trend towards a stable equilibrium is inevitable.

Let’s use a simple model to understand this better. This is based on ideas from evolutionary game theory (see The Selfish Gene by Dawkins). Consider a simplified society in which there are only two kinds of people: Socials (cooperators) and Antisocials (non-cooperators). When two people in this society interact, they must negotiate on how to share a fixed resource (e.g. food). Socials and Antisocials have very different negotiation styles, leading to the following different outcomes:

  1. Social vs Social: they cooperate and share the resource equally.
  2. Social vs Antisocial: the Social cedes the resource to the Antisocial rather than engage in non-cooperative behavior e.g. aggression. This leads to an incentive to be antisocial: win without a cost when interacting with Socials.
  3. Antisocial vs Antisocial: each decides to fight for the resource, and the winner (with each of them equally likely to win) takes the whole resource. But the fight comes at a cost (e.g. physical injury or legal jeopardy).

The above negotiation strategies result in the following payoff matrix:

V: value of the resource in a person-to-person transaction.
C: cost of fighting (instead of cooperating).

| meets Social | meets Antisocial |
If Social | V/2 | 0 |
If Antisocial | V | 1/2 (V - C) - 1/2 C |

What happens in this toy-model of a society? What breakdown between Socials and Antisocials leads to a stable equilibrium? Is that breakdown optimal for society? How can we tweak incentives to reduce the proclivity for rule-breaking?

Let 'f' be the fraction of people who are Antisocials (0 <= f <= 1).
So, the fraction of people who are Socials is '(1 - f)'.
Let 'S' be the average utility (value) of being a Social.
S = (probability of meeting a Social) x (payoff matrix value) +
(probability of meeting an Antisocial) x (payoff matrix value)
= (1 - f) x (V/2) + (f) x (0)
V/2 - f x V/2
If we plot 'S' as a function of 'f', we get a straight line that starts at V/2 when f is 0 and slopes down to 0 when f is 1.Let 'A' be the average utility of being an Antisocial.
A = (probability of meeting a Social) x (payoff matrix value) +
(probability of meeting an Antisocial) x (payoff matrix value)
= (1 - f) x (V) + (f) x {(1/2) x (V - C) + (1/2) x (-C)}
V - f x (V/2 + C)
If we plot 'A' as a function of 'f', we get a straight line that starts at V when f is 0 and slopes down to (V/2 - C) when f is 1.When f = V / (2C), the two lines S and A intersect. This is the fraction of Antisocials at which there is a stable equilibrium.

We can see quite clearly the mechanism by which society is driven towards the stable balance between Socials and Antisocials. When there are fewer Antisocials than the stable fraction, it pays more to be antisocial (the red line is above the green line to the left of the blue dot, in the graph above). So, some Socials will take advantage of that. They will change for the worse into Antisocials, increasing the Antisocials fraction towards the stable equilibrium. Conversely, when Antisocials are more pervasive than the stable fraction, it pays more to be social (the green line is above the red line to the right of the blue dot). This leads some Antisocials to change for the better into Socials, decreasing the Antisocials fraction towards the stable equilibrium.

We can also see that the stable equilibrium is not where every person receives the highest utility. At the stable equilibrium fraction ‘f’, the average utility of being social is the same as the average utility of being antisocial: S = A = (1 - f) x V/2. However, the optimal utility is achieved when everyone cooperates. In that case, each person gets a utility of ‘V/2’, which is greater than the equilibrium utility. But alas, in that optimal state, there are a few who decide to increase their personal utility compared to others by becoming antisocial, dragging down the utility for all towards the stable equilibrium. The equilibrium is stable not because it is optimal but because it is resilient to cheating.

How can we shape behaviors to reduce the preponderance of Antisocials? At equilibrium, the fraction of Antisocials is ‘V / (2C)’. To lower that fraction and still be in a stable equilibrium, we should increase the cost incurred for antisocial behavior by appropriately severe punitive measures. When the cost of rule-breaking (‘C’) is much larger than the value of winning by any means (‘V’), the fraction of Antisocials will be closer to 0. That is a stable equilibrium worth aspiring to.

Photo by Austin Kehmeier on Unsplash

Mindful Thinker | Software Engineer (Google, Amazon) | Theoretical Physicist (MIT) | Husband, Dad, Dog Dad

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