Pareto Distributions and Social Ills

You might have heard of the Pareto principle, more commonly known as the 80/20 rule. To paraphrase, the 80/20 rule describes systems where 20% of the inputs account for 80% of the outputs. For example:

• 80% of the work is done by 20% of the people.
• 80% of the wealth is owned by 20% of the population.
• 80% of our food comes from 20% of our land.

If you apply the principle recursively (e.g. within those 20% of the people who do 80% of the work, 20% of those people are responsible for 80% of their higher level of output, and so on with any subdivision), you end up with a Pareto distribution with a parameter of log₄(5). That is to say, the distribution is self-similar.

Wealth is usually agreed as being more-or-less Pareto distributed (in fact, it was the study of wealth distribution that lead Pareto to describe this distribution in the first place), though the parameter will be different depending on the level of inequality in the population under study. I think it's interesting to consider the interaction of this distribution with the sociological finding that individual happiness depends more on relative material well-being vs. one's neighbors than on absolute material well-being.

Let's start with the idea that the maximum size of a person's meaningful social network is approximately normally distributed across the population, and is not too dependent on the person's socio-economic-status. Strictly for illustration, we'll choose the mean maximum size of a person's social network as 100. Let's also assume that we tend to socialize with people with similar social status to our own. The question, then, is, under this system, how does the level of inequality that a person is exposed to vary with how much money he makes? And, further, how does his income affect his happiness?


Observing the slopes of these Lorenz curves, it's clear that a person nearer the right of the distribution (in our scenario, a member of the rich) will be exposed to much greater inequality than one further away. He is more likely to know people who have (what he'll consider) unjustifiably more income than himself, which will tend to hurt his happiness. Further, as inequality increases, there will be fewer "rich" who are exposed to more inequality within their own social circle, and who will be less happy with their lot as a result. An interesting corollary is that, in a less equal society, people on the poorer end would be exposed to less inequality within their social network - the perception of inequality is also distributed unequally.

There are a few outcomes that I think result from this dynamic. Speaking in broad generalizations, and ignoring the behavior of specific individuals, I think there will be a tendency for:

• The rich to become ever more individually motivated, as the increase in income from a moderate improvement in position grows exponentially as you become richer.
• A rich person's sense of well-being to be reduced. We try to live within our means, but in an unequal society, the rich will experience much greater volatility in their means than the rest of us do, making it harder to determine what the means are that they are trying to live within. This is stressful.
• The poor to lose motivation, as moderate improvement in relative position will not lead to a proportionate increase in income.

Some of this discussion conflates within-lifetime inequality to across-society inequality. I will try to address that, later.