Good For One

New Math

There’s a unexpected mathematics in charge of certain types of operations in real life. To wit, a sum of pluses can equal a negative. A combination of individual events of positive consequence can add up to an aggregate event that is of negative impact.

Positive + positive + positive + … = negative

That doesn’t sound like the old math, 1+1 = 2, does it?

Let’s consider three examples from everyday society which displays this anomalous behavior..

Wheat Farmer

Economics provides well-documented cases of the act of one leading to different results when all perform the act.

Wheat farmed by combine
Wheat farmed by combine

One wheat farmer growing an extra bushel raises his income by the price of a bushel.

If every wheat farmer growing an extra bushel, the value of each bushel of wheat falls.

The first farmer got more income. The second farmer got more income. The third farmer got more income. At some point, the bushel price dropped and the first, second, third, … and every farmer got less.


If one person doesn’t pay their taxes, the government will not grind to a halt. The services continue, so that one person is better off with more cash in their pocket. When you and I see them prospering by tax avoidance, we may decide to do the same. However, when many people do that, services from the government can’t be funded.

One person avoiding taxes, benefits themselves and doesn’t harm others. When all people do the same, the loss of government services will be severe.


If one person litters, someone else in the neighborhood may pick it up. The first person gains the freedom of not having to cleanup their own mess. If multiple people litter, the task becomes daunting. The others despair of ever cleaning it all up. The neighborhood deteriorates.

A similar logic drove the broken window argument which underlay the NYC police attention to small crimes, successfully resulting in increased neighborhood self-regulation and dramatically lower crime rates.

Mechanism of Odd Math

The basic concept is that there are a large number of people who are part of the system and a single action (or inaction) does not affect the system, yet the aggregate of many individual actions will affect the system.

A single action may seem good for us, but if everyone does the same, the result is bad.

Formally, this is explained as a fallacy of composition: the error of assuming that what is true of a member of a group is true for the group as a whole. That definition is cold and abstract, so I wrote this post to provide examples.

Let’s consider the fallacy of composition and Adam Smith’s Invisible Hand.

Invisible Hand

The Invisible Hand holds that the market aggregates individual needs into socially beneficial results. Yet with the fallacy of composition, we have seen cases where actions that benefited individuals yet lead to negative consequences for the group.

These is a limitation to the free market’s Invisible Hand. Summing individual selfishness does not always lead to a society good.

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