# Balance Mechanics 1: Groups, the Aggregate Economy and Fallacies of Composition

This is the first official lecture on balance mechanics and it will be about a fundamental issue: the difference between what you can say about individual economic units, groups of economic units and the sum of all economic units, i.e. the aggregate economy.

One of the most interesting aspects of balance mechanics is that it teaches you to always keep different kinds of statements for different levels of analysis apart – and to both detect and avoid fallacies of composition, i.e. the application of statements valid for individual economic units or groups of economic units to the aggregate economy.

What do I mean by the term “economic unit”? I mean by that everyone and everything that is relevant in the economy, i.e. individuals, firms, governments, countries etc. Groups of economic units can be defined at will: It can be all individuals, all firms, or – if you want – some kinds of households, some kind of firms etc.

Also important is that to each group in the economy corresponds a complementary group which are all economic units in the economy that are not members of that group. This means that the group plus the complementary group are the sum of economic units in the economy:

$group + \text{\textit{complementary group}}=\text{\textit{all economic units}}$

We can also – depending on our interest and field of analysis – define groups and complementary groups for certain types of economic units. For instance, we might be interested in the relation of banks between each other. Then we might define the aggregate of all banks and divide this aggregate into a group of banks and all other banks which would then constitute the complementary group.

Standing up while watching a play

It is best to illustrate this with a little example. Imagine a theater filled with the audience. Now one man sits up to improve his view (I take a man. They tend to be ruder than women). However, he will only be successful in improving his view if all other members of the audience stay seated. Or, expressed with the terms defined above: the group (here a group with just one member) will be successful in improving its view if the complementary group (all other members of the audience) stay seated. If everybody stood up, nobody would be able to improve their view.

This means that the statement “one can improve one’s view in the theater by standing up” cannot be applied to all of the members in the audience. To do so would constitute a “fallacy of composition“.

Now we can use three kinds of statements to sort out what is valid for individuals and groups of units, under what conditions it is valid and what is valid for the sum of all economic units:

1. Partial statement (valid for individuals or groups):  an individual or a group of members of the audience can stand up to improve its view.
2. Relational statement (which tells us under which conditions the partial statement is valid): an individual or a group of members of the audience can only improve its view if the rest of the audience stays seated.
3. Global statement (valid for all units): If all members of the audience stood up, nobody could improve their view.

Now, in this theater example the global statement might not be 100 % correct for each and every individual because some will certainly be able to improve their view while others won’t, depending on where you sit, the height of different audience members etc. It will most likely hold only on average. There will however be cases to be discussed later where the aggregate statement will hold for everybody and not only on average.

We can now define a fallacy of composition in terms of those statements: obviously, a fallacy of composition is when you apply a partial statement to the aggregate economy. There might be cases and conditions under which what is true for a single group is also valid for the aggregate. But those are normally special cases and not general cases. We will come to those cases later on.

You could of course also have the reverse, i.e. that you falsely apply a global statement to a group or an individual. I don’t know whether there is a term for that but that would evidently also be a problem.

Fallacy of composition vs. the rationality trap

The term “fallacy of composition” is used when you make an ex ante analytical statement about a certain situation. It does not depend on the concrete behavior of individuals. If behavior is concerned, i.e. if people actually tried to stand up to improve their view and found out that they could not actually improve their view because everybody did the same, it would constitute a “rationality trap”. Such a trap is that people individually behave rationally but their intention will be thwarted in the aggregate.

This is not to say that those people are dumb or do not understand that their standing up might be based on the fallacy of composition and might lead them into a rationality trap. Take the example of a fire breaking out in the theater. Everybody will be absolutely rational and right to stand up and run to the emergency exit. However, given that emergency exits are often very small compared to big audiences and fire tends to expand quickly, some will not get out, will be trampled down and burn. But it would hardly have been wise to stay seated and wait to be burnt alive. They had to take their chances.

Many economic situations (and other situations as well) are of this sort that one might know that some collective solution might be better but will have no chance of being realized so that people have to act rationally even if they get – on aggregate – into a rationality trap.

While balance mechanics is more about detecting fallacies of composition, one needs to find those fallacies to avoid rationality traps if possible. This is one of the appeals of balance mechanics.

While the above example is trivial, I will later show that quite a number of economics problems will be easier to analyze with the framework of groups, complementary groups and the three statements in your mind.