# When the Whole is Greater than the Sum of the Parts

A few years ago, our company was given the task of simulating bank mergers. From a pool of several hundred banks we simulated hundreds of mergers – large banks with large banks, small ones with large ones, mid-size banks with large banks and with small ones. This result was extraordinary and remarkable to say the least.

Suppose we take bank A and bank B. Suppose that the complexity of the banks – this was calculated using three years of quarterly balance sheets – is, respectively, C(A) and C(B). Once we merge them – this is done by merging the balance sheets – we obtain a new bank, which now has complexity C(A+B). Here are the possible outcomes:

Case 1. C(A+B) = C(A) + C(B) – occurrence 5%

Case 2. C(A+B) < C(A) + C(B) – occurrence 20%

Case 3. C(A+B) > C(A) + C(B) – occurrence 75%

What does this mean? In case 1, the whole is equal to the sum of the two components. This case happens when we merge two banks that have totally different businesses, say a retail bank and an investment bank. Such an operation would probably make little sense in the first place, but the conclusion is this: if you put together two components that don’t interact or compete with each other, or ignore each other, they can co-exist almost as if no merger took place. Case 2 is most interesting but let us analyze case 3 first. This is the case in which the complexity of the outcome is greater than the sum of the complexities of the components. This is the case in which the whole is greater than the sum of the parts. It also happens to be the case that more than 70% (some say even 80%) of mergers between companies fail. In essence, case 3 is that of competing businesses that are forced to fit into a new entity.

Who writes has experienced mergers from the perspective of the company which takes over another company and vice versa. In most cases the management of the company that has been taken over is more or less progressively phased out. This means that the individuals that know well the business of that particular company are let go. This leaves the management having to deal with a new and larger company and without fully understanding parts of its business. Moreover, companies usually have a particular culture. Merging forcefully companies with different corporate cultures never works. This is a recipe for disaster. In order to deal with a more complex and larger company one would logically assume that more competency is needed to cope with the situation. But the opposite happens – a greater problem is challenged with less competence. Case 2 is obviously the most desired one. A new and less complex – more efficient, lean – company is formed, allowing for cost cuts, improving efficiency and profitability. This case, in which the whole is less than the sum of the parts, is far less likely than case 3 but it is also the only one which has chances of survival. This is because only two businesses that are in synergy, and which have similar cultures, can produce a successful merger. In effect, very few mergers are successful and when they are not, a company that has been previously absorbed is destroyed and then spun-off in an act of genius (or desperation) called “return to our core business”.  The bottom line is that merging complex systems, such as banks, corporations or IT systems, is a risky exercise, with a very high likelihood of failure. Imagine how complex the merging of cultures must be.

So, the next time you wish for the whole to be greater than the sum of the parts, be careful. You may get what you wish for.

This simple example illustrates how conventional, three-dimensional linear thinking can quickly get people into irreversible trouble. Very few things in Nature follow laws that are linear. True, there do exist successful local linear surrogates, but they must be used with caution, especially outside of their domains of validity, which are not always easy to define. When non-linearities kick in, things often assume a counter-intuitive connotation. In a nonlinear regime A+B does not always equal B+A. Try, for example, finite rotations.