Mental Maths, Truth Tables and Making Better Partnership Choices

A lot of partnership decisions begin with a fairly sensible calculation. We have this, they have that and together, we might be able to do something neither of us could do alone. That is usually how it should work but when the problem is difficult, identifying complementary assets is only the beginning. The harder question is what those assets actually mean in relation to the problem, and what the combination tells you to do.

I recently found myself looking at a prospective partnership where the complementarity was obvious. We had things they did not have, they had things we did not have and there were some overlaps too. On paper, it looked promising, so I tried to make the logic underneath the partnership a little more explicit.

I put the problem in the middle and mapped the assets around it.

For each thing the problem required, I marked whether we had it, they had it, both had it, or neither did.

We have it	They have it	What it tells us
True	True	Shared capability. Useful, but perhaps not where the partnership adds most value.
True	False	Something we can contribute.
False	True	Something they can contribute.
False	False	A gap neither organisation currently fills.

The table did not tell us anything revolutionary. What it did was make the relationship between the assets and the problem much harder to gloss over.

Complementarity is not the conclusion

It is tempting to stop once you have found the complementary bits but the useful question comes next: So what does that combination allow us to do?

I came across this idea while reading Gibson and Isaac's Truth Tables as a Formal Device in the Analysis of Human Actions.

Their argument is much broader than partnership working. They use truth tables to explore how distinctions and choices can be organised into increasingly complex structures.

What interested me was their use of T and F not simply to establish whether a proposition is logically true, but to trace what happens when distinctions are repeatedly made and organised.

I wondered whether the same discipline could be useful in partnership scoping. Not to turn partnership into mathematics, just to make the choice visible.

Instead of relying on a general sense that two organisations are complementary, you can lay out the problem, the required capabilities and the contribution each organisation can make. Then you can see what follows.

It is a very simple form of mental maths:

problem → required capabilities → organisational assets → gaps → possible action.

The value is not in the arithmetic, it is in making the reasoning inspectable.

The interesting part is the gap

We naturally spend most of our time talking about what organisations bring but the real value of an asset depends on the problem it sits against.

And then comes the harder question

Even after mapping all of this, the table does not make the decision.

Partnerships involve trust, relationships, incentives, power, institutional history and judgement. Some things will never sit comfortably inside a True or False cell.

There is always the third category: "It depends."

Which is doing quite a lot of work in organisational life. The point is not to eliminate that judgement. It is to give it something to work with.

Partnership should make the problem more solvable

That is probably what I took from the exercise.

Does bringing these organisations together make the problem more solvable? The truth table gave me a simple way to explore that.

Map what the problem requires. Map what each organisation can genuinely contribute. See where the capabilities reinforce each other, where they overlap and where something is missing. Then work out what that combination actually makes possible.

The answer may be the partnership you expected. It may be a different partnership. Or it may be that the problem needs something none of you currently possess.