Stop arguing, and start drawing circles together

I remember being a big fan of Venn diagrams while studying set theory from mathematics, back in high school. I never touched any of this set theory, and all that jazz after that brief encounter.

It was only recently while trying to navigate some complex decision making, that I realised how useful set theory is, as a mental model for visual reasoning:

All it takes is a bunch of circles, that’s all there is here to help reason complex decisions. I’ll start with the most simplest decisions, and visualise them through sets, and slowly turn up the notch, progressively increase the complexity of the decisions, to show how this could also be visualised.

Throughout, let: U = Universal set (all possible work, opportunities, artefacts or problems), A = User Outcomes, B = Business Outcomes, T = technology feasibility.

I’ll take you through a couple of examples, starting with the “sweet spot”:

$$A \cap B \cap T$$

In this case, the feature that’s being planned to be built is aligning with the expected user outcomes, expected business outcomes, and is also feasible with the current technology. For eg. faster checkout performance, better for the business (more monies), better for the users who make payments, and also technically possible.

As someone doing product work, a term that’s usually thrown around quite a lot is alignment. If we look at this purely on a rational basis, without looking at the emotional component at all, alignment is ultimately about reaching an unified understanding of the collection of sets, and their relationships. In case of the “sweet spot” category, every set is aligned (user outcomes, business outcomes, and the delivery/tech team involed)

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Everyone agrees, but impossible to build:

$$(A \cap B) \setminus T$$

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Helps users, but pathetic business case:

$$(A \cap T) \setminus B$$

Could be a dream for users to have on the product, but very weak business case: for eg. accessibility concerns that are usually ignored, unless it becomes a part of compliance

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Helps business, but users really don’t care:

$$(B \cap T) \setminus A$$

Audit logs, account balance reporting etc, come under this category.

Now, what I’ve shown so far are the simple cases, which can also be explained verbally in a succinct line. However, we also see other more twisted cases:

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Misaligned incentives:

$$(A \setminus B) \cup (B \setminus A)$$

Category of use cases that either only benefit just the user, or just the business. There are no overlaps, at all.

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Valuable, but blocked:

$$(A \cup B) \setminus T$$

For eg: user wants offline mode for their favourite app, but building that capability requires larger architectural changes which wouldn’t be possible

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Most problems are nested within larger problems:

$$A_1 \subset A_2 \subset A_3 \subset U$$

There is often a hierarchy of problems which gets missed accounting for. While discussing with others, this visualisation helps us know at which level of hierarchy we’re discussing the problem. Often we mistake one hierarchy for the other.

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Requests (R) don’t match with Business goals (B):

$$R \cap B = \emptyset,\quad R,B \subseteq U$$

Let’s take an example of a CEO requesting for a dark mode to be added to the app, but then, adding dark mode doesn’t serve any user problem. It’s just a useless request coming in from an influential person, and the game becomes more political..

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The balanced roadmap:

$$(A \cap B) \cup \bigl(U \setminus (A \cup B)\bigr)$$

Sometimes, some features dont fall into the intersection of user <> business outcomes, but still worth doing as a strategic technical investment, helping strike the ideal balance of today, and tomorrow

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Ship obvious wins, while investing in platform health:

$$(A \cap B \cap T) \cup \bigl(U \setminus (A \cup B)\bigr)$$

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Mixing strategic bets with easy user wins:

$$(A \cap B) \cup \bigl((A \setminus B) \cap T\bigr)$$

Every disagreement is, at its core, a disagreement about boundaries. Alignment problems are usually about where one thing ends, where another begins, what belongs together, what doesn’t, what overlaps, what has been mistaken entirely, etc. All this is made super clear with the language of set theory. It gives a good technique to make these boundaries visible..

Everything around us is a relationship between sets, sets of sets, and sets of sets of sets:

Needless to say, that it just makes me want to stop arguing less, and just open up an Excalidraw instance, and start drawing colorful circles. Alignment is then, lot less of an hassle.