Dating is additive, but love is multiplicative

The world is full of pithy platitudes and mutually contradictory advice on risk-taking. "Don't be afraid to take risks," yet "Cross your t's and dot your i's." Should I be taking multiple low probability bets or crossing my t's as hard as I can on any given project? In the real world with finite time, I can't really do both. Part of the answer lies in a question that you'll only hear at a Bay Area house party - "Are you in an additive process or a multiplicative one?"

Additive and multiplicative processes refer to how an outcome is determined by its constituent components. In an additive process, the overall probability of success is determined by the sum of the individual probabilities, while in a multiplicative process, the overall probability is determined by the product of the individual probabilities. Although these are two ends of a continuum, and the classification depends on how you define the system and the level of granularity, it's a useful framework for conceptualizing goals and trade-offs.

Consider a bank robbery. For the heist to succeed, a series of crucial steps need to fall into place flawlessly: disabling security systems, cracking the vault, and making a clean getaway. If any step fails, the entire operation collapses. This is a multiplicative process, where the overall probability of success is the product of the probabilities of each step. Bank robberies are not for the ADHD personality; they're for the diligent and conscientious.

On the other hand, dating in the modern world with apps is more of an additive process. Your goal is to increase the number of first dates, and your success is determined by the sum of the individual probabilities of hitting it off on each date. As you go on more dates, your chances of finding a compatible partner increase, even if some dates have low probabilities of success. In this context, experimenting with a new opening line or profile picture is a low-risk move.

However, once you're in a relationship, maintaining that relationship becomes more multiplicative. For the relationship to thrive, you need to maintain attraction, communicate effectively, navigate conflicts, and support each other through life's challenges. If any one of these factors breaks down, the entire relationship is in jeopardy, as the success of the relationship depends on the product of the probabilities of each factor.

To further illustrate the implications of multiplicative processes, let's consider an example where numbers feel more natural. Let's say you are contemplating committing to an ambitious startup project with a binary payoff. If the project goes well, you'll make a lot of money. If it doesn't, you'll make nothing. You decide that unless you ascertain the probability of success to be >30%, you won't commit yourself to it.

For the project to succeed, you need to raise funding, hire engineers that can turn your idea into a product, and find product-market fit. Each of these consists of even smaller steps, each of which need to go right - a total of n steps. If any one of the steps, such as getting regulatory approval, is only 20% likely, this is already reason enough not to do the project, even if your probability of success on every other step is 99%. The higher the number of steps, n, the higher the bar for accuracy and performance on each step.

However, as a startup founder, if you treat everything you do as a multiplicative process, you'll likely fail. For example, a startup can't succeed without a high-functioning sales team. But if you're the head of sales or business development, it's probably time to get back to additive mode. One amazing salesperson can absolutely compensate for multiple lackluster sales people. Any one salesperson's underperformance is also unlikely to affect the performance of the others, given few dependencies. They all go after different clients and try to win independently. And they all get compensated for their own performance.

The more dependencies you add and the more cooperation you need, the more multiplicative things look. Specialization makes this more likely. This is why things look multiplicative at the firm level, where each department (eg.marketing) can't produce anything of value without other departments (eg. product/engineering). But within those teams, managers can make things less or more multiplicative. A product manager of a large company might have the resources to add engineers who add slack or redundancy to the system, such that things aren't quite so multiplicative. On the contrary, a product manager at a resource constrained startup might just need to make sure everyone is pulling their weight, either by focussing on management practices or hiring higher quality engineers.

Although multiplicative processes might seem more daunting, my guess is that we are hard-wired to underperform on additive processes. In organizations, people get punished for the chances they take, but the times they didn't swing for the fences remain invisible to the outside world. I suspect this has evolutionary roots and is closely related to the moral distinction we make between acts of commission and omission. This is true unless the incentives are strongly aligned, usually monetarily. If the employee is able to capture a significant proportion of the upside, that can, in theory, override the social cost of small failures.