Erik Bernhardsson    About

The mathematical principles of management

I’ve read about 100 management books by now but if there’s something that always bothered me it’s the lack of first principles thinking. Basically it’s a ton of heuristics. And heuristics are great, but when you present heuristics as true objectives, it kind of clouds the underlying objectives (and you end up with weird proxy cults like the Agile movement :japanese_ogre: — not that I disagree with it, I just wish they could derive it from a more systematic understanding of project management).

The other thing you need is a model of reality. I have an almost dogmatic belief that there is a mathematical model describing everything. Doesn’t mean that your model is correct of course. And I’m not super interested in the actual math here — more the dynamics. But there’s a set of models, each more and more complex, that describe reality more and more accurately. And I don’t mean it in a naïve, everything-is-math kind of way. I totally believe that humans are irrational, and all that stuff. But there’s some stuff that can be predicted, and the uncertainty can usually be predicted too, as well as human irrationality/psychology, market behavior, and many other things.

Anyway, my book would be structured roughly in order of these models, adding more and more detail to how reality functions and how to make optimal business decisions. I think of it as layers of an onion — every layer is an extension of the previous model where we add more and more complexity.


I even designed a cover! This is going to sell like god knows what.

I’m planning to publish it about 2040, once I’ve mastered all the pieces. No, but seriously, I would love to read a book like this. I’m still fairly new to the game so here are just some very rough sketch of what I want the topics to be like. If a book could write about management in this way, I’d pre-order 100 copies in a heartbeat.

  1. Decision making with perfect information
    • This is the most basic case of decision making and easiest to model
    • An example here: what’s the breakeven time if we upgrade our widget making machine for $100,000 so that it can make 1,000 more widgets per day?
    • Some of the key concepts in this chapter are:
      • ROI (return on investment) and how to prioritize across different projects
      • Diminishing return as a function of investment (concavity)
      • Marginal ROI vs average
      • Price sensitivity
      • How to allocate time across several different projects, thinking about it as a constrained optimization problem (Lagrange multipliers and the principle of optimizing striving for equal marginal ROI)
      • Opportunity cost (example: why almost all ideas are bad once you factor in the opportunity cost)
      • Pipeline/constraint thinking (all the Toyota stuff & Theory of Constraints goes here, as well as the “Lean” and “Agile” movements).
  2. Decision making given uncertainty
    • This is our first extension of the most basic model and it’s already getting a bit trickier
    • Topics:
      • Prior beliefs and Bayes’ rule (example: why common sense and experience is a great prior)
      • Explore vs exploit (side topic: Thompson sampling)
      • Rapid iteration vs long term planning (case study: hardware vs software development)
      • Proxy metrics (optimizing for shareholder value is hard, so let’s pick some metric that’s easier to measure/move but still has a high correlation)
      • A/B testing
      • “Known unknowns vs unknown unknowns”
  3. People management — agency problems
    • This is the first part of managing people — how do you deal with the fact that their needs are not always aligned with the company? I have a feeling a look through history could be quite useful
    • Topics (by no means exhaustive!):
      • Marxism and the theory that history is a struggle between employers and employees
      • Taylorism and the first wave of “Scientific Management”.
      • Why do startups have free lunches and ping pong tables and hedge funds don’t? (This is a theory I have — has to do with the fact that performance is a lot harder to measure at startups.)
      • Why do mediocre managers prefer long term projects?
      • Why a culture of instilling risk aversity hurts company performance? (Punishing managers disproportionally for making mistakes means risks are not taken, even when the expected value is positive.)
      • How performance bonus incentivizes risk taking? (This is sort of the opposite of the above point)
      • Why it’s so hard for companies to change? (Because managers have a vested interest in status quo (and are only looking for Pareto improvements))
  4. People management — information asymmetry
    • The second part of managing people analyzes another reason why people make poor decisions — it’s because they didn’t have full information. This happens more at big companies
    • There’s probably some really interesting stories from military tactics here. Leading troops under battle pushes decision making to its extremes and forces incredible dentralization of power. I suspect this is one of the better analogies for how to think about information asymmetry from the bottom to the top — i.e. you need to trust the grass roots to run autonomously.
    • A much more boring (but still important) topic is how to run an efficient meeting culture. Meetings (and emails etc) are the way humans tranfer information between each other and it has terrible bandwidth. Think about it as a 1,000 person company where each person is a modem that can do like 30 baud. How do you organize to propagate information the fastest from top to bottom (and then back up?)
    • Topics: TBA (because this is an area where my skills lack. I told you this book would be published in 2040!)
  5. People management — bounded rationality
    • Here we’re starting to get into behavioral economics. This is fun. This as the remaining piece that explains why managers make suboptimal decisions — they are not acting like rational economical agents.
    • It’s also psychology, of course. How to trick inspire people into doing things. Why people disagree. How to get people to change. And all that stuff.
    • Topics: TBA. I also haven’t structured my thoughts on this — will get back to you in 10-20 years with some more ideas. But basically it’s all the Kahneman/Tversky/Thaler stuff — Wikipedia’s List of cognitive biases but more fun.
  6. Operating in a market
    • The competitive advantage angle is basically Michael Porter stuff but I find his books excruciatingly boring and so let’s talk about it in other terms. I think there are really good stories to illustrate how this works (side note but this book is pretty good: Co-opetition).
    • I also think an understated market is the market of people aka recruiting. So some of the more nuanced points of hiring top performance would end up here.
    • Topics:
      • Moats: network effects (Metcalfe’s law), scale advantages, proprietary technology, regulatory capture, etc.
      • Collusion and defection
      • Other competitive advantages: brand
      • Suppliers and wholesale transfer pricing
      • Induced demand
      • First mover advantage
      • Case studies: TBA (but I want LOTS of them here! fun war stories! YAY!)

Please pre-order my book! It will be delivered straight into your brain around the year 2040 by Amazon’s brain implant chip.



Erik Bernhardsson

... is the CTO at Better, which is a startup changing how mortgages are done. I write a lot of code, some of which ends up being open sourced, such as Luigi and Annoy. I also co-organize NYC Machine Learning meetup. You can follow me on Twitter or see some more facts about me.