Genius is (mostly) comparative

by Amir Bolous4 min read5th Jan 20213 comments

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Introduction

Some of the best advice I've received has been to turn short-term games into long-term games. In the past, I interpreted this as prioritize actions that further long-term goals over those that generate short-term rewards. After digging a bit deeper and thinking at a different level of abstraction, I now see this piece of advice in a different dimension.

I think that the core principal behind this piece of advice is that we are very bad at grasping the effect of compounding. From a young age, we are told that "we get out what we put in."

I think that while this is close to the truth, the quote would be better amended to "we get out what we put in scaled by some multiplier."

If Mozart and I spent 30 minutes composing a new piece of music, I'm sure that our final work would end up looking very different. The unfortunate byproduct of this is that we attribute what we currently see (in terms of progress, results, success, etc.) to absolute advantage over comparative advantage.

So jargon aside, what does that mean? Let's look at the conical example of comparative vs. absolute advantage in Economics.

Comparative vs. Absolute Advantage in Economics

Jane and Toby are two friends who just moved in together. Naturally, they want to minimize the amount of time spent on chores in order to maximize their amount of free time (constrained by each person's time being equally valuable). There are two main chores that need to be completed: cleaning the dishes and doing the washing. They want to figure out how best to split these two tasks so they decide to collect some initial data independently.

Cleaning Dishes

  • Jane: 10 minutes to clean 5 dishes (rate of 0.5 dishes/min)
  • Toby: 10 minutes to clean 2 dishes (rate of 0.2 dishes/min)

Doing the Washing

  • Jane: 10 minutes to wash 2 shirts (rate of 0.2 shirts/min)
  • Toby: 10 minutes to wash 1 shirt (rate of 0.1 shirts/min)

At first glance, we see that Jane is more efficient than Toby at completing both chores, so maybe Jane should do both chores to minimize the time spent on chores? Although this idea in principle may seem to work, Jane and Toby know that time is a scarce resource. This means that while Jane could complete more chores than Toby in the same amount of time , this is not the best allocation of time and resources. Let's try to understand why by looking at opportunity cost. Opportunity cost is defined as the best possible alternative we sacrifice as a result of our current decisions.

What does that mean in the context of chores? It means that when Jane decides to clean 1 dish, the opportunity cost is 0.4 washed shirts. This is because 1 clean dish costs 2 minutes of time (think of time as a currency here) and 1 shirt costs 5 minutes. So 2 minutes that could have been spent washing shirts would produce "2/5 or 0.4 shirts" Equipped with this in hand, let's determine the opportunity cost for each task and individual

Cleaning Dishes

  • Jane: Opportunity cost of 1 clean dish = 0.4 clean shirts
  • Toby: Opportunity cost of 1 clean dish = 0.5 clean shirts

Doing the Washing

  • Jane: Opportunity cost of 1 clean shirt = 2.5 clean dishes
  • Toby: Opportunity cost of 1 clean shirt = 2 clean dishes

When we reformulate our data in terms of opportunity cost, an interesting trend emerges. Although Jane is more efficient at doing the washing, Toby has a lower opportunity cost for doing this task. Since only 2 clean dishes are sacrificed (instead of 2.5) at the expense of 1 clean shirt, it makes sense for Toby to allocate his time to complete this task. For cleaning the dishes, the opposite is true, Jane has a lower opportunity cost, so it makes sense for Jane to clean the dishes.

Long-story short, even though Jane is able to complete both tasks more efficiently (i.e. she has an absolute advantage in both tasks), having her do so would be an non-optimal allocation of resources. Intuitively this makes sense, if they pool their resources, they can pursue two tasks independently at the same time and make some headway in each one.

What's incredibly cool about this is that by this definition, everyone will have some comparative advantage. Absolute advantage is what we already have in the bank which will be different for each person, comparative advantage however is what we turn that into.

Generalizing Comparative and Absolute Advantage

In the real-world, we often mistake comparative advantage for absolute advantage. I recall two notable memories when I did just that in grade school.

  1. When I was young, although I enjoyed maths, I was never by far the best mathematician. In class, my friend Jacob would often solve the problems in half the time it took me to read the question. After this kept happening again and again, I settled for the only explanation that would not hurt my ego: he must just be naturally better at maths.
  2. In high school, one of my favorite classes was P.E. We would circle through a couple of different sports every couple of weeks to try a taste of everything. Regardless of what sport we were playing, my buddy Max always seemed to crush the competition. Eventually, when we started playing Badminton, my other friend - Dave - got really excited. He'd been practising Badminton for the last two weeks and was ready to show Max off - as you can imagine this never happened. Again, the most reasonable conclusion was that Max was just genetically a better athlete.

In both instances, I assumed that Jacob and Max got to where they are now because of absolute advantages. I attributed what I currently saw to some inherent advantage as opposed to one that had been compounded over time. Of course, absolute advantage has a play here; maybe Jacob was born more naturally intelligent, or Max a better athlete. But a person's skill progression or knowledge accumulated is not solely because of these advantages. In most instances, this is fostered with hard work and perseverance. What may begin as an absolute advantage is compounded with time and effort, increasing the output (and the bit I had critically not realized in the past) per unit input.

This same idea can be extended to all aspects of our lives we term extraordinary. Why do some people "naturally" pick up concepts in maths more quickly? Why are some people more "intrinsically" artistic than others? Why do some people "trust their guts" to make good investment choices? People don't lie when they say the secret is practice, hard work, and mentorship. These systems work because of compounding accumulated knowledge and experience. Playing long-term games is thus, about compounding our work to increase our multiplier and turn an absolute advantage (where we start) into a comparative one (where we end up).

Closing Thoughts

I find myself falling into this trap most often at the highest level of accomplishments: the Feynmans, Bolts, and Musks of the world must have accomplished what they did because of absolute advantages. It's easy to attribute accomplishments that seem out of our reach to factors beyond our control. It's much harder to acknowledge that if we put in the work, we can also stand on the shoulders of giants.

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3 comments, sorted by Highlighting new comments since Today at 8:38 AM
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Hi Amir, I believe we have two different topics here. Comparative advantage in traditional sense only cares about what is good choice right now; it does not include the considerations of future growth in skills. It kinda says, if you are 3× worse at X but only 2× worse at Y, don't despair; you should produce Y and trade it for X, and this will be beneficial to both sides.

Actually, the considerations of future growth can be used as an argument against following the comparative advantage blindly. Like, maybe the reason why others are so much better at X than at Y is because "Y doesn't have a future". Perhaps practicing X improves your X skills significantly, but practicing Y doesn't improve your Y skills at all. (X = technology, when you do it, you invent new methods, build new machines, train your employees; Y = agriculture, doing the same thing over and over again; of course this is oversimplification.) In which case perhaps you should sacrifice the short-term gains from possible trade and keep doing X anyway, until you level up enough that X becomes your comparative advantage.

But the full analysis would be quite complicated here, because we would need to know the learning curves for X and Y, your optimal strategy would depend on what other players would do... and if we are assuming a dynamic world, who knows, tomorrow a new Z might enter the game and completely change the situation. (Like, if the reason for your disadvantage is simply lack of practice, e.g. you are younger than other players, it might make sense for you to immediately switch to the new Z where everyone starts from zero.)

I wish I had some simple personal example of "not using comparative advantage because of strategic considerations", but nothing specific comes to my mind right now.

Hey Tristan, thanks for the feedback! What you're saying is right of course, to clarify, I meant minimize the time spent on chores constrained by each person's time being equally valuable. I'll clarify this in the post but I'm not trying to present comparative advantage from an optimization standpoint as far as trying to draw an allegory between the [comparative vs. absolute] dichotomy and the [learned skill vs. innate advantage]. Hope that makes sense!

I believe that you have misunderstood the concept of comparative advantage.

At first glance, we see that Jane is more efficient than Toby at completing both chores, so maybe Jane should do both chores to minimize the time spent on chores? Although this idea in principle may seem to work, Jane and Toby know that time is a scarce resource.

If the goal of both parties is to minimize the total time spent on chores, having Jane do all the chores is the ideal solution. Each person working to their comparative advantage only makes sense if the two parties are, in some sense, trading chores to maximize their own gain, but unwilling to make one-sided sacrifices for the other.

This is why the principle of comparative advantage is so prevalent in free-market economics, where all parties are assumed to be trading for mutual gain. But the concept doesn't really make sense as a global utility optimizer.