Ordering People
I’m currently going through a concerted period of personal development, and one of the steps in that process is to identify unhelpful patterns of thought and behavior in myself, and either decide that it’s there for a good reason, or else discard it. And at the risk of airing my inner jerkishness for all to see, I’ve decided to do this thinking in public. Maybe it will help others working through similar issues, or maybe it will just help me concretize my thoughts, but either way, here we are.
The topic I’m working through today is one that’s been in my head from a very early age, namely that some people are just better than others. What does that mean exactly? Well hopefully we can agree that one person can be more athletic than another, or more kind than another, or more intelligent than another. So suppose that two people are identical in every way, except that on one of these traits, say athleticism, person A has “more” of it (setting aside complicated discussions of learned vs innate ability) than person B. Then it makes sense to say that in some absolute sense person A is “better” than person B, unless for some reason you consider athleticism to be a bad thing. This idea that all people can be meaningfully ordered with respect to one another is known as a Total Ordering.
The Problem with Total Orderings
You may have noticed that there was a big assumption in the above example, namely that person A and person B were identical in all ways but one. Obviously for real people with real complicated personalities, they will be better in some ways, and worse in others.
As a very simple example, suppose now we have three people, A, B and C, and for each of them there are two traits we care about, intelligence and athleticism. Assigning each trait a score between 1 and 10, where 1 is “bad at this thing” and 10 is “awesome at this thing”, suppose they wound up as follows:
Then we would be able to say that Person A is “better” than Person B (since 6>4 and 10>7), and Person A is also “better” than Person C (since 6>5 and 10>4), but we would not be able to say one way or the other whether Person B is better or worse than Person C (4<5, but 7>4)! This situation wherein some things can be meaningfully compared but others can’t, is known as a Partial Ordering.
The Problem with Partial Orderings
In the above example things didn’t look too bad. Sure, we couldn’t directly compare Person B with Person C, but that’s not the end of the world, we can’t expect our mental models to be perfect. But actually the situation is much worse than this, because in reality people have a huge number of defining characteristics, not just 2. And if two people have N many characteristics, it means that the chance that they are comparable to one another is roughly 1/2^(N-1), which shrinks very quickly as N gets large:
That last row with N=100 is such a small probability that even if you were considering all humans on earth, the chance of any two of them being comparable is essentially zero.
So this approach of decomposing people into descriptive traits, and ranking those features against each other seems like a dead end, but what if we had a way of comparing different traits to one another? For example suppose we thought that being intelligent was 2x more important than being athletic, but only 0.5x more important than being kind? Then we could weigh all of the traits and add them up to get a single number, which would then not only give us a Partial Ordering, but would provide the Total Ordering that we wanted at the start! This is what’s known as computing a Weighted Sum.
The Problem with Weighted Sums
While it’s true that simply weighting traits and adding them up would solve the problem of not being able to compare people to one another, it leads to some very counter-intuitive results. For example, suppose that we had three people, A, B and C, each of them having scores for intelligence, athleticism, and kindness, and each of those traits having an associated weighting as given in the last section:
These are three very different types of people: Person A is a dumb scrawny Mother Teresa, Person B is your average Joe, and Person C is a genius Olympian who’d be happy to stab you in the back in a business deal. But despite these dramatic differences, our Weighted Sum considers all three of these people to be exactly the same, each receiving 42 goodness points. (For example for Person A: 2 x 2 + 1 x 2 + 4 x 9 = 4 + 2 + 36 = 42.)
Note that this doesn’t have anything to do with the specific weightings chosen here, it’s a feature of the overall approach: By mapping everyone onto a single continuum, it means that we can compare anyone to anyone else, including pairs of people who have no business being compared.
Clusterings, Restrictions, and Final Thoughts
There are two ways to salvage this weighted-sum notion of comparability, both having different but related issues:
- Only compare people to others who are similar to them. This is related to the idea of Clustering, where we group people with similar traits together. This sidesteps the issue of comparing radically different people to one another entirely.
- Consider only a restricted notion of “betterness” rather than a universal one. For example “who would be a better salesman” (Answer: genius Olympian), or “who would make a better romantic partner” (Answer: Mother Teresa).
In both of these cases we are slicing up our original goal of having a universal idea of “betterness”, either by considering only a limited group of people, or limited types of “betterness”. So in other words the only way to salvage our original idea of comparing everyone on everything is to either not compare everyone or not compare everything.
There are definitely other ways of thinking about these questions that I didn’t touch on, for example the way that distances blur together when the number of dimensions gets large, or the fact that aptitude in one area often correlates with aptitude in other areas, but I feel like this has been enough to drive home the conclusion in the subtitle: That people may be “better” than some of their peers, or “better” in certain aspects of their life, but once the group of people and set of considerations gets large enough, it doesn’t make sense to put anyone on a pedestal.
