Tuesday, April 6, 2021

Published April 06, 2021 by with 0 comment

Thinking in terms of probabilities

We suck at probability. A common trap we fall into is failing to realize this and thinking in terms of absolutes.
What's an example of this? One I've encountered many times is something like 'if you work hard you can stop being poor' or 'everyone decides their own wealth'. Is this true? This is what I mean...there is no absolute yes or no answer. Consider the following plot (source data):



The following statements are all true:
  • some kids from the poorest households end up wealthy
  • some kids from the wealthiest households end up poor
  • most poor kids stay poor
  • most rich kids stay rich
  • parental wealth is a good predictor of your wealth as an adult
Many people will see someone claim that last bullet and jump to 'what about this guy that grew up poor and made it?' The plot clearly shows that's possible and doesn't negate the last bullet. Thinking in terms of what's likely is a better model for this.

Another common example is the classic 'it's cold today so global warming isn't real'. If you don't think of the distributions of temperatures, this is an easy fallacy to fall victim to. Here are two plots of temperature distributions for Denver, Colorado summer highs in 1900 and 2000 (respectively):






There are clearly cold (for summer) days in both. There is also a clear shift towards higher temperatures in 2000 vs 1900. That 'the distribution has shifted towards higher temperatures' is the best mental model for global warming in my opinion. If you want to see more of these I pulled them from this page.

This could go on forever but I hope the general idea is clear. Many things are distribution-based and can be understood much more easily if thought of in terms of 'how does this distribution shift/compare?'

If you're interested in a great book on this general topic, I liked 'The Drunkard's Walk'.


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