0

I have seen comments on the web that because the 80/20 rule is fractal, it applies to the sub groups. In other words, if the top 20% of causes drive 80% of outcomes, then the top 4% of causes must drive 64% of outcomes, etc.

Can that be extended both ways? If the top 20% of causes drive 80% of outcomes, then the bottom 80% of causes drive 20% of outcomes. Extending that, you'll get the top 36% of causes driving 96% of outcomes.

This wikipedia discussion describes it; but the resulting plot (red line here) doesn't look smooth.

I have to admit I don't understand the mathematics, so I would appreciate an intuitive explanation for why it does/doesn't make sense to extend the 80/20 rule this way.

Guest
  • 87

2 Answers2

1

The red line to which you link (like all descriptions of datasets) is only approximate and so maybe you should be more tolerant of imperfect estimation.

That said, I think the claimed 'fractal nature' of the 80/20 rule may be based more on a hypothetical probability model than on reality, especially if you're trying to use it for the 'top 4%'. 'Fractal nature' may be a concept worth contemplating casually, but not necessarily embracing seriously.

A large and reliable dataset for the top 4% of any strongly right-skewed population must be pretty hard to find.

  • I have often had to caution clients and students that "exponential trends do not continue." Put another way, for practical purposes, the far right tail of supposedly exponential data may not be worth detailed scrutiny.

  • I'd say this caution applies even more appropriately to far right tails of supposedly Pareto data.

BruceET
  • 56,185
  • Thank you Bruce. From what you said, it sounds like we shouldn't try applying the Pareto heuristic recursively i.e. 80 / 20 --> 64 / 4 --> 51.2 / 0.8 because it's probably not meaningful. I'm trying to get a sense for the principle behind why it isn't meaningful. Does it have to do with the non-random nature of the sub-samples, so the Pareto distribution based on an assumption of random sampling wouldn't hold? Or does it have to do with insufficient N, where at a 4% sub-group, there's too much variability around the 64% to make it mean anything? – Guest Dec 18 '20 at 21:51
  • It has to do with the approximate modeling of real-life data, useful for some purposes, not necessarily for all. // For example, in many applications it is OK to model test scores, people's heights, etc. as normal--even though all normal distributions put some probability below $0.$ Even with a sample size of several billion you won't find anyone with a negative height. // Use the model when it works, but beware that it might not always apply. – BruceET Dec 18 '20 at 22:30
1

The 80/20 rule is a catchy slogan, commonly repeated in many places, but do not take it literally. There are examples where it holds, there are also many counterexamples where the numbers are not exactly this. In Wikipedia, and other sources, you can easily find multiple examples where the numbers are not exactly 80/20, e.g. the 1% rule. The TL;DR about the rule is that for many phenomena, the majority of outcomes is generated by the minority of events, but the actual numbers would vary on case-by-case basis.

Tim
  • 138,066
  • Thanks Tim, I follow that the specific 80 / 20 figures aren't definitive i.e. it could be 90 / 20, or 80 / 10. I'm just curious, for a given heuristic (taking 80 / 20 as an example), is there a general principle that would/wouldn't support extending the heuristic backwards and forwards i.e. 80 / 20 becomes 64 / 4 and 51.2 / 0.8 in one direction, and 96 / 36 and 99.2 / 48.8 in the other direction? – Guest Dec 18 '20 at 21:55