Talk:Pareto principle

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This really needs an example.

Contents 1 Proper Quote? Cite? 2 Explanation 3 Recursion 4 Examples of misuse 5 Software engineering

[edit] Proper Quote? Cite?

This page states "It was named after the Italian economist Vilfredo Pareto, who observed that 80% of income in Italy was received by 20% of the Italian population."

The Vilfredo Pareto page states "In 1906 he made the famous observation that twenty percent of the population owned eighty percent of the property in Italy, later generalised by Joseph M. Juran and others into the so-called Pareto principle (also termed the 80-20 rule) and generalised further to the concept of a Pareto distribution."

So which is it, income or property?

[edit] Explanation

I don't know much about business, but I think the examples of misuse need brief explanations. It's not clear to me at all that the application to employees is either untestable or useless to the firm (if those are the reasons it's a misuse), and I also don't understand why the application to advertising is useless. —JerryFriedman 19:41, 24 Jan 2005 (UTC)

For the benefit of the many, let's elaborate on "A clear misuse of Juran's assumption (...)":

In manufacturing, systems are designed so that everybody contributes a pre-defined amount of work, especially in synchronous settings such as assembly lines. Nobody could argue for applying the Pareto principle there.

In agriculture and mining, individual contributions are sometimes measurable (e.g. baskets of apples picked per shift). A for-profit organization seeks out the better workers, so the bottom part of the distribution is not be represented at all. Family and community operations often find a way to gainfully employ persons with less strength (e.g. 11-year-old girls) or with disabilities (e.g. blind people), but their number is not large enough to warrant a Pareto distribution.

Which brings us to the only economic system many readers have experience of: The services sector.

There is a place for "stars" in fields like moviemaking and advertising. In these fields, moneymaking ability is often modeled as 80:20, and even as 90:10 or 99:1 (think of the distribution of pay for fashion models).

In other service areas, such as software development, it has been argued (and many influential minds such as Frederick Brooks and Joel Spolsky have devised methods for measuring and quantifying this) that a top designer, programmer, or QA person is roughly ten times as effective as an average one.

It can be argued that this observation does not carry to other areas of computing such as system administration.

Finally, the difference between top waiters (or shoe salespeople, mail delivery people...) and average ones may not warrant Pareto analysis at all.

elpincha 00:41, 4 Feb 2005 (UTC)

[edit] Recursion

O.K. I may be missing something here but the examples of how the set is recursive don't seem consistent to me. The idea of a 64:4 rule makes sense in a linear fashion (80 - 16):(20 - 16) but that doesn't seem to pan with a 51.2:0.8 rule. The 64:4 rule also seems to suggest that the remaining top 16% of the work accounts for the remaining top 16% of the output which is inconsistent with this principle. It seems to me that a 40:10 rule (10% of effort yields 40% of results) would make more sense (80/2):(40/2) (or 80/n:20/n)

The Pareto principle is *not* a ratio and can not be reliably manipulated as though it were a ratio to produce equivalent formulations. To avoid the "ratio" analogy, I'll make up a new operator ":::" to represent the Pareto principle. If J is the consequences percentage and K is the causes percentage, and J:::K is the Pareto principle stating "J of the consequences stem from K of the causes", then J:::K does not necessarily imply that (J-16):::(K-16), nor does it imply that (J/n):::(K/n).

However, it is claimed that the Pareto principle can be reduced recursively.

Let f(X, N) = (X/100)*f(X, N-1), for N > 1; f(X, 1) = X.

J:::K implies f(J,N):::f(K,N), for N >= 1.

Also the principle can be "expanded".

Let g(X, N) = ((100 - g(X, N-1)) * (X/100))+g(X, N-1) for N > 1; g(X, N) = X.

J:::K implies g(J, N):::g(K, N).

Using 80:::20: 80% of the 80% of consequences stem from 20% of 20% of the causes. This multiplies out as 80% * 80% consequences from 20% * 20% causes, which gives 64% of the consequences from 4% of the causes.

We can express this reduction using the recursion function 'f(X, N)' for "reduction" given above where X is 80 and the reduction step N is 2:

f(80, 2):::f(20, 2)

= [(80/100)*f(80,1):::(20/100)*f(20,1)]

= [0.8 * 80 ::: 0.2 * 20]

= 64:::4.

The next recursive step is: f(80, 3):::f(20, 3)

= [(80/100)*f(80,2):::(20/100)*f(20,2)]

= [0.8*64:::0.2*4]

= 51.2:::0.8.

The "expansion" of the 80:::20 rule is:

g(80, 2):::g(20, 2)

= [((100 - g(80, 1)) * (80/100)) + g(80, 1):::((100 - g(20, 1)) * (20/100)) + g(20, 1)]

= [((100 - 80) * 0.8 + 80:::((100 - 20) * 0.2 + 20]

= 96:::36.

Expanding again: g(80, 3):::g(20, 3)

= [((100 - g(80, 2)) * (80/100)) + g(80, 2):::((100 - g(20, 2)) * (20/100)) + g(20, 2)]

= [((100 - 96) * 0.8) + 96:::((100 - 36) * 0.2) + 36]

= 99.2:::48.8.

68.100.145.9 16:20, 21 November 2005 (UTC)

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I added some explanations on this recursion thing to the article. They'd help me to understand it; I don't know about others... But without some sort of explanation, I believe the paragraph should be removed entirely from the article.--Niels Ø 15:52, 15 February 2006 (UTC)

And then I thought some more about it, and removed the paragraph entirely. It appears to be unreferenced, perhaps original research, and I don't think it's "true" in the same sense the 80-20 rule as such is true, viz. (1) that it is often cited in various situations, (2) it is actually not far from being correct in many of those cases, and (3) even when it is far from being accurate, it may point to a fact that needs to be taken into consideration. Here's what I removed (ncluding my own attempts to explain):

The principle can be viewed as recursive, and may be applied not only to the top 20% of causes; thus there would be a "64-4" rule (64% of the consequences stem from 4% of the causes), and a "51.2-0.8" rule, and so on (80% = 4/5 or four fifths, 64% = (4/5)² or four fifths of four fifths, 51.2% = (4/5)³; 20% = 1/5, 4% = (1/5)², 0.8% = (1/5)³). In the opposite direction, Tipton Cole has observed that the Pareto Principle applies to the residue of its first application, yielding a "96-36" rule. If 20% of the causes are responsible for 80% of the consequences, the other 80% of the causes are only responsible for the remaining 20% of the consequences. Applying the principle recursively, the 64% least consequential causes are responsible for only 4% of the consequences, and hence the 36% most consequential causes are responsible for 96% of the causes.

Among my reasons to discard it is the following figure, where I think the curve found by the recursive principle is just too weird-looking. (The other curve is a hyperbola fitted through (0,0), (80%,20%), and (100%,100%) - it may not be a lot more "correct" in any particular situation, but at least it looks less strange.)

--Niels Ø 13:31, 16 February 2006 (UTC)

And then Michael Hardy re-added a brief version of it. It seems that it's OK one way (64-4 rule), but perhaps not the other way (96-36 rule).--Niels Ø 19:57, 18 February 2006 (UTC)

[edit] Examples of misuse

Is there a reason to remove the examples of "misuse"? If not, I'll re-add them. Mnbf9rca 01:29, 18 February 2006 (UTC)

[edit] Software engineering

I think this section is correctly to be stated, "The first 90% of the code accounts for the first 90% of the development time. The remaining 10% of the code accounts for the other 90% of the development time" - see [90-90_Rule] 198.49.180.40 22:11, 13 November 2006 (UTC)