Dislocation Percent Calculation for Subjectively Ranked Entities

This is a way of measuring the degree of disorder of ranked items, which have perhaps no exact numerical proportionality but only values as, for example, of our behavior which may be considered as contrary to a set of values, or of items in a list.

Let's suppose there are ten things important to us, and we can rank them, for example recreational (non-prescription) psychoactively consumed substances. Let's suppose that society has certain attitudes or values about different chemicals, that are out of line with reality. We're just assuming this for the sake of the example, with rather artibraty assumptions about "reality" and "society".

Let's rank chocolate, tobacco, alcohol, cocaine, heroin, marijuana, eucalyptus, caffeine, LSD, and amphetamines with an economic measure, according to their cost in terms of personal time, property, and medical expenses, with 10 as the worst, and 1 as the least.

10- Tobacco-- over 300,000 die annually, 10 years early, and probably 10 times as many are paying medical expenses related to tobacco smoking, etc.
9- Alcohol-- Car accidents, loss of job productivity, alcohol related illness.
8- Chocolate-- Obesity, heart disease, diabetes, unwanted pregnancy, etc.
7- Cocaine
6- Amphetamines
5- Caffeine (both uppers cause driving accidents)
4- Heroin
3- Marijuana
2- LSD
1- Eucalyptus
Unwanted pregnancy!?
Now let's see how the public probably ranks these. I'll put the original numbers next to the items, for reference.

10- 7 Cocaine
9- 4 Heroin
8- 3 Marijuana
7- 6 Amphetamines
6- 2 LSD
5- 9 Alcohol
4- 10 Tobacco
3- 5 Caffeine
2- 8 Chocolate
1- 1 Eucalyptus

How out of order are the priorities in the second list? Let's think for a minute what that means. Consider the series of numbers from 1 to 10: 1 2 3 4 5 6 7 8 9 10. Now move one of those numbers forward, like move the number, 4, to between 7 and 8. Now the list is 1 2 3 5 6 7 4 8 9 10. How far out of order is this new list? Let's look at the movement of the number, 4, a step at a time.

1 2 3 4 5 6 7 8 9 10 starting position
1 2 3 5 4 6 7 8 9 10 one move
1 2 3 5 6 4 7 8 9 10 2nd move
1 2 3 5 6 7 4 8 9 10 3rd move

The 4 moved 3 times, so we say the list is out of order by 3. Again, let's consider moving the 1 all the way to the end of the starting list. It would go over the 2, the 3, the 4, and so on. It would pass 2, 3, 4, 5, 6, 7, 8, 9, and 10, to end up this way:

2 3 4 5 6 7 8 9 10 1

The "out of orderness of that list is 9. The 1 went past 9 other elements. Suppose it did that in the list of (1 2 3 5 6 7 4 8 9 10). Same thing; 9 moves. And the 4 moved 3 times, so in the list (2 3 5 6 7 4 8 9 10 1), the "out of order" measure is 9 plus 3, or 12. Can we tell by looking briefly at a list, how "out of order" it is, that is, how many elements were moved over? Yes, we can simply count the number of elements that are under other ones. Like in (2 3 5 6 7 4 8 9 10 1), 1 is above 9 items, and 4 is above 3; 9 + 3 = 12. How about this list: (10 9 8 7 6 5 4 3 2 1). 1 is above 9 items, 2 is above 8, and so on down to 9, which is above one item. The total is 9+8+7+6+5+4+3+2+1 = 45. It doesn't matter which element was moved first.

In (10 9 8 7 6 5 4 3 2 1), the list is simply upended, and the out-of-orderness is as much as it could possibly be, so the maximum for a list of 10 is 45. For 11, it would be 45+10=55; for 12, 55+11=66; for 13, 66+12=78, and so on. Let's take a look at the psychoactive list, now. The original numbers are re-ordered this way: (1 8 5 10 9 2 6 3 4 7).

7 is above 3 numbers (8, 10, and 9).
4 is above 5 numbers (8, 5, 10, 9, 6).
3 is above 5 numbers (8, 5, 10, 9, 6).
6 is above 3 numbers (8, 10, 9).
2 is above 4 number (8, 5, 10, 9).
9 is above 1 number (10).
10 is above 0 numbers.
5 is above 1 number (8).
8 is above 0 numbers.
-----------------------
Total = 22
Percentage dislocation = 22/45 = 49%

I like comparing various views people have about what are the worst "drugs," based on various measures, like economic cost, medical cost, family disruption and so on. The "dislocation percent calculation" provides an objective way of talking about such things. Furthermore, it can be used as a measure of discrepancy between someone's own avowed values, and one's behavior.

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