First Principles
Sam Aurelius Milam III
Statistical Analysis
In
the field of statistical analysis, even the basics are complicated.
For example, here's a description of the second simplest idea in the entire
field, population standard deviation.
| For
a finite set of numbers, the standard deviation is found by taking the
square root of the average of the squared deviations of the values from
their average value.
—from Standard
deviation
Wikipedia |
The
Wikipedia
article includes a simple example calculation. For my purposes, the
most important thing to notice in that example is that the denominators
of the equations include the term n, where n represents the
size of the population being studied. Population size is fundamental
to statistical analyses but, for the purposes of this article, it's most
important when it's equal to one. Anybody who works through the example
calculation for a population of one, rather than for a population of eight,
as is shown in the example, will discover that, for a population of one,
the variance is zero and the population standard deviation is the square
root of zero. I think that might be what's called a trivial solution.
Whatever the terminology, the result isn't useful for statistical predictions.
It's
assumed, in the example, that the population represented in the calculation
is the entire existing population. If such a calculation is done
for a random sample, taken from a larger population, then Bessel's Correction
is applied. Bessel's Correction replaces n with (n
- 1). When n equals 1, then (n - 1) equals zero.
The mathematicians insist that division by zero is prohibited. So,
by the accepted mathematical conventions, with Bessel's Correction
reducing the denominator to zero, it isn't possible to calculate a sample
standard deviation for a population of one, whether or not it would be
statistically useful.
More
advanced statistical calculations use equations that can boggle the mind.
However, in any such analysis, the same thing is true. Whatever is
being calculated will include the term n or (n - 1), in the
denominator, somewhere in the calculation. When n equals 1,
the calculations are either useless or impossible. That circumstance
might not have a name, but I think of it as The First Principle of Statistical
Analysis. It tells us that it's impossible to statistically predict
the behavior of an individual.
The Principles of Liberty
The
Principles of Liberty are presented in detail in Pharos and
in The Sovereign's Library. The first of those seven principles
tells us that there isn't a cause of action until there's a victim.
Thus, a person cannot legitimately be punished merely because of something
that he might do, or that he's capable of doing. Punishment can be
legitimately administered only in response to actual harm, provably caused
by the actual behavior of an actual perpetrator. It isn't acceptable
to punish somebody based on mere speculation about something that he's
capable of doing, or that he might do.
Bad Policies
Many
bad policies exist in our society, mostly based on dogma and opinion, and
without much regard for such principles as those noted above. Individuals
are restricted, punished, or both, as a consequence of such policies.
The policies apply to individuals who haven't caused any harm at all, often
based entirely on some completely unsupportable statistical expectation
that they might do so. The best example of such bad policies, because
its consequences are so pervasive and so draconian, because the policy
has been so mindlessly embraced, and because any opposition to it provokes
such instant and vehement denunciations, is the punishment of drunk drivers.
Statistical
analysis can provide an estimate of the probability of alcohol related
accidents within a population of drunk drivers. The larger the population,
the more confidence there will be in the estimate. The smaller the
population, the less confidence there will be in the estimate. When
the population size is one, then it isn't possible to make an estimate
at
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