Cost of Human Life

 

Seasons of Love

Five hundred, twenty-five thousand, six hundred minutes
Five hundred, twenty-five thousand moments so dear
Five hundred, twenty-five thousand, six hundred minutes
How do measure, measure a year?

If that question isn’t hard enough, How do you measure a Human Life?

How about Love? While that is a great, and musical, answer, it does not fit into an economist’s Cost-Benefit Analysis. In order to properly do such an analysis, such as computing the cost of the release of a ton of carbon, it is necessary to measure the value of the lives lost, deaths, as a result of that release. And deaths do result from the release of a ton of carbon. The problem is that cost varies depending on the country while the release of carbon causes world-wide deaths. The cost a life/death in the Untied States should not be 9 times the cost of a life/death in India or 55 times the cost of a life/death in Somalia. The problem is that these costs are computed on the lifetime earnings of a human, and those earnings,  the life expectancy, and number of earning years, varies from county to county. What would be desirable is to have a single cost for a human life regardless of country since those deaths may occur in an any country.

Rather than focusing on the earnings, which can be highly variable, perhaps it is wiser to focus on the consumption. The problem again is that the life expectancy varies, and the living standard varies from country to country. However, there is a world-wide poverty standard, which is the amount necessary to keep a human alive (e.g. food and housing). 

The World Bank places the extreme poverty rate at $2.15 per day in 2022 US Dollars. This equates to $784.75 per year. The Bible states that human life span, not life expectancy, is supposed to be four score, 80 years. People can live longer than this, but they can also die early than this. For this calculation, we need a life span, not a life expectancy. 80 years seems like a reasonable standard. This means that the minimum cost to maintain a human life is arguably $63,000. This also means that the difference in wages, earning years, or life expectancy in different countries has been ignored. $63K may seem too low to those of us in the United States, but that is from our frame of reference. That same $63K may be a fortune to a member of an indigenous tribe in the Amazon jungle.

Calculations done where the deaths are limited to a single county, for example seat belt laws, may apply different values for a life, but $63K is certainly better than assuming that a life elsewhere in the world has no value. That way there are no shithole countries, even if there are shithole people making that statement.

Social Security

 The Name Game

Come on everybody
I say now let's play a game
I betcha I can make a rhyme
Out of anybody's name
The first letter of the name
I treat it like it wasn't there
But a "B" or an "F"
Or an "M" will appear

The NAME is Social Security INSURANCE

Social Security (full disclosure, I am collecting Social Security. Hey, there have to be some perks to being 71) is an INSURANCE program.  An insurance program is NOT a Ponzi scheme. An insurance program is the OPPOSITE of risky behavior.  Payments into an insurance program cease being my money as soon as I make a payment. The fact that everyone with a wage pays into this insurance program does not make it any less of an insurance program. A payment from an insurance program is NOT an entitlement. The fact that the administrators of the program are the government does not make it any less of an insurance program.

Claim: Social Security is a Ponzi scheme.

A Ponzi scheme is one that collects money and makes payments, allegedly as interest, from the principal, in order to trick someone into believing that they are receiving interest. The payments into Social Security are made before you reach retirement age and the payments from Social Security are made after you reach retirement age. This is no different than any insurance. You make payments to an insurance company before a claim and receive payments from the insurance company after a claim. The fact that the payments into insurance happened before the claim, in the past, and the payments from insurance happened after the claim, in the future, does not make it a Ponzi scheme.

Finding: False.

Claim: The stock market has a better rate of return than Social Security.

The mean rate of return is not relevant here. The rate of return on an individual’s investment is what is relevant The average return on investment for the stock market might be 5%, but that might be one investor having a -5% rate of return and another investor having a 15% rate of return. In social security everyone has the same rate of return, so this is not a valid comparison. We don’t live in Lake Wobegon where all of the children are above average.

Finding: True, but irrelevant.

Claim: Money paid into Social security is your money.

Tell that to MetLife! Once you made a payment to Social Security Insurance, it ceased being YOUR money. If you die before retirement age, the payments are NOT part of your estate. The fact that the payments from Social Security are based on the payments you made into Social Security does not mean that while in the Social Security Trust Fund, it was your money. And besides, are the payments by employers into Social Security based on your wages, your money, or the employer’s money?

Finding: False

Claim: Social Security is a government program.

I love the sign “Government keep you hands off my Social Security." Uh…the government collects the payments, and the government pays the benefits. Is YOUR ”Social Security” the payments you made or the benefits that you receive.  Both are government actions, hands.

Social Security is a government operated INSURANCE program. The fact that is operated by the government does not make it NOT any less an INSURANCE program, I do not get Social Security. I get payments from Social Security Insurance. I might call it AMICA, but that is only its name, not what it is. AMICA never pretends that is not an insurance company.

Finding: True but it is a government INSURANCE program, NOT an entitlement.

The rINOs objecting to Social Security are “republicans In Name Only. They object to any government, including the constitutionally mandated Republic that is the United States. They seem to have forgotten the pledge we all make.  “I pledge allegiance to the flag of the United States of America and to the Republic for which it stands, one nation under God, indivisible, with liberty and justice for all."

Decisions

 

Cocaine Blues

Into the courtroom my trial began
Where I was judged by twelve honest men
Yes as the jury started walkin' out
I saw that little judge commence to look about

Why twelve honest men on the jury?

A jury is charged with making a finding of the truth. But we live in a random universe. So how certain can we be certain that the jury’s finding is indeed the truth? The scientific standard is 3 Sigma, 3σ. If the odds are 50%, True and False, then if the jury consisted of only 1 person, then a finding of Truth would only have a 50% chance of being certain, which is no better than the odds. If the jury consists of two persons, then the chances that both persons made a finding of truth is one out of four outcomes, which means that two people have a 75% percent certainty of being correct. To reach a scientific standard of certainty, it requires that 12 members make a finding. If all twelve members make a finding that the evidence is true, then there is a 99.976% certainty, while 3 Sigma is 99.97% certainty, that they are correct.

Might the jury still be certain but wrong? Remember the wisdom of Abraham Lincoln that “you can fool all of the people some of the time, and some of the people all of the time.” The evidence might have fooled the jurors such that at least one of their findings of truth should have been false. In statistics this would be called a false positive. It is also possible that any juror could have a bias such that a finding NOT in evidence affected their decision. For that reason even a 99.976% certainty does not mean that the jury might still be wrong. That is why findings of trial by jury should always be reversible.

Similarly, the scientific standard can be used to determine when a decision might have passed a lower standard, such a 1 Sigma, or the mean plus one Standard Deviation.  Decisions by a group are no more certain than the odds if no Standard Deviation is used. Most decisions do NOT require a decision by the whole group and thus a decision that is greater than the mean will be more timely. The group decision passes the 1 Sigma test for certainty only if it is by 68% percent of the group. It takes a group of at least three  to approximate such certainty. If the group has, for example, 435 members, but that group has only two parties, and decisions are on a party line, the certainty is only 50%, which is no better than the odds. Which is why the most important decisions affecting the group, such as declarations of war, require 2/3, approximately a certainty of 1 Sigma. It also means that decisions of say a Supreme Court of nine members should not be considered certain unless they are 6-3 decisions. Judges are bound by the same rules of math as are juries. What is good for the goose, is good for the gander.

Correlation is not Causation

 Taking a Chance on Love

Here I go again

I hear those trumpets blow again

All aglow again

Taking a chance on love

Are you considering chances, randomness, when you are doing regressions?

Statistician George Box famously said that all models are wrong, but some are useful. However if they are very wrong, but their regression has a good correlation, they may also be misleading.

Models are typically developed from regressions of observed data. That regression is generally linear but can also be non-linear. However regression, is only the process of developing coefficients that are validated against an assumption of the pattern in the data. A fundamental question which is often embedded in that regression is an assumption that the data is of a deterministic event which is being observed. This can lead to a regression of the data that is completely wrong although it appears highly correlated.

For example, a random event will produce a normal distribution of data. One such normal random distribution is the logistics distribution, also known as the hyperbolic secant squared distribution. If its range is 0.5, which it should be in a on/off, yes/no, heads/tails, distribution, then it should have average odds of 50%, i.e. 0.5.  This means that, no matter what the value is of the mean, the range, s, should be 0.5. This requires that the average value of the distribution be 0.5 and its Cumulative Distribution Function should vary between zero and 1 without repeating. The chart of this distribution, with a mean of zero, is shown in Figure 1.

Figure 1

As a random event, it does not repeat and is a plot of ½*sech²x. However, if the data was erroneously thought not to be random, and will repeat, the substitution of a traditional trigonometric cosine, for the hyperbolic secant, i.e. ½*cos²x, has almost the same shape as the logistics distribution function around a mean of 0, although it does repeat as shown in Figure 2..

Figure 2

If the data from the logistics distribution between -4.0 and 4.0, which is equivalent to random nonzero x data with a mean of 4, was used to fit to the equation a*cos²(x*b) using a non-linear regression, the amplitude of the cosine would be a= 0.33491 and the inverse of the period, b/2π, of the cosine would be, b=0.479546 as shown in Figure 3. This is a smaller amplitude and a longer period than the theoretical value of the repeating event. However the regression with the random data would be quite good, with a coefficient of determination of 0.784252 and a correlation coefficient of 0.88558. 

Figure 3

However, like the trigonometric deterministic function, the regression repeats, while the observed random data does not repeat. Care should be taken to examine the original premise of the data being random or deterministic. If the Cumulative Distribution Function, CDF, of the regression were shown, as it is in Figure 4, it would erroneously show that its value increases as the observation increases. It would also erroneously assume that at the mean, in this case zero, the CDF at the mean is 0%, not 50% as it should be. The regression of data only suggests the correlation within the range of the data. Caution should be used when making assumptions outside of the range of that data.

Figure 4

If the regression had been to the hyperbolic secant squared, a*sech²b*x, then the amplitude, a, would be ½, b would be 1, which is consistent with a period of 2πi which only repeats in the imaginary plane, the Coefficient of Determination would be 1 and the Correlation Coefficient would also be 1. A good correlation of the data with a deterministic equation, in this case almost 0.78, could mean that the data is actually random and will not repeat, even if the regression assumes that it will repeat.

 

Ties

 

Let’s Hear It For The Boy

Let's hear it for the boy
Let's give the boy a hand
Let's hear it for my baby
You know you gotta understand
Oh, maybe he's no Romeo
But he's my lovin' one-man show
Oh, whoa-oa-oa
Let's hear it for the boy

Let's hear it for the TIE!

In an elimination game, there is no such thing as a tie. That is why there is sudden death, extra innings, extra time, shoot outs, tie breakers, etc. In reality this is only because the regular contest ended in a tie. The result of any game is a win, a loss, or a tie (or a push for the sports bettors among you). A tie is NOT like kissing your sister. A tie is a legitimate and necessary outcome of every contest. The GAME, the Harvard-Yale Football Game of 1968, ended in a dramatic 29-29 tie, and the Harvard fans in attendance at the Harvard Bowl were jubilant, which  I hope was not how they would feel about kissing their sister.

If there was not the possibility of a tie, then there would never be be a game. In the group stage of the FIFA World Cup, a win is awarded 2 points, a tie is awarded 1 point and a loss is awarded no points. Life is a lot like that group stage. If there was not a reward for a tie, then why play? A win is only the result of a single contest. If you tie, also known as a draw, then you did something that is NOT losing.

Let's add win, loss, tie as among those trinities, a subject of previous blogs.

  https://dbeagan.blogspot.com/2023/01/interest_30.html, https://dbeagan.blogspot.com/2022/09/triads.html. 

Pretending that there are no ties, or that a tie is the same as a loss is arguably why the US is in the condition that it is currently. And maybe that is why soccer...er, fútbol, is the most popular team sport in the world, because it rewards and acknowledges a tie. Viva la tie! Don’t ever change.

Planning II

 

Who’s Afraid Of The Big Bad Wolf

Number three said nicks-on-tricks
"I will build my house with bricks."
He had no chance to sing and dance
'Cause work and play don't mix

And you wonder why there are engineering codes.

Practical Pig built his house of bricks perhaps because the Engineering Building Code considered that there might be the huffing and puffing of a Big Bad Wolf. It would be much cheaper, and less work, to build his house of hay or twigs like his Brother Pigs, but as the story goes, neither of those houses could withstand the blowing of the Big Bad Wolf

And this is why the bean counters at Southwest Airlines should be ashamed of themselves. They built their system to withstand normal operations, but it would fail when confronted with just a little bit of abnormal operations like a winter storm over a holiday season. The measures that might have anticipated and dealt with a winter storm over the holidays might have been more expensive, just like bricks, but eliminating those measures and pocketing those savings is like building your house out of hay or twigs.

Any operation that plans only for normal conditions is NOT an operation at all. Stuff happens. You better be able to deal with it.  Planning on being lucky is NOT a plan.

Planning

 

I Want To Be Happy

I'm a very ordinary man
Trying to work out life's happy plan
Doing unto others as I'd like to have them doing unto me

In life's happy  plan, are things random or deterministic?

By definition, a random number has two parameters: its location, μ, and its scale, σ. To define a deterministic number, the scale must be equal to zero, which is equivalent to saying that there is only one parameter, its location.

If the scale is non-zero, the system is random. If the scale is zero, the system is deterministic. Is the universe in which we exist random, or deterministic? By this it is meant the universe as a whole, not an object within that universe. The properties of an object within the universe can be deterministic even when the shape of the universe is random. The scientific standard for the properties of an object is 3 Sigma, 3σ, that is setting σ as close to zero as possible. This means that you are 99.7% certain that the location is the only value. In particle physics, an even more strict standard applies, 5 Sigma, 5σ. This means that you are 99.99994% certain that the location is the only value.

These percentages are due to the 68/95/99 rule of normal distributions. That is

·        68% of the observations are within 1 Standard Deviation, σ, of the mean, μ; that is μ ± σ,

·        95% of the observations are within 2 Standard Deviations, 2σ, of the mean, μ, that is μ ± 2σ,

·        99.7% of the observations are within 3 Standard Deviations, 3σ, of the mean, μ, that is μ ± 3σ.

There are distributions which have only one parameter. The most common of these is the Exponential Distribution. Its Probability Density Function, PDF, can be stated using a single parameter, λ, as

 λ*e^-λ*x for x>0 and x∈ R.

Its Cumulative Distribution Function, CDF, which is the integral of its PDF, is

1- e^-λ*x for x>0 and x∈ R.

Its mean is 1/λ. Its median is 1/λ.   Its variance, which is the square of the Standard Deviation, is 1/λ². Its skewness is 2. It does not meet the 68/95/99 requirement and is therefore not normal.

This can be translated on the x- axis from an origin of (0,0) to an origin of (μ,0). Then it has two parameters, λ and μ. Its PDF can be stated as y= λ*e^-λ*(x-μ) for x>μ and x∈ R. With these two parameters, the mean is μ+1/λ. Its median is μ+1/λ. But its variance remains 1/λ² and its skewness remains 2. And it still is not normal.

The Gaussian Normal Distribution also has two parameters, μ and σ. Its PDF is conventionally stated as

1/(σ√(2π)) e^{-½*((x-μ)/σ)} for x∈ R.

With these two parameters, the Gaussian Normal Distribution’s mean is μ. Its median is μ. Its variance, whose square is the Standard Deviation, is σ. Its skewness is 0.

The Exponential Distribution is often used in analyses where the location, µ, is known to be zero, for example, the average travel distance from the home in any direction. In this case the home is defined as at location = 0. Fitting the observations of the trip length with respect to the home to an Exponential Distribution gives the mean and median trip lengths.

However when the location is not zero, then an Exponential Distribution should not be used, for example, observations of the size of widgets that are being manufactured. In this case, you would like the observations to tell you the location and standard deviation of the observations and see if those meet the location and variance requirements for the size.

To combine the features of the exponential and random distributions, it has been proposed that there be an Exponentially Modified Gaussian distribution, EMG, which includes all three parameters, but the Probability Density Function and the Cumulative Distribution Function become very complex. The PDF is

λ/2 e^(λ/2 (2*μ+λ*σ^2-2x) ) erfc((μ+λ*σ^2-x)/(√2 *σ))

where erfc(x), the complementary error function, is 1-erf(x), or

(2/√π)* ∫_x^∞ e^(-(t^2) )

The Cumulative Distribution Function of the EMG, the EMG’s CDF, the integral of its PDF, is

Φ(x, μ, σ)-1/2 e^(λ/2 (2μ+λ*σ^2-2x) ) erfc((μ+λ* σ^2-x)/(√2* σ))

where Φ(x, μ, σ) is the is the CDF of a Gaussian distribution.

The mean of an EMG is μ+1/λ. Its median is the value of x at which the EMG’s CDF is 50%. The variance is σ²+1/λ². Its skewness is (2/(σ³λ³)) (1+1/(σ²λ²))^-3/2.  By inspection, the skewness takes on a value between 0.00 and 0.31.

The Gaussian Distribution is not the only Normal Distribution. The Logistics Distribution, also known as the Sech Squared, the square of the hyperbolic secant, Distribution, is a normal distribution which has a PDF of

(1/(4*s))* sech² ((x-μ)/(2*s))

where s is a scale parameter which is equal to √3/π *σ. Its CDF is

(1/2)+(1/2)*tanh((x-μ)/(2*s))

Its mean is μ. Its median is μ. Its variance is s²π²/3. Its skewness is zero.

The CDF of the Logistics Distribution is identical to a logit choice of 0 or 1 at a location of μ where the odds of making a choice of 1 are 50%. In this case the value of s is 0.5, 50%.

A doubling of the logit choice CDF is almost identical to the CDF of a translated exponential distribution. A Standard Normal Logit Choice Distribution is proposed to always have a
σ = √3/0.5π= .91 and have a PDF of sech²(√(√3/π) (x-μ)) for x>μ and x∈ R. This means that it has a CDF of tanh(√((√3)/0.5π) (x-μ)) for x>μ and x∈ R. 

The plot of an exponential association, which is the CDF a conventional exponential distribution, and, the CDF of a Standard Normal Logit Choice Distribution, where μ=0, is shown in Figure 1. The correlation between the two equations between x=0 and x=3 is 0.999. 

Figure 1 Exponential Association and  CDF of Standard Normal Logit Distribution

This suggests that the universe is random, and not deterministic, because the universe has a σ  = 0.91.