The Social Security Administration provides an online “actuarial table,” that is, a death chart, listing the fraction of males and females at each age that are expected to die in one year from all causes. For instance, according to the table, a fraction of .014326 of all 63-year-old males in the U.S., or just over 1.4%, will die within one year. Each age and each sex annually face different dice of life.
The table makes possible a rough estimate of the chance that one or more of the five reactionary Supreme Court Justices, namely Scalia, Kennedy, Thomas, Roberts, and Alito, will die within five years, by the end of Obama’s last summer in office, provided Obama is reelected.
Here I will ruin a perfectly good long chain of probability/statistical calculations and reveal the ending up front: 50.7%. Let that sink in a moment, all those contemplating sitting home or voting third party in November 2012.
Pass below the orange squiggle of fate for the gory details and concluding remarks. Beware, the details get a bit geeky. Skip to the remarks if math makes you dizzy.
Gory details.
So, if a 63-year old male has a probability of .014326 of dying in the coming year, he has a probability of (1 - .014326) of surviving the year. If and when the man turns 64, he faces new dice for the ensuing year. The probability that a 64-year-old male dies within a year is .015453.
For our 63-year-old male, however, the event that he will die at age 64 occurs only if (a) he survives the first year and (b) dies in the second. The probability is calculated as:
(prob of surviving 1 year at age 63) × (prob of dying within 1 year at age 64).
Likewise, the probability that the 63-year-old male dies at age 65 is:
(prob of surviving 1 year at age 63) × (prob of surviving 1 year at age 64) × (prob of dying within 1 year at age 65).
See the pattern? The respective probabilities that our 63-year-old male will die at age 63, 64, 65, 66, and 67 are ( “P( )” below means the probability of the event in the parentheses)
P(die at age 63)
P(survive age 63)P(die at age 64)
P(survive age 63)P(survive age 64)P(die at age 65)
P(survive age 63)P(survive age 64)P(survive age 65)P(die at age 66)
P(survive age 63)P(survive age 64)P(survive age 65)P(survive age 66)P(die at age 67)
The event that our 63-year-old male dies within the next five years (dies before age 68) is the union of the above events, that is, he dies at age 63, or 64, or 65, or 66, or 67. The probability that the 63-year-old male dies within five years is then the sum of the above individual year death probabilities. Using the actuarial table table entries gives that probability for our 63-year-old male to be just under .082, or 8.2%.
Thomas is 63. Scalia and Kennedy are both 75. Alito is 61. Roberts is a youthful 56. All in all, the gang is a rather youthful bunch who, taken individually, can be expected to put in many more years on the bench.
It is collectively where the laws of probability build up. The crucial question is what is the probability that Obama will get the chance to replace one of these SC justices? This event would happen if one or more of them die within 5 years.
Say we sum up those above 5 yearly probabilities for Thomas and get a number, call it rT , representing the probability that Thomas dies within 5 years. That was calculated as rT = .082 above. His chance of surviving 5 years is then 1 - rT . Likewise tally up the five yearly probabilities for Scalia, Roberts, Kennedy, and Alito to get their 5-year death probabilities; let’s call them rS , rR , rK , rA.
The probability that all of them survive 5 years is the product of their individual 5-year survival probabilities:
(1 - rT )(1 - rS )(1 - rR )(1 - rK )(1 - rA ).
And finally, the probability that one or more of them die within 5 years is found simply by subtracting the above probability from 1:
1 – [(1 - rT )(1 - rS )(1 - rR )(1 - rK )(1 - rA )] .
The calculations are a piece of cake in “R”, a free and amazing computer program for scientific calculations and graphing. The script (list of calculation commands) for doing the calculations in R is pasted below. If you have installed R on your machine, just copy the script and paste it in R at the command prompt. The quantity .507 will appear at the end, representing the probability that one or more of those justices will have to be replaced in the coming 5 years due to death.
(If you have some interest in trying out R, you will find mountains of tutorial and documentation websites to help you get started. Used at its simplest level, R is a fantastically powerful and easy to use graphing calculator, which could and should replace those awkward-to-use, expensive handheld graphing calculators in high school science and math classes. I will diary on that notion someday. Numerous courses at the college level are already using R. R use has snowballed in the scientific world and is catching on in the corporate world.)
The R script of Supreme Court fate:
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# R script to calculate the probability that one
# or more of the 5 reactionary Supreme Court justices
# will die within 5 years (that is, by the last
# summer of Obama's second term of office).
#
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#----------------------------------------------------------------
# Yearly age-specific death probabilities during the next 5 years
# entered into vectors.
# Thomas, age 63; Scalia, age 75; Roberts, age 56;
# Kennedy, age 75; Alito, age 61.
# Data from Social Security Administration actuarial table (2007).
# http://www.ssa.gov/...
#----------------------------------------------------------------
prob.Thomas=c(.014326,.015453,.016723,.018154,.019732)
prob.Scalia=c(.040010,.043987,.048359,.053140,.058434)
prob.Roberts=c(.008551,.009174,.009848,.010584,.011407)
prob.Kennedy=c(.040010,.043987,.048359,.053140,.058434)
prob.Alito=c(.012315,.013289,.014326,.015453,.016723)
#----------------------------------------------------------------
# Calculate the probability of death during the next 5 years.
# If p[i] is the probability of a justice's death in year i then
# the probability of death during the next 5 years is given by
# P(death in 5 yr) = p[1] + (1-p[1])p[2] + (1-p[1])(1-p[2])p[3]
# + (1-p[1])(1-p[2])(1-p[3])p[4] + (1-p[1])(1-p[2])(1-p[3])(1-p[4])p[5].
# This is just P(death in year 1) + P(survives year 1)P(death in year 2)
# + P(survives year 1)P(survives year 2)P(death in year 3) + ... etc.
#----------------------------------------------------------------
p=prob.Thomas
death.Thomas=p[1]+sum(cumprod(1-p[1:4])p[2:5])
p=prob.Scalia
death.Scalia=p[1]+sum(cumprod(1-p[1:4])*p[2:5])
p=prob.Roberts
death.Roberts=p[1]+sum(cumprod(1-p[1:4])*p[2:5])
p=prob.Kennedy
death.Kennedy=p[1]+sum(cumprod(1-p[1:4])*p[2:5])
p=prob.Alito
death.Alito=p[1]+sum(cumprod(1-p[1:4])*p[2:5])
#----------------------------------------------------------------
# Calculate the probability that one or more justices die during the
# next 5 years as one minus the probability that all 5 survive the
# next 5 years.
#----------------------------------------------------------------
prob.any.deaths=1-(1-death.Thomas)(1-death.Scalia)(1-death.Roberts)
(1-death.Kennedy)*(1-death.Alito)
#----------------------------------------------------------------
# Print the results.
#----------------------------------------------------------------
death.Thomas
death.Scalia
death.Roberts
death.Kennedy
death.Alito
prob.any.deaths
#
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Remarks.
Certainly, the figure of 50.7% is only a rough estimate. The actuarial tables are simply proportions from the Social Security records over all lifes and deaths of males at given ages in the U.S. The SC justices grew up under relatively economically privileged circumstances and might be expected to have somewhat lower individual death probabilities than males of their ages in the U.S. at large. Certainly they have access to privileged health care too. However, Thomas as an overweight black male might face somewhat higher risks than expected. As well, the other justices might be carrying family histories of heart attack, stroke, or cancer, increasing their individual risks.
Additionally, there are other circumstances which could lead to an opportunity for Obama to replace one of these justices. Retirement, potentially due to disability, ailment, family emergency, or just plain desire to leave the stress behind, could loom for any of these justices within 5 years.
Conclusion.
One presidential duty in which Obama has delivered in exemplary Democratic fashion is the selection of Supreme Court justices. Not even the Nader-est of Naderites can fault his picks.
If a Republican president is permitted to pick a replacement for any of the five reactionaries, or heaven help us, a replacement for any of the four liberals, the action will cement into place for the bulk of our lifetimes a criminally activist court that willfully subjugates constitutional guarantees to corporate and monied desires.
It is painfully apparent by now that Obama’s Department of Justice is unwilling to move on many matters deemed critical by DKOS readers. It is also apparent that the Obama administration is unwilling to use its executive branch powers to uphold many of its regulatory responsibilities.
My hypothesis is that the Obama administration has concluded that any executive action they take will not survive a lawsuit that winds up in front of the present Supreme Court. The five toadies have shown, shamelessly and repeatedly, that they will throw the Constitution out the window to make their corporate masters happy.
The above calculations have revealed that the chance that Obama could have the opportunity to replace one of the five toadies is surprisingly large. This fact alone should sober up every Democrat towards the importance of the task at hand.
I don’t care how disgruntled you are with Obama (it’s probably not as much as I am). You will not face a more important election in your lifetime. You will not face a more crucial political task than to get Obama reelected.
Do you get it? This Supreme Court, if it survives, is going to overrule Obamacare. This Supreme Court, under the care and nurturing of a Republican administration, will allow the dismantling of every piece of New Deal and Great Society progress. Voter Rights? Social Security? Medicare? Environmental Protection? Workers Rights? Civil Rights?
Talk primary, talk third party, sit out the election, and watch these things you take for granted disappear.