George HW Bush passed away- some non-partisan math comments

George HW Bush passed away recently. When he was alive there were 5 living ex presidents. Now there are 4. What is the max and min number of ex presidents? This we will answer. What is the prob of having many living ex-presidents?

What is the max number of ex-presidents alive at the same time? List the times this has happened. Your answer should be a list of statements of the following form:

 Shortly after X took office there were Y ex-presidents: Z(1), Z(2), ... , Z(Y).

I leave a little white space in case you want to try to figure it out, though the point of this post is not to quiz you.
















ANSWER: The max number of ex-presidents alive at the
same time is five. This has happened four times.

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ONE: In 1861 just after Lincoln took office there were five living ex-presidents:
Martin van Buren (died in 1862), John Tyler (died in 1862), Millard Fillmore (died in 1874), Franklin Pierce (died in 1869), James Buchanan (died in 1868).

Key factors: (1) Between 1836 and 1860 there were no 2-term presidents, (2) Martin van Buren lived a long time after being president.

TWO: In 1993 just after Clinton took office there were five living ex-presidents:
Richard M. Nixon (died in 1994), Gerald Ford (died in 2006), Jimmy Carter (still alive as of Dec 2018), Ronald Reagan (died in 2004), George HW Bush (died in 2018).

Key factors: (1) Nixon, Ford, Carter, Bush Sr were the equivalent of 4 one-terms, and (2) Reagan lived a long time after being president.

THREE: In 2001 just after George W. Bush took office there were five living ex-presidents:
Gerald Ford (died in 2006), Jimmy Carter (still alive as of Dec 2018), Ronald Reagan (died in 2004), George Bush (died in 2018).  Bill Clinton (still alive as of Dec 2018).

Key factors: (1) Ford, Carter, Bush Sr. were effectively 3 one-terms, and (2) Reagan lived a long time after being president.

FOUR: In 2017 just after Donald Trump took office there were five living ex-presidents:
Jimmy Carter (still alive as of Dec 2018), George  HW Bush (died in 2018).  Bill Clinton (still alive as of Dec 2018).  George W Bush (still alive as of Dec 2018).  Barack Obama (still alive as of Dec 2018).

Key factors: (1) Carter, Bush were both one-termers,  (2) Clinton and W are relatively young for presidents and in good health, and  (3) Carter and Bush Sr. lived  a long time (Carter is still living!)

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I want to see this record broken! I want to see 6 living ex presidents! (Darling asks why I want to see that. Its a good question which I will partially address later.) Hence I want to see Donald Trump impeached or resign or leave office!  I was hoping it would would happen before one of Carter, Bush Sr, Clinton, W, Obama died. Oh well.

So now what? Is it possible that we will see 6 living ex-presidents in our lifetime. Factors: prez longevity, prez age, one-term vs two-term, and since I am asking about in OUR lifetime, our longevity.

Lets assume that neither The Donald nor any other president resigns or gets impeached or leaves office before their term is up. We assume that the presidents after Trump are  Alice, Bob, Carol.

Scenarios:

ONE: Donald Trump loses to Alice in 2020, Alice loses to Bob in 2024. None of the ex presidents dies before 2025. Then we would have, in the first day of the Bob presidency, which would be  in  2025,  6 living ex presidents:  Carter, Clinton, W, Obama, Trump, Alice.

This needs Carter to live to be about 100 (the others are much younger). Possible!

TWO: Donald Trump loses  to Alice in 2020, Alice loses to Bob in 2024 . Bob loses to Carol in 2028. Carter passes away before 2025 but the other ex presidents are alive in 2029. Then we would have, in the first day of the Carol presidency, which would be in 2029, 6 living ex presidents:Clinton, W, Obama, Trump, Alice, Bob.

This needs W, Clinton, Trump  to live to be about 83 and Obama to live to be 72.  Possible!

I'll stop here, but you can make up your own SCENARIO THREE which requires some people to live to 87.

Scenario ONE seems unlikely. TWO and THREE are plausible; however, there is another factor. I am assuming a long string of one-termers (that was flagged as not-a-word. Oh well.)  Lately incumbency has a big advantage: Clinton, W, Obama were all two-termers. Incumbency is powerful for two reasons that reinforce each other:

The incumbent can DO things, can LOOK presidential.

Since the incumbent has these advantages people are scared to run against him or her.

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Math problem: What is the probability that we will see 6 living ex presidents by 2029? To solve this you would need to know

Longevity statistics. But of what group? by Age? by profession? of ex-presidents? That seems to narrow for good statistics.

Incumency statistics. How likely is it for a Prez to be re-elected? Again, too small a sample size. And Trump seems like an outlier. I suspect that if Jeb or Hillary were president they would get re-elected because of the incumbency advantage. But Trump is so unusual that it might not hold. One thing in his favor: it is unlikely there will be a challenge from his own party. One thing in his disfavor would be a third party challenge. But ENOUGH. My point is that it would be hard to do good stats here.

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So why do I care about seeing 6 living ex-presidents in my lifetime? I have a reason but its not a good reason.

Early in the Nixon Presidency LBJ died. I noticed that there were ZERO living ex-presidents. I knew that LBJ was dead, and JFK was dead, and I suspected (correctly) that Eisenhower and Truman were dead, and I knew FDR was dead. Before that we have Hoover and others who were of course dead. I was SO PROUD of myself for KNOWING this (to be fair I was 12 years old). This sparked my interest in presidents and especially in the question of most/least living ex-prez.

Now for the obvious question on the other end of the spectrum:

What is the min number of ex-presidents alive at the same time? And when did it occur (list all times)

White space for those who want to try to figure it out or look it up.
























ANSWER: Zero. This happened six times.

ONE: When George Washington was president there obviously were zero living ex-presidents.

TWO: Shortly after John Adams became president George Washington died. At that time there were zero ex-presidents.

THREE: During Ulysses S Grant's term Andrew Johnson, the prior president died. Lincoln was dead by assassination and all prior presidents were dead of old age  or similar (e.g., James Buchanan died at the age of 77, Franklin Pierce (an ancestor of Barbara Bush (nee Pierce) was 65 and died of cirrhosis of the liver, from alcoholism.)

FOUR: During Theodore Roosevelt's term Grover Cleveland died, and all other ex-presidents were dead.  Recall that the prior prez, McKinley, had been assassinated.

FIVE: During Herbert Hoover's term, following Calvin Coolidge's death (Hoover's predecessor), there were no ex-presidents.  This partially explains why Coolidge didn't run- he had health problems.  Note that Harding died in office.

SIX: During Nixon's term, in 1973, Lyndon Johnson died. At that time there were zero ex-presidents.  This was because Lyndon Johnson died young (65), Kennedy was assassinated, Eisenhower was old while president.


NOTE: I would have thought that since FDR served so long and died in office either during FDR's term or Harry Truman's term there would be a time with no living ex-presidents.  Early in FDR's term there was only one living ex-president: Hebert Hoover. However, he didn't die until 1964. Hence he lived through the presidencies of FDR, Truman, Eisenhower, Kennedy, and part of Johnson's.  This is NOT the most presidents an ex-president has lived through after they step down. That honor might go to Carter who has lived through the presidencies of Reagan, Bush Sr, Clinton, W, Obama, and, as of this writing, a few years of Trump.  I have not checked if this is a record but I will once Carter passes away.

NOTE: In most of the cases above a recent president had died prematurely. Grant- Lincoln, Roosevelt- McKinley, Hoover- Coolidge, Nixon- Johnson and Kennedy.)

NOT: Since Obama, W, and Clinton are all relatively young, and presidents dying in office is now very rare (the last one was JFK in 1963)   I doubt this will happen again. But politics and history can surprise you.