I saw this piece on the Daily Poster, and this is just baiting to me, given the mortality hook: Dems Could Lose Their Majority At Any Moment
Many pundits are already suggesting the Democrats’ control of Congress will only last until the 2022 midterm elections. But a single, unforeseen Senate vacancy could instantly kill a once-in-a-generation opportunity to pass their agenda, from new gun regulations to a badly-needed minimum wage hike, from voting rights legislation and new worker protections to a promised public option.
The Senate is split 50-50, and 10 Democratic senators are from states whose Republican governors could replace them with GOP appointees in the event they are rendered incapacitated by a health event. Among that group, six are over 70 years old. The pandemic has provided ample evidence that such health events can occur at any moment — and that’s especially true for septuagenarians and octogenarians. And while deaths of younger senators have been rare, three such casualties have occurred in the last 30 years.
I had done a post back in February on Senators dying in office, but I was simply doing a historical look. Let’s look at doing some probabilistic predictions, shall we?
Listing the vulnerable senators
Okay, so who are those 10 Democratic Senators the Daily Poster authors have in mind? They list a few of them:
In January, days after Democrats took power in Washington, Vermont Senator Patrick Leahy was briefly hospitalized. Leahy, 80, said he “had some muscle spasms” and was given “a clean bill of health.”
Bernie Sanders, Vermont’s other senator, is 79 and had a heart attack during his presidential campaign last year.
Vermont Gov. Phil Scott is a Republican, and would have the power to appoint a replacement — one who would likely be from his party — if either of the state’s senators were unable to finish their terms.
Four other Democratic senators who are older than 70 represent states with GOP governors with the power make appointments to fill Senate vacancies — Jeanne Shaheen of New Hampshire, Elizabeth Warren and Edward Markey of Massachusetts, and Manchin in West Virginia. In all, 34 Senate Democrats are at least 60-years-old.
And there were four other senators they had in mind, but you know what? We’ll ignore the 4 senators under age 70. It is true that their mortality rate is going to be a lot lower, so let me not worry about them.
Here is our list of senators:
Patrick Leahy, 80 years old, male
Bernie Sanders, 79 years old, male
Jeanne Shaheen, 74 years old, female
Elizabeth Warren, 71 years old, female
Edward Markey, 74 years old, male
Joe Manchin, 73 years old, male
Now, I could get tricky and try to figure out a specialized one-year mortality rate for each of these people, and include something about COVID, do age-nearest-birthday, yadda yadda.
I’m not doing that — because I’m just trying to get to order-of-magnitude results.
I will use the 2017 Social Security Period Life Table — that is, the mortality based on the general population from calendar year 2017.
Here are our death probabilities for each person [from the Social Security table, so I’m keeping its full number of digits]:
Patrick Leahy, 5.8206%
Bernie Sanders, 5.2649%
Jeanne Shaheen, 2.2522%
Elizabeth Warren, 1.6878%
Edward Markey, 3.2394%
Joe Manchin, 2.9587%
And now I’m going to take a little detour in talking about calculating probabilities.
Assumptions in probability
Going back to my introduction to probability:
What we’re really interested in is how likely all 6 of these people will NOT die over one year.
So going to our rules of probability — probability of NOT dying = 1 – probability of dying.
Here is that result, and I’m lopping off a couple of the decimal figures, because I’m focusing on only a few significant figures result:
Patrick Leahy, 94.18%
Bernie Sanders, 94.74%
Jeanne Shaheen, 97.75%
Elizabeth Warren, 98.31%
Edward Markey, 96.76%
Joe Manchin, 97.04%
Okay, now you may be wondering how to go from that to the probability that all of them survive one year more. I didn’t get to this bit yet in my probability videos (as I’ve done only one), but we have to make assumptions about how these probabilities interact with each other.
Basically, we assume whether or not each individual survives is independent, so that we can multiply probabilities to get the probability they all survive. (In real life, their survival is not exactly independent, but I would rather not explain that for this particular example. Instead, here is an old post on broken heart syndrome and why deaths aren’t independent for some people.)
Here is the probability that all six people survive one year, using our assumed mortality rates:
(I’m not dignifying this with additional decimal places)
So the probability that this is NOT true – that not all of them survive, or, in other words, that at least one of them dies in one year, is 19%.
That is a pretty hefty probability.
That is almost a 1-in-5 chance.
Stress-testing the calculation
So, I started out with 2017 historical mortality as my initial assumption for mortality rates, but senators likely have better longevity than the general population. I think the 19% probability estimate for at least one death in the group is way too high.
Let us stress test our assumptions: that is, changing our mortality assumptions in large ways (within a reasonable range) and see what results. I will stress the assumptions in two ways: much lower mortality rates and pandemic-driven higher rates.
For our stress in the lower mortality direction, let us assume the mortality rate for senators is half that of the hoi polloi.
This is not necessarily an extreme assumption; mortality experience of U.S. credentialed actuaries has been about 65% of the general population. A 50% mortality assumption seems like a reasonable reflection of the access to medical care and high-end lifestyle senators enjoy.
With this halved mortality assumption, what is the probability that at least one of the six listed senators dies in the next year?
So that about halves the likelihood. And that seems more in the range of probability I expect. It’s still a substantial probability, but definitely not as substantial as 19%.
I could boost the mortality rates due to COVID, but these folks have all been vaccinated, and I don’t really think this is a big issue. But let’s suppose, for stress-testing purposes, to just increase the mortality rates by 15% as our “high mortality” scenario.
With that boost to our original assumed mortality, the probability at least one dies in the next year rises from 19% to…. 22%. Not a huge difference in terms of likelihood for this sort of rough estimation.
Entire distribution of the number of deaths
So maybe you’re interested in how the distribution of the number of deaths shakes out under the three different assumption sets.
It’s not really very interesting:
We already calculated the probability of 0 people dying, so the main question is how many more than 0 when a death does occur. Basically, if a death occurs, it’s far and away most likely to be only one death. There is a greater than 1% chance for 2 or higher deaths for our baseline and 15% extra mortality assumptions, but less than 0.5% chance for halved mortality.
Fun for homework question, bad for political risk management
That the probability at least one dies in the next year is so high in our baseline is mainly driven by the two oldest senators among the six: Leahy and Sanders. They have about a 5% mortality rate given their age and sex, and that’s actually pretty high. Mortality grows rapidly above age 80.
Note that above I focused solely on 6 old Democratic senators in states where Republican governors would select their replacements. I didn’t consider old Republican Senators who are in states run by Democratic governors (and which would get to pick their replacements… which is not necessarily a sure thing. Here is a page on how different states deal with senatorial vacancies.)
In my prior piece on the old folks’ home that is the Senate, I noticed that the number of people who have died in the Senate has dropped considerably, as longevity in the U.S. has increased in general.
I wasn’t considering the partisanship of those deaths.
This is a cute problem to give your actuarial science students for homework. They could even do it by hand! (There are only 64 combos to consider for 6 senators, but if the students are smart, they can take a practical approach…. or just do it in a spreadsheet, like I did.)
Trying to make strategic political moves based on this kind of probabilistic reasoning is foolish, due to a variety of reasons. Rather than digging further into the foolishness of trying to calculate death probabilities of only a handful of people (as opposed to what insurers do, which involves thousands of people at least), let’s just consider the politics and why we’re thinking about the possibility of a Democratic senator dying in the next year.
With razor-thin majorities in the House and Senate, along with reapportionment coming up, there is some expectation that loss of control of at least one of the two legislative bodies in the 2022 election… and now some are waking up to the fact that the control can be lost well before 2022.
Of course, something like that happened when they tried to pass the ACA. You’d think people would have had some conversations before now. That brinkmanship was over 10 years ago. Of course, since 2010, the Democrats have had a rough road.
As for the filibuster, I’m neutral on the option being available as a procedural move in the Senate. The only thing is that the Democrats may want to remember the last time Republicans took advantage of a procedural change the Democrats enacted in the Senate.