What is the probability that the US President's most prominent foreign and domestic rival die in the same year of his election?

Question

I am greatly curious on whether the probability of some US president's greatest foreign and domestic rival dying in about half a year after his election has a way of being rigorously calculated.

To put it more precisely, let us say that some Democratic candidate named "X" has won the US presidency. So,

1. The leader of Russia, named Y, has died three months after the President's election.

2. The prominent leader of the Republican party, named C, has died two months after the leader of Russia.

And furthermore,

3. The prominent rival, named B, of X in his own Democratic party has died one month after the leader of the Republicans.

What is the probability of this happening?

Answer 1

I am guessing that you are interested in investigating the question:

Was there any foul play?

Were these 3 people really assassinated instead of whatever is the cause that appears in the media?

So you are interested in assessing what is the probability of foul play, i.e., President X taking action to kill Y, C, and B, given that Y, C, and B are dead. First of all let me note that the action to kill Y, C, B can be broken to independent actions. for example, you can ask about killing Y but not the others, or any other combination. But let's see the case where we are interested whether all three people were killed by President X. Let's denote the event that action to kill person $i$ as $K_i$, and let's denote the event that person $i$ died as $D_i$. Also let's say that if we write two events next to each other separated by a comma, we mean that these events happened together (so instead of writing a $\cap$ I write a "," to be more compact). You want to compute:

$$P(K_y, K_c, K_b | D_y, D_c, D_b )$$

Using Bayes' rule we can write the above probability as

$$P(K_y, K_c, K_b | D_y, D_c, D_b )= \frac{P(D_y, D_c, D_b|K_y, K_c, K_b)\cdot P(K_y, K_c, K_b)}{P(D_y, D_c, D_b)}$$

So we need to know three quantities/probabilities to calculate what we want:

• The probability that President X will try to kill these 3 people (that's $P(K_y, K_c, K_b)$,
• The probability that given that he tries to kill them he is successful. That's $P(D_y, D_c, D_b|K_y, K_c, K_b)$
• The probability that they die (of any cause, natural or otherwise). That's $P(D_y, D_c, D_b)$

To compute these probabilities you need some kind of modelling, based on various assumptions. For example we might assume that President X will try to kill all these people with probability 0.5. And once he tries to kill them he succeeds with probability 1. The accuracy of your prediction depends on the accuracy of your modelling.

The interesting thing though is that even if your model is not very accurate is some areas, other parts can influence the final result greatly and thus you can make some parametric studies. For example, we intuitively understand that it is quite unlikely for three specific healthy people to die within months of each other. You will make assumptions on that too of course, but the end result will probably give you a high probability that President X did it. Then you can start varying parameters/assumptions on your model and see how this affects the final result.