The probability here should be substantially below the square of the other one, basically because once it happens the first time, there will be less time left for it to happen a second time. You can verify with a Poisson calculator (e.g. compare x=1, mu=0.7 versus x=2, mu=0.7).

@StevenK fish!

@8 what?

@StevenK oh you mean as a translation of Poisson?

@StevenK yes !

@StevenK I think generally the whole “squared” idea is a bit misguided or oversimplified anyway. There are multiple things that could cause 1 death that would mean the chance of a second death are much higher, e.g. an attack of some kind, a disease, etc.

Because they’re all so old I guess everyone is going off of age related causes, but it would also be different if 99 senators were in their 40s and one was 96 (as an extreme example)

In that case, the second death would be less likely than the first death, but in the first example(s) the second death would be more likely/predictable than the first

@Gen Yes, and I'm not sure how to weigh all those factors. But I'm saying that, as a baseline, if deaths are totally independent, the probability of at least 2 deaths is less than the square of the probability of at least 1 death.

Seems underpriced at 37 when the one death market is at 72 (since .72 squared is about .5)

@Conflux think it should be less than squared, I wouldn't assume equal probabilities of a first and second death. For example, someone with Grassley's demographics is 25% more likely to die than any other demographic currently in Congress:
https://www.ssa.gov/oact/STATS/table4c6.html

@PatMyron Why do you think that means it shouldn’t be squared? Like, one death leaves a healthier population? Seems like probably a marginal effect

@Conflux safe to say whoever passes is quite unhealthier than those remaining ;)

but seriously those dying are over a decade older and more likely to be male than the congressional averages:
https://en.wikipedia.org/wiki/List_of_United_States_Congress_members_who_died_in_office_(2000%E2%80%93)#2010s

Looking at deaths back to 2006 (when average congress age reached levels similar to today) we had 28 deaths in the past 17 years. Modelling deaths as a Poisson distribution with a mean of 28/17, there is only a 49% chance of more than one death in a year. Plus we are 3% into 2023 already and no deaths, so the odds should be even lower.

Congress deaths: https://en.wikipedia.org/wiki/List_of_United_States_Congress_members_who_died_in_office_(2000%E2%80%93)

Congress age over time: https://www.nbcnews.com/data-graphics/118th-congress-age-third-oldest-1789-rcna64117

@StanPinsent Congress continued getting older after 2006: https://www.businessinsider.com/congress-oldest-history-gerontocracy-lawmakers-2022-9

"old fraction" is probably a better predictor of deaths than average age.

Related, 1 death market