Uncertainty Wednesday: Pascal’s Wager and Impeachment

I have been enjoying writing about current events as part of Uncertainty Wednesdays, such as the Notre Dame fire and the Boeing crashes. Today’s edition is about impeachment following the Mueller report. One of the great early thinkers about uncertainty was Blaise Pascal who made many important contributions to mathematics (among them Pascal’s triangle which is a staple of learning math).

In a posthumously published work Pascal sets out a simple argument for believing in God which has become known as Pascal’s wager: a belief in God imposes a finite cost during one’s lifetime but with some small probability offers an infinite benefit of an eternal heavenly afterlife (he was thinking of a Christian God but the argument applies to many other religions that have a similar concept). Conversely if you do not belief in God you have a finite gain versus a small probability of an infinite loss from an eternity in hell. With this setup the rational choice is to believe in God.

Pascal’s wager is an important contribution to thinking about living under uncertainty because it separates out the probability of states of the world (God exists, God does not exist) from the payoffs of different decisions when those states are realized. In doing so it makes clear that when payoffs can be very large in either direction (here infinite gain or infinite loss), then even small probabilities have a huge impact on decisions. Importantly no amount of prior research or forecasting can meaningfully resolve this analysis. Pascal’s wager can thus be seen as an early (maybe the earliest?) contribution to a line of thinking about the importance of extreme payoffs that today is being carried on prominently by Nassim Taleb.

What does any of this have to do with the question of impeachment? Well, one analysis of whether or not the Democrats should move to impeach Trump in the wake of the Mueller report has centered around the impact on the 2020 presidential elections. Some make the argument that impeaching now reduces the Democrats chances of winning in 2020. But if you look at Pascal’s wager, let’s say you find some evidence that give you a small reduction in the probability that God exists, that still does not change the decision because the payoff is so extreme.

I believe a similar logic applies here if you consider the payoffs to be the longterm consequences for limits on the behavior of all future presidents. You can either impeach or not and then the president either wins re-election or does not. If you impeach there is a small cost if Trump is reelected but a massive gain if he is not. Conversely if you do not impeach there is a massive cost if Trump is reelected and a small gain if he is not. Why? Because impeachment is about congressional oversight of the behavior of a president. It is a crucial part of the checks and balances of the system of government in the United States.

The crucial part here is that this logic is independent of whether you think impeachment will succeed in removing the president. In fact, I assumed that it will not succeed and that Trump will be able to run in 2020 in any case. Another way of phrasing the analysis is as follows: do not give up on a fundamental principle for tactical gain (here the fundamental principle being congressional oversight). The fundamental principle has huge (infinite) upside/downside whereas tactical gains are always small by comparison.