Pascal’s Wager

I had to work full-time through my undergraduate degree (through grad school too, but that’s not relevant here) and most of my electives were taken because a class fit my schedule rather than because I was interested in the class. So when I showed up for the first day of Philosophy 101 I have to admit I was more interested in meeting my humanities requirement than in the class itself. I was surprised to find myself enjoying the class, and even more surprised to find a use for some of the topics we learned in the class – the utilitarian fallacy was one, but I’ll save that one for later; this week I am more interested in talking about Pascal’s Wager and how it might be extended beyond its originator’s original intent.

Blaise Pascal (1623-1662) had a struggle with religious faith for much of his life, finally resolving many of his conflicts when he posed religious belief as a problem in logic rather than of faith. Pascal realized that there was an asymmetry in religious belief versus non-belief and this asymmetry made a huge difference. The short version is that Pascal was weighing a lifetime of behavior versus an eternity of reaping the fruits of that behavior. Here are some of the options Pascal saw:

  1. There is a God and we live a good life (e.g. denying ourselves the temptations and pleasures to which we might otherwise succumb): A lifetime of self-denial to be rewarded with an eternity in Heaven
  2. There is a God and we live a life of dissolution and fun: A lifetime of fun and pleasure “rewarded” with an eternity of torment in Hell
  3. There is no God and we live a good life: A lifetime of self-denial with no reward after death.
  4. There is no God and we live a life of dissolution and fun: A lifetime of fun and pleasure with no punishment after death.

The way Pascal saw it was that he faced the certainty of a lifetime spent however he chose to spend it – either in fun or in self-denial – while he faced the possibility of an eternity of punishment or reward. So in choosing his behavior he was wagering a mere lifetime of behavior versus a potential eternal payback. Pascal concluded that it made sense to act as though God existed since the worst case (finite pleasure followed by infinite punishment) was so much worse than the alternative (finite pleasure followed by nothing). Or, put another way, if the downside is sufficiently dire then it makes sense to try to avert it, even if the potential upside (in this case an eternity in Heaven) is as hypothetical as the worst case. One way to think about it is that a lifetime of self-denial and discipline is (relatively speaking) fairly cheap and easy to do compared to an eternity of torment. Pascal’s Wager is a form of cost-benefit analysis.

So let’s think about this outside the original scope of Pascal’s thinking.

My homeowner’s insurance is a sort of Pascal’s wager. I can (in theory) choose whether or not to buy insurance – the cost of the insurance is relatively minor compared to the cost of our house and belongings. I might pay insurance for decades and never need to use it, in which case I’m out the cost of the insurance premiums. Or I might choose to go without insurance and if nothing happens then I’ve saved myself a few tens of thousands of dollars. On the other hand, if my house burns down and I’m uninsured then I’m out everything – it makes sense to buy insurance to avoid this option, even if the odds are that I’ll never need to use it.

Much of what we do – especially in the realm of preparing for the worst – is a sort of Pascal’s wager. In each case we’re making a decision to spend a finite amount of resource (money, personnel time, equipment) in order to try to avert a disaster. So, for example, preparing for flooding in New Orleans is a no-brainer – the fact that the city is prone to flooding is far from hypothetical and we know how bad the results can be, both financially and in human terms. So, unless we are prepared to abandon New Orleans and let it return to swampland then it makes sense to take actions to protect the city against a certain flood. Similarly, preparing for earthquakes in California makes sense, as does preparing for wildfires in the American West.

OK – these are easy ones because we know that flooding in New Orleans and earthquakes in California are certain to happen with regularity. But then let’s think about some of the other challenges we face.

The world hasn’t seen a nuclear attack since 1945, the number of the world’s nuclear weapons is decreasing annually, and (so far) we have been able to pretty much control both nuclear weapons and fissile material. On the other hand, we know that not all nuclear powers (or wanna-be nuclear nations) are as trustworthy and reliable as we would like and we know that there are terrorist groups who would want to attack us with nuclear weapons. And we know how devastating a nuclear attack can be – perhaps not infinite and eternal torment, but a pretty close approximation for those affected. No matter how unlikely such an attack might be, it would seem to make sense to take what actions we can to avert such an attack, and to prepare to respond to help to mitigate the aftereffects. The question to ask is how much we should do to avert or prepare.

Pascal’s wager is based on the possibility of an infinite bad side, so virtually any sacrifice can be justified. In addition, Pascal was thinking only of himself as an individual. But when we think about even something as horrific as a nuclear attack we are talking about a finite bad side, and when we think about the cost of averting such an attack or preparing for the aftermath we are talking about costs to society. To take an extreme example (and yes, I know this is unrealistic, but it is illustrative!) – suppose we decide to spend every last dollar in our national budget to try to prevent a nuclear attack against one of our cities, and to put plans into place to deal with the aftermath in the event an attack were to happen nevertheless. We would certainly be better-prepared and likely safer from terrorist attack if we devoted our entire federal budget to this end. But at what cost? We’d have to eliminate federal funding for roads, environmental protection, education, scientific and medical research – all programs that make a difference in the lives of everyone in this country. Social programs would vanish as well – programs that, whether you agree with them or not, make a vital difference to millions of Americans. Grants to states would also cease, with the exception of those related to nuclear preparedness, affecting millions more.

This makes the calculation a lot more difficult. Consider – in both cases (nuclear attack or the possibility of going to Hell) the probability of the threat is unknown. But the stakes for Pascal were his individual torment versus his individual sacrifice while in nuclear defense and preparedness we are talking about a torment that might affect millions and a cost that would affect tens or hundreds of millions. How do we even begin to make this calculation? Obviously we can’t abandon all of the responsibilities of government to concentrate on this one aspect of security, but neither can we do nothing. The question is what DO we do – how much should we invest as an insurance policy against a nuclear attack?

The question becomes even more complex when we consider other, lesser concerns. A dirty bomb attack, for example, is hardly an inconsequential event, but it pales in comparison to a nuclear attack. On the one hand, a dirty bomb attack is thought to be more likely than a nuclear attack; on the other hand, it is also far less damaging. So do we put more resources into trying to avert (or plan for) a dirty bomb because it’s more probable, or do we put less resources into this effort because it’s less likely? I suppose we could try to develop a mathematical formula to try to pin this one down – we could include variables that would include the probability of an attack, the number of lives that could be saved, the probability that our efforts will be successful, the cost (financial and societal) of a successful attack, and so forth.

The problem is that virtually every term would be a guess – in reality we have no idea of the probability that we’ll be attacked by any given weapon – there has never been a radiological attack and there have been no terrorist attacks with nuclear weapons. But we can’t assign a probability for the future based on a past record of no events. Similarly, we can’t really calculate the cost of a successful attack – we have no data points at all for a radiological attack and there are no examples (even in testing) of the effects of a nuclear attack in a city such today’s Los Angeles, New York, London, Mumbai, or any of the other major cities of today. We can guess, but if we claim that whatever numbers we’d put into our equation are anything other than a guess, we’d be deluding ourselves. In these cases, Pascal’s Wager can be no better than semi-quantitative.

Let’s take one quick example – the average US home costs about $250,000 and the average homeowner’s insurance policy is about $500 annually – about 0.2% of the cost of the home and somewhat less than that fraction of the cost of the home plus belongings. But there are a lot of caveats – my insurance is reduced by having smoke detectors, deadbolts, a home alarm system, and so forth. It’s also reduced by the dearth of insurance claims and the low crime rate in our part of town – just as those who lack these factors will pay a higher rate. The insurance companies are out to make money and the only way to do that is to very carefully weigh the premiums they charge against the probability that a loss might exceed the total amount of premiums paid over the life of our insurance policy. They make use of every scrap of information available – including their extensive experience – to make these calculations. Compare this to our trying to determine our society “insurance rate” against a terrorist attack of the sort we’ve been discussing. We can guess at the amount of loss we might see (one estimate is that costs could run into several tens of billions of dollars or more when longer-term economic impacts are tallied).

If we pay the same fraction for RDD “insurance” as I do for my homeowners insurance then we could justify spending, say, $200 million annually to protect against a potential loss of $100 billion. But, having said that, it’s not quite that simple for the reasons I noted above. Not only that, but we also have to ask ourselves what we are guarding against for our $200 million – is this just to guard against a dirty bomb attack, or against any attack that can lead to a $100 billion loss? Do we assess each possible event (and its potential cost) independently and add up the sum of all of these to determine our terrorism “insurance premiums” or do we take credit for measures that might be protective against multiple types of attacks? And how do we assess the likelihood of an attack? Do we assume, as did FBI Assistant Director Majidi in February, 2011 that the risk of a WMD attack is 100%, do we point to the fact that there have been no large-scale WMD attacks since the 1995 sarin attacks in Tokyo (and none at all since the 2001 anthrax attacks), do we look at the number of plots that have been discovered (and the fact that they’ve been thwarted), or do we just give it our best guess? And for that matter, how do we factor in the cost of our military, which combats terrorism as well as defending our nation and safeguarding our allies. Again – the best we can hope for is to be semi-quantitative and to try to justify our assumptions as best we can. But, at the same time, we should be honest as to where we are guessing.

There are some obvious answers to what actions we can justify taking – in any cost-benefit assessment we should take actions that are cheap and easy to accomplish because the resources put into them are trivial compared to even a slight risk from a modest event. Spending tens of millions to prevent an attack that could cost hundreds of billions – even if the probability is low – makes sense. Even spending billions of dollars can be justified if the probability is high enough. The question – again – is not whether or not we spend to protect ourselves, but how much spending can be justified.

To take one final step, we can also look at our own behaviors and actions. It makes sense to take actions that are relatively simple and cheap to protect ourselves from harm. When we buy locks for our doors we are spending a few hundred dollars to protect us, our families, and our belongings from theft or harm, just as when we pay our insurance premiums we’re spending a relatively small sum to protect against the risk of loss. Smoke detectors are cheap, as are seatbelts and vaccinations and so many other actions we routinely take. But how many people are willing to bunker down 24/7 in an armored home to reduce our risks even more? At some point we have to accept some degree of risk in our lives unless we’re planning on divorcing ourselves from the world. Or, put another way, taking maximal precautions to safeguard our lives would mean giving up our lives, just as taking maximal precautions to safeguard our nation would mean giving up on all of the other governmental responsibilities and services. Certainly we should protect ourselves – but with finite resources to spend and all of society to consider we have to be judicious in our expenditures.

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