Flipping Pascal's Wager on Its Head

In his famous Wager, Pascal contemplates whether one should choose to believe in God. (Maybe we can't directly choose to believe in God any more than we can simply choose to believe that the Sun is purple; but we can choose to expose ourselves to conditions, such as regular association with devoted theists, that are likely to eventually lead us to believe in God.) Although there's some debate about how exactly Pascal conceptualizes the decision, one interpretation is this:

Choose to believe: If God exists, infinite reward; if God does not exist status quo.

Choose to not to believe: If God exists, infinite punishment; if God does not exist status quo.

Suppose that your antecedent credence that God exists is some probability p strictly between 0 and 1. Employing standard decision theory, the expected payoff of believing is p * ∞ [the expected payoff if God does exist] + (1-p) * 0 [the expected payoff if God does not exist] = ∞. The payoff of not believing is p * -∞ + (1-p) * 0 = ∞. Since ∞ > -∞ (to put it mildly), belief is the rational choice.

Now maybe it's cheating to appeal to infinitude. Is Heaven literally infinitely good? (There might, for example, be diminishing returns on joyful experiences over time.) And maybe decision theory in general breaks down when infinitudes are involved (see my recent discussion here). But finite values also work. As long as the "status quo" value is the same in both conditions (or better in the belief condition than the non-belief condition), the calculus still yields a positive result for belief.

If not believing is better in the absence of God, it's a bit more complicated. (Non-belief might be better in the absence of God if believing truths is intrinsically better than believing untruths or if believing that God exists leads one to make sacrifices one wouldn't otherwise make.) But if Heaven would be as good as advertised, even a smidgen of a suspicion that God exists favors belief. For example, if life without belief is one unit better than life with belief, contingent on the non-existence of God, and if Heaven is a billion times better than that one-unit difference and Hell a billion times worse, then the expected payoff for believing in God is p * 1,000,000,000 + (1-p) * -1, and the expected payoff of not believing is p * -1,000,000,000 + (1-p) * 0. This makes belief preferable as long as you think the chance of God's existing is greater than about one in two billion.

So far, so Pascalian. But there's God and then there's the gods. It seems that a more reasonable approach to the wager would consider theistic possibilities other than Pascal's God. Maybe God is an adolescent gamer running Earth in a giant simulation. Maybe the universalists are correct and a benevolent God just lets everyone into Heaven. Or maybe a jealous sectarian God condemns everyone to Hell for failing to believe the one correct theological package (different from Pascal's).

If so, then the decision matrix looks something like this [click to enlarge and clarify]:

In other words, quite an un-Pascalian mess! If the positive and negative values are infinite, then we're stuck adding ∞ and -∞ in our outcomes, normally a mathematically undefined result. If the values are finite but large, then the outcome will depend on the particular probabilities and payoffs, which might be sensitive to hard-to-estimate facts about the total finite goodness of Heaven or badness of Hell. And of course even the decision matrix above is highly simplified compared to the range of diverse theistic possibilities.

But let me suggest one way of clarifying the decision. If God is not benevolent, all bets are off. Who knows what, if anything, an unbenevolent God might reward or punish? Little evidence on Earth points toward one vs another strategy for attaining a good afterlife under a hypothetical unbenevolent deity. I propose that we simplify by removing this possibility from our decision-theoretical calculus, instead considering the decision space on the assumption that if God exists God is benevolent. Doing that, we can get some decision-theoretic traction: a benevolent God, if he/she/it/they reward anything, should reward what's good.

This, then gives us mortals some (additional) reason to do whatever is good.

Here's something that's good: apportioning one's beliefs to the evidence. The world is better off, generally speaking, if people's credence that it will rain on Tuesday tends to match the extent of the evidence that it will rain on Tuesday. The world is better off, generally speaking, if people come to believe that cigarette smoking is bad for one's health once the evidence shows that, if people come to believe in anthropogenic climate change once the evidence shows that, if people decline to believe in alien abductions given that the evidence suggests against it, and so on. Apportioning our beliefs to the evidence is both a type of intellectual success that manifests the flourishing of our reasoning and a pragmatic path to the successful execution of our plans.

This is true for religious belief as well. Irrationally high credence in some locally popular version of God doesn't improve the world, but in fact has historically been a major source of conflict and suffering. Humanity would be better off without a tendency toward epistemically unjustified religious dogmatism. Nor should a benevolent God care much about being worshipped or believed in; that's mere vanity. A truly benevolent God, with our interests at heart, should care mainly that we do what is good -- and this, I suggest includes apportioning our religious beliefs to the evidence.

The evidence does not suggest that we should believe in the existence of God. (We could get into why, but that's a big topic! We can start by considering religious disagreement and the problem of evil.) If a benevolent God rewards or at least does not punish those who apportion their belief to tge evidence, a benevolent God should reward or at least not punish non-believers.

If God does not exist, we're better off apportioning our (non)belief to the (non)evidence. If a benevolent God exists, we're still better off not believing in the God. If God exists but is not benevolent, then decision-making policies break. Thus, we can flip Pascal's wager on its head: Unless we reject decision theory entirely as a means to evaluate the case, we're better off not believing than believing.

Does It Matter If the Passover Story Is Literally True?

My opinion piece in today's LA Times.

You probably already know the Passover story: How Moses asked Pharoah to let his enslaved people leave Egypt, and how Moses’ god punished Pharaoh — bringing about the death of the Egyptians’ firstborn sons even as he passed over Jewish households. You might even know the ancillary tale of the Passover orange. How much truth is there in these stories? At synagogues this time of year, myth collides with fact, tradition with changing values. Negotiating this collision is the puzzle of modern religion.

Passover is a holiday of debate, reflection, and conversation. Last Passover, as my family and I and the rest of the congregation waited for the feast at our Reform Jewish temple, our rabbi prompted us: “Does it matter if the story of Passover isn’t literally true?”

Most people seemed to shake their heads. No, it doesn’t matter.

I was imagining the Egyptians’ sons. I am an outsider to the temple. My wife and teenage son are Jewish, but I am not. My 10-year-old daughter, adopted from China at age 1, describes herself as “half Jewish.”

I nodded my head. Yes, it does matter if the Passover story is literally true.

“Okay, Eric, why does it matter?” Rabbi Suzanne Singer handed me the microphone.

I hadn’t planned to speak. “It matters,” I said, “because if the story is literally true, then a god who works miracles really exists. It matters if there is such a god or not. I don’t think I would like the moral character of that god, who kills innocent Egyptians. I’m glad there is no such god.”

“It is odd,” I added, “that we have this holiday that celebrates the death of children, so contrary to our values now.”

The microphone went around, others in the temple responding to me. Values change, they said. Ancient war sadly and necessarily involved the death of children. We’re really celebrating the struggle for freedom for everyone....

Rabbi Singer asked if I had more to say in response. My son leaned toward me. “Dad, you don’t have anything more to say.” I took his cue and shut my mouth.

Then the Seder plates arrived with the oranges on them.

Seder plates have six labeled spots: two bitter herbs, charoset (fruit and nuts), parsley, a lamb bone, a boiled egg, each with symbolic value. There is no labeled spot for an orange.

The first time I saw an orange on a Seder plate, I was told this story about it: A woman was studying to be a rabbi. An orthodox rabbi told her that a woman belongs on the bimah (pulpit) like an orange belongs on the Seder plate. When she became a rabbi, she put an orange on the plate.

A wonderful story — a modern, liberal story. More comfortable than the original Passover story for a liberal Reform Judaism congregation like ours, proud of our woman rabbi. The orange is an act of defiance, a symbol of a new tradition that celebrates gender equality.

Does it matter if it’s true?

Here’s what actually happened. Dartmouth Jewish Studies professor Susannah Heschel was speaking to a Jewish group at Oberlin College in Ohio. The students had written a story in which a girl asks a rabbi if there is room for lesbians in Judaism, and the rabbi rises in anger, shouting, “There’s as much room for a lesbian in Judaism as there is for a crust of bread on the Seder plate!” Heschel, inspired by the students but reluctant to put anything as unkosher as leavened bread on the Seder plate, used a tangerine instead.

The orange, then, is not a wild act of defiance, but already a compromise and modification. The shouting rabbi is not an actual person but an imagined, simplified foe.

It matters that it’s not true. From the two stories of the orange, we learn the central lesson of Reform Judaism: that myths are cultural inventions built to suit the values of their day, idealizations and simplifications, changing as our values change — but also that only limited change is possible in a tradition-governed institution. An orange, but not a crust of bread.

In a way, my daughter and I are also oranges: a new type of presence in a Jewish congregation, without a marked place, welcomed this year, unsure we belong, at risk of rolling off.

In the car on the way home, my son scolded me: “How could you have said that, Dad? There are people in the congregation who take the Torah literally, very seriously! You should have seen how they were looking at you, with so much anger. If you’d said more, they would practically have been ready to lynch you.”

Due to the seating arrangement, I had been facing away from most of the congregation. I hadn’t seen those faces. Were they really so outraged? Was my son telling me the truth on the way home that night? Or was he creating a simplified myth of me?

In belonging to an old religion, we honor values that are no longer entirely ours. We celebrate events that no longer quite make sense. We can’t change the basic tale of Passover. But we can add liberal commentary to better recognize Egyptian suffering, and we can add a new celebration of equality.

Although the new celebration, the orange, is an unstable thing atop an older structure that resists change, we can work to ensure that it remains. It will remain only if we can speak the story of it compellingly enough to give our new values too the power of myth.

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Revised and condensed from my blogpost Orange on the Seder Plate (Apr 27, 2016).