Pascal’s Wager

1. Ambiguity, Pessimism, and Religious ChoiceTigran MelkonyanProfessor of EconomicsUniversity of Nevada, Renotmelkonyan@cabnr.unr.eduandMark PingleProfessor of EconomicsUniversity of Nevada, Renopingle@unr.edu

2. Pascal, 1670, Pensees 194:…I know …I must soon die, but what I know least is the very death I cannot escape.

3. Adam Smith, Theory of Moral Sentiments, 1759, Part I, paragraph I.I.13: “The foresight of our own dissolution is so terrible to us …. [that it] makes us miserable while we are alive… . The dread of death [is] the great poison to happiness…. it afflicts and mortifies the individual.” • Adam Smith, Theory of Moral Sentiments, 1759, Part I, paragraph I.II.11: Fear … is a passion derived altogether from the imagination, which represents, with an uncertainty and fluctuation that increases our anxiety, not what we really feel, but what we may hereafter possibly suffer.

4. Pascal’s Wager Pascal, 1670, Pensees 233: “God is or He is not. But to which side will we incline? …What will you wager? … You must wager. It is not optional… Let us weigh the gain and the loss in wagering that God is. … If you win, you win everything, if you lose you lose nothing. Do not hesitate then; wager that he does exist.”

5. Pascal’s wager: Presents faith as a choice made under uncertainty • Jeff Jorden, Chapter 1, Gambling on God: Essays on Pascal’s Wager: “Pascal’s wager brought about the advent of decision theory. • Iannaccone, L.R., Journal of Economic Literature, 1998: “For the most part, however, the problem of religious uncertainty has received little attention and scarcely any formal analysis.” • Theory Question: What theoretical conclusions about the faith decision can we derive from decision theory? • Policy Question: What should evangelists do to win converts?

6. Dilemma Version of Pascal’s Wager • The Dilemma: Better to believe in God if God exists, and better to not believe in God if God does not exist. God either exists or does not exist. What to choose?

7. Religion 1 True Religion 2 True Adopt Religion 1 Adopt Religion 2 A Model of Religious Choice • Definition of Religion: A set of beliefs about the afterlife, and an associated set of prescriptions for how to live life. • Does not presume belief in a supernatural being (God or gods) • Atheism: As much a religion as any theism • Definition of (Religious) Faith: The act of adopting a religion • Involves courage, not matter what choice is made, because one face uncertainty and possible regret • It is courageous to be an Atheist and courageous to be a Theist. • Fundamental Assumptions: • Religions are mutually exclusive: If one is true, the others are not. • For each religion, finite expected payoffs can be assigned to truth states.

8. Two Extremes and a Middle Ground • Total Ambiguity: Cannot use the concept of probability at all when considering alternative religions (i.e., ) • No Ambiguity: Can formulate a unique probability distribution over the alternative religious “truth” states (e.g. ) • Middle Ground (General Model): Can identify a probability range for each religious truth state (e.g. )

9. Alpha Maxi-min Expected Utility Preferences • Linear combination of maximum expected utility and minimum expected utility, weighted by the “degree of pessimism.” • DM is total pessimist • DM is total optimist • DM is the general Hurwicz decision maker

10. Parameterizing Ambiguity • Utility obtained from religious alternative x is a linear combination of that obtained from the no ambiguity case, where an “anchor probability distribution” is applied and the total ambiguity case, where no probability distribution is applied

11. Results • Theorem 2: The qualitative impact of a change in the degree of ambiguity depends upon the degree of pessimism. • When DM is sufficiently pessimistic, the utility of any action decreases as ambiguity increases. • Conversely, when DM is sufficiently optimistic, the utility of any action increases as the degree of ambiguity increases. • Intuition: Increasing ambiguity admits additional probability distributions, some of which will increase max expected value and some of which will decrease min expected value.

12. Results • Theorem 3: DM will choose the “anchor choice” when beliefs are sufficiently unambiguous, while the “Hurwicz choice” will be chosen when beliefs are sufficiently ambiguous. • Decreasing ambiguity makes the anchor probability distribution more relevant, and makes the degree of pessimism less relevant • Increasing ambiguity makes the gap between the maximum outcome and minimum outcome more relevant, and makes the anchor probability distribution less relevant • When the degree of ambiguity is high, • Optimism points DM toward the max max choice • Pessimism points DM toward the max min choice.

13. Results • Irrelevance and Dominance Under Complete Ambiguity: • Complete ambiguity removes impact of probabilities and places emphasis on payoffs • A religious alternative is irrelevant, under complete ambiguity, if its max-max and max-min are each less than some other alternative. • A religion is dominant under complete ambiguity, if its max-max and max-min are each greater than those for all other religious alternatives. • Evangelism Implications: • Emphasize high payoff (e.g., heaven) for adoption • Emphasize high penalty (e.g., hell) for non-adoption • Ambiguity can help win converts by de-emphasizing probabilities

14. Results • Theorem 4: Optimists are more likely than pessimists to find appeal in a choice with a large difference between the largest possible payoff and the lowest. • Conversely, pessimists will tend to find more appeal in a choice where this difference is small.

15. Practical Application • Facts (2008): Christianity and Islam are the two largest religions in the world, with 2.1 billion and 1.5 billion followers, respectively. By comparison, the number of Atheists is small, included among the 1.1 billion classified in the catch all category atheist/anti-theistic/anti-religious/secular/agnostic. • Question: Why is Atheism unpopular relative to Christianity and Islam? • Answer: Ambiguity (combined with relative expected payoffs). Atheism will not likely be either the max-max (optimistic) or max-min (pessimistic) because it does not offer heaven for adoption or hell for non-adoption • Ancillary Prediction: Atheists will be more pessimistic, as a group, than theists, (because pessimists are disproportionately attracted to religions with a smaller gap between the best and worst possible outcome.) (There may be hell expected for non-adoption, but no heaven expected for adoption.)

16. Unanswered Questions • Do people create God? Or, does God create people? • Do people act in faith by choosing a religion? Or, does God give people the faith that leads them to their religion? • Our theory does not answer these questions. • It could be that religions have been developed by humans, and have evolved toward a form that is consistent with how people, with varying degrees of pessimism, make choices under varying degrees of ambiguity? • It could be that people have been developed by a God who values faith, so faith can be expressed as people make religious choices while facing the ambiguity associated with death.

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