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Bayesian evaluation for the likelihood of Christ's resurrection (Part 1)

March 22, 2016

Let's say that you're meeting someone new. You talk for a while, and the conversation turns to birthdays. You reveal that you were born in January, and your new friend says, "Oh, really? I was born in January too!" He seems earnest - he's not obviously joking, sarcastic, or ingratiating. From the little you know of him, he's not any more likely to be delusional or deceptive than anyone else.

Now, based only on his earnest word, would you be willing to believe that your new friend really was born in January? Note that I'm not looking for 100% certainty here. A willingness to entertain the idea, to give it at least a 50-50 shot of being true, is all that's required.

Also note that I'm not asking whether this event is likely to happen. Obviously, the probability that you and a random other person shares the same birth month is about 1/12, so it may be said to be "unlikely". Rather, I'm asking whether you would believe this person, given that this unlikely event has already occurred.

So, how would you respond? Would you say, "I find your claim to be highly dubious. There's only 1/12 chance that you were born in the same month as me"? Or would you simply reply, "Oh, hey, that's neat!"

I'm going to assume that you're willing to believe your new friend. I think you'll agree that it takes a special kind of jerk to say "I don't believe you. You must be lying or mistaken. It's just too unlikely for us to share the same birth month". In that case, what if it turns out that you share the exact same birthday? You mention that you were born January 23rd, and he claims the same. Would you still believe him?

Let's continue the same line of thought: what if you then tell him your mother's birthday, and what do you know - it turns that the date is also his mother's birthday! Your fathers, too, turn out to share a birthday. "Wow", he says, "so the three members of our family all share the same birthdays - amazing!" Would you be willing to believe him on this?

If so, at what point in comparing family birthdays would it become too unlikely for you to believe? That is, if you continued on to compare your grandparents and uncles and cousins, and they all continued to have the same birthdays, at what point would you say "I cannot believe this - this is too unlikely to be true", in spite of your friend's earnest insistence?

Decide on an answer, and remember it. Write it down somewhere. We'll come back to this answer in the coming weeks. Make a firm statement like, "I would be willing to believe up to 3 shared birthdays - myself, mother, and father - but if he claims 4 or more shared birthdays I would begin to be skeptical".

Let's try another example. Let's say that you run into an acquaintance whom you haven't seen in a while. You exchange greetings and ask how he's been recently, and he excitedly tells you - "Guess what! I've actually won the jackpot in the lottery last month! I'm rich!" As before, he seems earnest - he's not obviously joking, sarcastic, delusional, or deceptive. Would you believe him, based only on his earnest word? Again, only a willingness to entertain the idea, just granting a 50 - 50 chance of it being true, is all we're looking for here. Would you give him at least even odds that he's telling the truth?

And if you would, how about if he claims to have won two consecutive jackpots? How about three? At which point would you say "That's just too much for me to believe"?

Next, let's switch over to other gambling games. Say that a friend claims to have had a very lucky night at the card tables. He says that he got a royal flush in a 5-card stud poker game. Would you believe him? What if he claims to have gotten two royal flushes last night? What if he claims three? At what point would you say, "I don't believe you. You seem earnest and all, but the chances of that happening are just too small"?

How about if he were playing Texas Hold'em, and claims to have had multiple pocket aces? Say that he claims to have had two, three, four, or five pocket aces last night. At what number does it become too unlikely to be true, despite your friend's earnest claim?

We can ask similar kinds of questions in many different ways. What if someone claims to be born as a part of twins, triplets, quadruplets, or quintuplets? What if someone claims to have recently been struck by lightning? Or that they were a victim of two or three such strikes?

Remember, in all these cases, that we're not looking for certainty. Just a willingness to grant even odds - a 50-50 likelihood for the statement is true - is enough to say that you'd believe your friend. Also, we're not asking whether these scenarios are likely; rather we're asking if you'd continue to believe this earnest person, despite the fact that he's claiming that an unlikely event happened.

Answer these questions. Give a specific number in each case: we want answers like "four royal flushes" and "two lightning strikes". Write them down somewhere - we'll come back to them later.

Next week, we'll turn to the question of Jesus's resurrection.


You may next want to read:
Basic Bayesian reasoning: a better way to think (Part 1)
The role of evidence in the Christian faith
Another post, from the table of contents

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