Re: Laskey's wager

[Jonathan Weiss]

At 6/23/99 06:34 PM, Kathryn Blackmond Laskey wrote:
>I would like to tell a very personal story, to get the reactions of people
>on this list to an interesting intellectual puzzle.
...
>Now, I would like to ask you to consider:� what probability do YOU place on
>the propositions:
>
>- That God exists?
>- That God really talked to me and redirected my life at a critical moment?
>- That writing this email is one of the things God is calling me to do?
>
>Let me also ask you:� Are the probabilities you assess your "real beliefs"
>(what does that mean)?� What probabilities to you think you SHOULD assign
>(not in a moral sense, but in a pragmatic sense)?
>

Kathy,

There are lots of things in this and your other recent writings that I'd really enjoy discussing with you in private.  You have a great deal of courage (more understandable in light of the experiences and decisions you describe, but still remarkable), and I look forward to a long discussion sometime (probably after UAI!).

However, let me publicly address an interesting decision-analytic view of your initial "critical" decision and more to the point, of your continuing decision to accept the validity of your original decision.  It seems you have turned around Pascal's payoff matrix so that the payoff for believing in God (although with a somewhat different interpretation of "God") is higher than for not believing, whether or not God exists. 

In the example as you've reported it, you have a decision problem in which the prior probability is irrelevant.  Suppose somehow (don't ask me how) you received conclusive (to you) proof that God does not exist.  Would it change your belief?  Would  you change your behavior?  Or would you continue on what is a productive and rewarding path regardless?  (Or if the position of God is vacant, might you decide to fill the position with a God of your own invention, who would always exist for you? -- Sorry, I'm straying from my main point.)


I find it difficult to talk about "deciding to believe", much the same as I would to talk about "deciding to fall" if I found myself somehow in midair after being pushed off of a high platform.  A graduate school buddy of mine used to ask people whether they believed some proposition (e.g. "more than 25 percent of 30-year-old males are bald") and then, whatever they said, would jokingly offer them a quarter, then a half dollar, etc. to change their beliefs.  What does this mean?  In a similar vein, is it sensible to "decide what your prior probabilities will be"?

Now, it's fine to talk about "deciding to act as if you believe", or accept a bribe to change your verbal report about a belief, or to decide to adopt a hypothetical set of priors.  But that's not the same thing as "deciding to believe".  I'm sure there must be many cases where someone was intellectually persuaded that it would be beneficial to believe in something (e.g., faith healing) but couldn't just decide to believe, even if there was evidence (e.g., a parade of healed sufferers).  And on the other side, there is the Spanish Inquisition ("Nobody expects the Spanish Inquisition!") -- it certainly changed some people's behavior, but did it change anybody's beliefs through decisions based on rational self-interest? 


Parting questions:  Does it make any sense to define a probability over an event whose states cannot be discriminated, even in the limit, by potential observations?  (This goes beyond the usual clarity test, although that too is an issue as pointed out by others.)  Would "eternal damnation" be considered an observation, or are we limited to observations in the physical world we now inhabit?  Regardless of your degree of belief in God, who will take the following proposition:  "You pay me $1 today, and tell me whether or not you believe God exists; as soon as God's existence is definitively proved or disproved, I will pay you $1000 if you are right and if you are wrong I will refund your $1."  (That might be an even better deal than the life insurance companies have -- at least they eventually have to pay somebody.)