RE: How Quaint and a revisit of the Atheist Wager

Actually, that also points up one of the major issues with Pascal's Wager, on which the Atheist Wager is based.

Pascal's Wager is basically an application of game theory. It's of some historical interest because it predates the whole idea of game theory by more than a century, if I remember correctly. But now that there's a proper theory to analyze it, it's pretty easy to see where the flaw in the logic is.

At each step of the game, you have to lay out all the choices, not just some of them. Pascal identifies the choices as simple belief or disbelief. But there are literally thousands of variations on the "belief" theme out there, all of which are mutually incompatible: belief in one implies disbelief in all of the others.

Realizing that, the question is no longer a simple one - the player has completely inadequate information on which to base the decision, which really only leaves chance as an option. At that point, Pascal's Wager becomes essentially indistinguishable from the Atheist Wager, formulated the way you did.

However, game theory gives us ways to still evaluate this revised game and decide the "optimal" strategy. There's a cost associated with each "belief" choice during life, representing the sacrifices one makes for such belief (tithing, time spent in worship, etc.) - typically the "atheist" choice is normalized to represent the zero cost. Then, there's the cost after death - if you chose a correct "belief" option, this is a very high negative cost (meaning, it's a good thing), while an incorrect "belief" is a very high cost (hell, damnation, whatever), and a correct "atheist" choice is zero (nothingness).

The only two distinct strategies available are: "atheist" or "belief" (in some randomly chosen religion). Any given strategy has a very low probability, p, of being "correct", but we can compute an "expected cost" for each strategy.

Assigning some variables, let p be the probability that "atheist" is the correct choice. Let q be the conditional probability of the chosen religion being the correct choice, given that atheist is the wrong choice. Let H be the value of the heavenly reward for making a correct "belief" choice (this is a negative number, as positive numbers represent costs), let D be the cost of damnation, let W be the cost of worship.

The atheist strategy has value zero if correct, and costs D if incorrect, so the expectation in choosing atheism is D(1-p). Any given belief strategy has a cost of W+H if correct, a cost of W+D if another belief was correct, and a cost of W if atheism is correct. The expectation is Wp + (1-p)(q(W+H) + (1-q)(W+D)), which simplifies to W + Hq(1-p) + D(1-p)(1-q) with a little algebra.

So, atheism is the better choice (has lower expected cost) iff:

In other words, if:

The magnitude of human emotional response (our assessment of how good pleasure is or how bad pain is) is roughly logarithmic with the magnitude of the stimulus, and since heaven and hell both represent large-magnitude stimuli, our valuation of them varies with their logarithms, which tends to reduce the difference as the stimuli get larger. So on that assumption, the specific values of the variables with capital letters grow logarithmically.

The left-hand side of the equation gets limited by q - which is inversely proportional to the number of belief options, which we've suggested is at least as small as 10-3. The D-H term is a large number - H is a large benefit (negative number) and D is a large cost (positive number), so the result is large - but remember they grow logarithmically, so they have to be truly enormous to overcome the q term for even relatively modest values of W.

This isn't a complete analysis, though. There's the possibility that none of the world's belief systems are correct, and all choices in the analysis result in damnation, in which case we have to introduce another small probability measure and include an almost infinite number of possibilities for the "right" choice. In the long run, this increases the probability of damnation - roughly equivalent to an infinitely tiny q. So the more belief options there are available, the better atheism looks.

Another point is that, in practice, the cost of worship, W, isn't uniform across all belief choices - it's much easier to be a Unitarian Universalist than to be an Orthodox Jew or a Sufi Dervish, for example. Some belief systems may even have a negative cost of worship - Wicca looks pretty fun, what with the ritual sex and all.

Which all basically comes down to a mathematical justification for your statement that "so many people also believe in a completely dissimilar system that there's an equal chance that your god/dogma is a complete farce."

I have a copy of The Cambridge Companion to Atheism, an interesting book that gives a lot of technical, theoretical information about atheism and how it relates to other world religions. One of the interesting statistics they have is that atheism correlates positively with intelligence and education - academia and science are the bastions of atheism. Before I read it, I had assumed that to be true, but I assumed that there would also be a positive correlation with hard science vs soft science. I figured it would be the physicists and mathematicians who were the most atheist, but that's not how it turns out. It's the anthropologists who are the huge standouts - the survey indicated that 65% of the anthropologists (among the faculties of large American universities) answered "none" to the question, "What is your present religion?" Compare this to only 33% among physicists or mathematicians.

Apparently, the more you get a chance to look at other peoples' religions, the more obvious it becomes that the one you grew up with is just as much a human invention. You can give a pretty solid proof, using only undergraduate level physics, that the gods described by virtually all major religions are overwhelmingly unlikely, but it seems that seeing is still believing - or rather, disbelieving.

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