12 August 2007

Pascal's diversified portfolio


I have to let you in on a secret - I don't read that many blogs. But I have a select group that I read as much as humanly possible. Which is why I get immensely pleased when I come across a blog post that I like.

This is one. And, as always, Bronze Dog does a smashing job. Which he referred to a post at PZ Myers' excellent blog (which I read less regularly), Pharyngula.

These posts are about something written by the increasingly unbalanced Scott Adams who created the Dilbert cartoon. I normally like Dilbert. Not passionately or anything like that, hell, give me Ernie/Piranha Club any day. But I find it better than some of the cartoons out there. Fred Basset, anyone?

Adams has been writing all sorts of weird shit in his blog lately, and given his comic timing (I love bad puns) in the strip, you would have to say that he is most definitely not taking the piss.

I mention this because if there is one thing that is guaranteed to make me angry, it's mention of this stupid concept.

Pascal's Wager has always been something that has annoyed me. The first tine that I heard it was at school when my roommate - who was previously an atheist from an atheist family - suddenly found religion in a big way. And this was one of the fastest transformations I ever saw - it all took place over a two week period.

Anyway, he ran Pascal's Wager by me. For those who need their memory refreshed, Pascal's Wager goes like this:

If I believe in God, and I find out that He doesn't exist, then I have lost nothing.

If I don't believe in God, and I find out that He exists, then I have lost everything.


Pascal had formulated a lot of what became known as Game Theory, and his reasoning was sound, except that he didn't realise one thing - he had made the assumption that only the Judeo-Christian-Islamic god existed.

Or, to put that another way, if God promises annihilation for non-believers, than what about non-believers in Shiva, the Destroyer?

Anyway, Dog suggests the following alternate probabilities to Pascal's Wager about a deity of which we know no details:

1. What if the deity punishes people for doing evil deeds and rewards them for doing good deeds, with no regard for beliefs?

2. What if the deity punishes people for blindly believing in him and rewards them for thinking critically and thus doubting him?

3. What if the deity rewards everyone, regardless of what they do or believe?

4. What if the deity rewards people on a random basis?

5. What if the deity only punishes those who step on cracks in a sidewalk?

6. What if the deity doesn't care at all about human beings and only thinks about them as a meaningless, uninteresting by-product of a brane/string experiment he conducted 13.7 billion years ago?

7. What if the deity just throws everyone's souls up on the roof, where they get stuck?


And so on and so forth. I thought of another possible outcome:

8. What if the deity is a liar?


Oh, the confusion that one would cause. And of course, this is before consideration of competing deities, to whom all the outcomes above might also apply.

Being the financial nerd that I am, I thought at that I'd take a view of this through the window that is Portfolio Theory. Portfolio theory says a variety of things, but the one most important thing that comes out of portfolio theory is this: for a set level of risk, you can increase your return by diversifying your portfolio.

Or to put that another way, "Don't put all your eggs in the one basket."

So let's take a diversified approach to investment in a god as proposed by Pascal:

Option 1 - Belief in god A but he doesn't exist.

Believing in a god would appear to have a rather high risk/return trade-off - the potential return is eternal life, however, your potential risk for this return is also infinite and given that there are quite a few gods out there, who knows if you've picked the right one?

Normally, you can't say that infinity A is greater than infinity B, so there is no way of knowing if the risks outweigh the potential returns, but you can say this: the chance of you picking the wrong god is enormous from the outset.

So for us to load all our belief credits into the one slot machine is obviously a high risk investment.

Option B - Belief in a portfolio of gods.

This would appear to satisfy a prudent approach to investing in a high risk asset class, which is what theistic belief clearly is. The problem with this is that there are many more gods that we can read about before we can profess a belief in them.

I should clarify from the outset that my problem with the word "belief" is another thing that Dog expressed frustration with in his post. Is it enough to just say that you believe in a deity?

Most theists would say yes to this. After all, quite a lot of them will say they believe, however they may actually believe something completely different. However, this is not what most of the rest of us understand by the word belief. The problem with this perspective is that a token statement of belief is clearly not belief, if the person who says it believes something completely different.

Most of us understand belief to be what we predominantly think is the case about something, when we do not know the answer. For example, if we're holding an apple, and we drop it, we know it's going to hit the ground. This is called "knowledge". However, if we drop the apple, and we think that a magic invisible hand is going to catch it before it hits the ground, this is called "belief".

There is nothing that could cause us to "know" that this magic invisible hand will catch it - you would have to be pretty darn sure to say that you knew that a hand or other such appendage would catch it.

So obviously, while belief implies some level of disbelief, it is an outright lie to say that you believe in something when you don't.

Which means that for us to have a meaningful definition of belief for the purpose of this post, we'll have to eliminate those who only pay lip service to believing in something.

In other words, we'll define belief as being that where we've studied the deity in question a little bit and decided that we have more than just a token level of faith that they'll be there to greet us at the other end.

So it is possible to believe in a portfolio of gods based on this approach. How do we construct this portfolio?

Those who understand portfolio theory know that there are many ways to construct this portfolio. In investment, there are active methods that look at various different criteria, all of which involve chopping and changing between different assets in order to reduce risk and maximise return.

There are also passive methods where assets are bought and held for a long time based on a number of criteria, though normally, the criterion is a popularity measure, such as a major index. These are all designed to get a return that matches the index or some other benchmark.

I propose that we appeal to popularity and create a passively managed index portfolio based on popularity. This makes it easy.

Our Judeo/Christian/Islamic god gets in first.
The Taoist pantheon is next - the Jade Emperor is a particular favourite of mine - followed by Vishnu, Brahma and Shiva. The remaining spots in the core portfolio would be filled by the remaining major deities out there.

Now on to creating a satellite investments sub-portfolio with lesser deities. I've always had a thing for Huitzilopochtli and Quetzalcoatl, so they're in. And just because I'm Australian, the Rainbow Serpent gets the nod, too. Flying Spaghetti Monster and Invisible Pink Unicorn? They're in.

How much of an investment do we make in all these deities?

Reading the holy books of each and professing a belief should be enough I think. We don't want to make this too onerous.

And this is where our diversified approach cleans up - you get as many bets into different deities as possible.

It also minimises the downside of the other possibility that Pascal overlooked:

What if all the deities exist, and they have to fight amongst each other to see who gets to punish unbelievers?

What better way to do this, than to reduce those deities who are out to get you?

Of course, prudent investing also says to wait until the evidence is in before committing. For me, Pascal's Diversified Portfolio is just going to have to wait until I have enough evidence to start putting my portfolio together. I don't want to find the religious version of Enron in my portfolio.

My advice?

Theistic belief is the kind of high risk/high return investment that makes derivatives appear positively safe by comparison.

This is for ultra-ultra-ultra-aggressive investors only, folks.

10 comments:

MichaelBains said...

I think that, if #6 is True®, then we are merely bacteria in the Poop of teh Godz.

RAmen.

Dikkii said...

RAmen to that - and this really begs the question, wouldn't an entity capable of this kind of engineering be really uninterested in the detail? Which is what we all are.

Greg said...

Interesting method you're proposing, Dikki.

I like the idea of getting some more complex financial instruments happening too. What about "swaps" - people could acquire the right to swap afterlives with someone from a different religion. "Sure, I'm eating this pork seethed in its mother's milk ... but I've got 'swaps' with the Catholic over the road."

The measures are interesting too. Following the Fama-French thing, perhaps we could use the popularity index to look at "(Holy) Book-to-Market value" opportunities. Under-appreciated faith may trade at a premium.

Of course, we'd need an equivalent for the cross-variance scores between the individual religions to find the uncorrelated and counter-cyclical picks. This might not translate so well, but it seems to me that Mennonites and the Amish are more similar than, say, Sufism and the cargo cults. Could "time since bifurcation" be a suitable proxy measure for similarity?

Maybe "number of heretics killed divided by subtlety of theological difference" might be a better measure of religious closeness.

KitKat said...

He would reach out His Noodley Appendage and catch the Apple.

Dikkii said...

G'day Greg. Good stuff:

What about "swaps" - people could acquire the right to swap afterlives with someone from a different religion.

Oh, I like this idea. I like the idea that jews and muslims who eat bacon can get some kind of "pork-products credit" from catholics. It could be like a carbon credit trading market.

Under-appreciated faith may trade at a premium.

You'll note that for simplicity, I went for a passive portfolio. Future opportunities could explore a more actively traded market in faith - could we create a value vs growth dichotomy?

Of course, we'd need an equivalent for the cross-variance scores between the individual religions to find the uncorrelated and counter-cyclical picks. This might not translate so well, but it seems to me that Mennonites and the Amish are more similar than, say, Sufism and the cargo cults. Could "time since bifurcation" be a suitable proxy measure for similarity?

This could prove the undoing of my suggested portfolio as it is. You'll see that based on popularity, the Judeo-Christian-Islamic god is vastly overweighted in the portfolio. Where only a token level of belief is required, maybe we could invest that token amount, and then use the rest for deities who don't correlate quite so closely.

I would concur that Time Since Bifurcation is a very good measure for similarity, albeit if we used the inverse of the measure.

Maybe "number of heretics killed divided by subtlety of theological difference" might be a better measure of religious closeness.

Again, such a measure would see us overweight on the Judeo-Christian-Islamic god thanks mostly to the inquisition and the lack of substantial theological difference between the world's major monotheistic religions.

But I'm sure this is a problem that we could get around.

Dikkii said...

Kitkat, you have faith that could move mountains.

KitKat said...

I actually think Pascal's Wager is pretty much why so many of those capitalist pig A-merrycans believe in God. It's like insurance to them.

I particularly like Bronze Dog's points #1 and #2.

If this God is as omnipotent and wise etc. as they say, surely he/she/it doesn't have such an ego that non-believers are doomed to hell simply for not sucking up to him/her/it? Surely this all-seeing, all-knowing dude can see through the bullshit?

Dikkii said...

You know Kitkat, I once said to a fundamentalist Christian who was proselytising at Melbourne Uni, that, "If God exists, surely you don't think that he's going to approve of the toadying that you're doing?"

He tried for about 10 seconds to tell me that he wasn't sucking up and then gave up and went away.

I maintain that if God is Omni-insecure, which is what appears to be the party line, the grovelling expressed by your average fundie is still going to try His patience.

MichaelBains said...

Pascal's Wager is pretty much why so many of those capitalist pig A-merrycans believe in God. It's like insurance to them.

As funny as some might find it, that is still too frickin' true. I mean it to the extent that I hear it being the "reasoning" by nearly as many folks as have given any other reason.

Probably the only reason I've heard from more people is the stupidest one of all: "Belief in God(s) has been around forever so it MUST be True!"

The reason I don't cruise the Atheist Blogosphere so much anymore is that such silliness is so seriously simple to contradict, and I get saddened seeing teh nutters' cluelessly skull-slammin' themselves against reason's rocky shores.

I've enough nutterdumb of more mundane varieties in my own silly life, thankyaverymuch.

Errr... Yeah. {-;

Dikkii said...

Probably the only reason I've heard from more people is the stupidest one of all: "Belief in God(s) has been around forever so it MUST be True!"

MB, this is why a lot of normally rational people go for, not just religion, but a variety normal, household and garden variety woo.

And you're right, it's frustrating that us rational folk feel like we're banging our heads against a wall a little bit.

But the fact that it still annoys us should at least speak volumes about the disruptive influence that it continues to have on our lives, even if we're not actually religious ourselves.