BCC: Trusting GAs More than Ourselves

[pelagius]

There is an interesting post at By Common Consent entitled, Trusting GAs More than Ourselves. I want to comment about it here because, well, I just prefer posting at the guard. The BCC post is a response to the idea that even if you believe GA's are clearly fallible and that they make mistakes frequently, as long as you believe that GAs have a higher probability of being correct then you do, then you should follow them as if you believe they are infallible (see, Authority Roulette). The BCC post changes the setting in a couple of ways: (1) the post posits that most decisions aren't mutually exclusive. You can choose an intermediate position between your or really aggregated rank and file members' best judgment and a GA's judgment. For example, if a GA says you should have 4 snicker bars a day but an on average rank and file members think 2 is optimal, then you may choose to eat 3 as an intermediate position. (2) On average general authorities are more correct than you or rank and file members (they have less bias on average). (3) If you aggregate lots of rank and file members opinion then the average bias will still be large but the position will have virtually no variance and since a single GA opinion or even an aggregate of 15 members is likely to have significantly more variance. Given that the author argues that,

A simple average of all the non-General Authority perspectives and the insights of the General Authority — i.e., a composite position that treats the General Authority as just another voice — will really be no different from the non-General Authority perspective discussed in the previous paragraph. However, if the General Authority is assumed to have unusually low mean squared error, then a weighted average of the General Authority and non-General Authority perspectives may sometimes be better than the General Authority perspective alone, or the simple average of rank-and-file perspectives alone, or (certainly!) our own individual perspective alone. (Mathematically, a large enough sample of rank-and-file perspectives will always, and indeed should always, totally swamp a single General Authority perspective, given the assumption above about biases. But including a higher-quality General Authority perspective may substantially improve a perspective based on an average of a small or moderate number of rank-and-file perspectives.)

I am not on the assumption (3) train but I want to evaluate the "model" on its own terms. Are the implications in the preceding paragraph correct? Yes, but I don't think they're very sharp and they really don't get at the heart of the implications. Furthermore, the model is overkill. It doesn't need to be so strong in order to make the claim that it may to be optimal to incorporate the position or opinions of non-GAs and GAs for maximum spiritual benefit. Assumption (3) is just not needed. Even if GAs have less bias and less variance it still my be optimal to take a position that is a weighted sum or average of the GA position and non-GA position. Non-GA information may still be very useful in terms of your spiritual life.

Okay, this post is going to get geeky. Sorry, guys. I want to reformulate the model by noticing that it is basically spiritual portfolio theory. This is a simplification but it really goes through without loss of generality (I think). First, we basically have two spiritual assets. The first is the GA asset. Let's suppose it has a payoff of 10 (the higher the payoff the closer you become to spiritual truth or God, etc), but that the standard deviation of the payoff is 20. The second is the crowd asset (non-GA asset). Really this asset is an equal-weight average of 1000s of rank and file members positions which causes the variance of the payoff to go to zero. However, the payout is lower: 5. What are the possible positions? Well, because the crowd asset has no standard deviation, all the feasable allocations are on the following line:



The implication is clear here. Every possible position is optimal in the sense that that each gives you the same spiritual payoff to risk tradeoff. Thus, a person can believe that GAs have spiritual insight and that following the direction of GAs will give a higher spiritual payoff than following non-GA opinion, but they choose not to. Why? Because they are more risk averse. It's an interesting implication, but it is also a bit weird and I ultimately I wonder how useful it is. Furthermore, it is the main implication of the "model."

However, the third assumption isn't even needed to get the desired implication of the author: that it my be optimal to incorporate non-GA information. Assume the GA asset payout is the same: E(payout) = 10 and the standard deviation is 20. This time, assume that the non-GA asset payout is 5 and the standard deviation is 25. So the GA asset is superior in ever way. It produces higher spiritual payout with lower variance. However, as long as the correlation between the two assets are low then it may be optimal to include non-GA information. For example, assume the two assets are uncorrelated then the payoff space is the following:



Everything, above the minimum variance position may be optimal and is some positive combination of the non-GA and GA information. To me this is a better setup. A person chooses to use GA and non-GA information to come-up with a spiritual position and that position gives them the highest possible trade-off between spiritual risk and spiritual payoff. Furthermore, the person never completely ignores the GA position. They always include it positively because just using the non-GA asset is clearly sub-optimal. Notice, neither of these implications comes from the fact that the person thinks that the non-GA information is superior over any dimmension. The GA information has greater payout on average and lower variance. Non-GA information is useful in this model because it is not highly correlated and its effects are driven by a notion of spiritual diversification and not any notion that non-GA opinions are superior. I prefer this formulation; it doesn't reject the superiority of GA spiritual insight (for either the expected payout of variance), but it still preserves the notion that non-GA information is useful and maybe vital.

[Archaea]

If I read what you're saying in technical terms, you are stating, a person will be benefitted from a maximum payout if one incorporates a weighted average of GA perspective in tandem with a nonGA perspective?

[pelagius]

Originally Posted by Archaea

If I read what you're saying in technical terms, you are stating, a person will be benefitted from a maximum payout if one incorporates a weighted average of GA perspective in tandem with a nonGA perspective?

That is pretty close to what I am stating. Technically, I am arguing that a person may benefit from GA and non-GA perspectives because it gives them a better spiritual benefit to spiritual risk trade-off given their preferences for spiritual benefit and risk. Furthermore, this implication still exists even though I assume the GA perspective is superior by itself in every way. I think that is a cooler result than the original post I linked to. He got a similar bottom line, but in my view had to use a back hoe to get it. I used a spoon (sorry, a little hyperbole). Its a spiritual diversification argument. Ultimately, I am not sure how useful it is, but I do like the fact that it presents a potential benefit from GA and non-GA spiritual perspectives even though it accepts entirely superior GA spiritual insight. Of course, the problem is that very few people like to frame spiritual things in terms of portfolio theory. For me, its a joyful experience.

[fusnik11]

Not to go down too far of a tagent, but I interpret the temple pagenatry as instructing us, not to follow our physical prophets, but to follow the spiritual ones that God places in each one of us. In other words, full spiritual experience, full communion with God occurs when we stop trusting the flesh of man and cleave unto the spiritual arm of God. And I think the temple explicitly teaches us this principle. Thought for those that go to the temple, the messengers presented aren't physical beings, they aren't even born yet, they are, IMO, a spiritual manifestation of our relationship and dealings with God. God deals with each one of us individually and tells us what each one of us needs to know.

Now when I figure out how to do that I'll let ya'll know.