Thanks, I'd love to see what you come up.

I agree that it is a big simplification, but I don't know how much of a practical problem that is, given that a lot of people can get things wrong that would be fixable even by the two-resource model. Still, I fully support having a range of different models of different complexities!

This is a great formalization of a three-resource model - time, money and mental energy - which clearly gives much better answers than a two-resource model of only time and money in cases where mental energy is a relevant resource, which is often true.

Despite that, it still feels woefully incomplete/simplified, given how important it is to get something like this right. One of these is that there are lots of resources (N is large) and trading is not cost-less between them; you have to draw the line somewhere, however, and can draw it as needed by a given exercise. I think more importantly than that, it comes down to the fact that while money is fungible and savable, time and mental energy (and many other key resources) aren't. Resources that are use-it-or-lose-it, but vital to pretty much everything, like time, have highly variable marginal value, which makes the calculations very different than described in the paper. I'm going to try and expand/formalize this concept more.

I throw the box into the corner of the room with a high pitched scream of terror. Then I run away to try to find thermite.

Edit: then I throw the ashes into a black hole, and trigger a True Vacuum colapse just in case.

The article's conclusion is that "people decide they want to convert for emotional reasons, but some can't believe it at first, so they use apologetics as a tool to get themselves to believe what they've decided they want to believe."

So we expect apologetic literature and speakers as a market niche wherever there are emotionally manipulative (claimed) rewards and punishments attendant on belief. Some rewards and punishments are quite real, like social status, praise, and condemnation. Others are fictional, like afterlives and the deep satisfaction of living according to divine law.

Similarly to mainstream religion, there is plentiful apologetic literature, speakers, and films for political ideologies. The social rewards of being in a political group are real; the future consequences that are promised if only enough elections can be won may or may not be real.

Given religions where beliefs are not rewarded or punished, we'd expect little or no consumption of apologetics. Shinto, neopaganism, and Unitarian Universalism fit that. However, there is certainly plenty of apologetic literature for secular humanist atheism, which also lacks the rewards/punishments. That looks to almost entirely undermine the hypothesis.

There is also basically no apologetic literature for believing in the greatness of particular sports teams, despite the large social rewards of being in a fanbase and the promised vicarious glory of psyching your team up for a win by your fervent support. OK, so to me the hypothesis is dead. Something more is going on than simple market response to rewarded/punished belief.

Any ideas what?

There were three times in my life when I consumed apologetics. First was when I was evangelical Protestant and it was a tool for the religious imperative of winning converts. Second was when I could no longer believe my childhood religion, but still believed in God and the importance of Jesus, and so I read the apologetics of other religions to see which was most likely true, and I ended up converting Catholic for a while. Third was when I became infatuated with the principled style of libertarian political ideology and needed the apologetics to "understand" why nothing fit.

Based on my own anecotal experience, then, my next hypothesis would be that apologetic argument and literature is demanded when people are (1) committed to a theory (for any reasons good or bad) and (2) also committed to acknowledging the facts, and (3) the facts don't fit the theory in a straightforward way, and (4) complex fits of facts to theory are tolerated.

Religions that propose explanations would then be expected to have apologetics, and religions that don't propose explanations would not. All political ideologies would be expected to have apologetics, because it's an unfortunate fact of life that the consequences of politics are very complicated. Secular humanist atheists, insofar as they propose explanations for life, the universe, and everything, similarly end up occasionally faced with bizarre and extraordinary scenarios that defy simple explanation, and so they have apologetics. Some sports fans may, after a loss, blame the coach, the refs, the weather, and other factors, but at least in my experience most are willing to believe the other team played better. Oddly, we even end up with pro-science apologetics sometimes; at least I remember my physics and chemistry professors spending inordinate time mis-explaining phenomena when they were committed to the phenomena being explainable primarily by that week's lesson.

It seems to fit. And it suggests that the process leading to apologetics can be interrupted at two places, as described elsewhere by Eliezer. First, don't be committed to a theory. Don't make a belief part of your identity. Let your beliefs be faithless and blown about by the winds of evidence. Second, count facts that require detailed explanations as contrary evidence even if the explanation is adequate. (This is not strictly Bayesianly correct but it seems like a good approximation.)

If you're the smartest person in the room, you're in the wrong room.

As a family with a highly aspirational high school student and as a public school board member in a community where we have recently extensively debated AP grade weighting, we have had many conversations on this subject. In my opinion, the energy in the debate is indicative of a society overly focused on simplistic quantitative measures. "Simplify and Exaggerate" is a media trend that dilutes rational thought on complex issues in many areas.

In my recent conversations with admissions departments and faculty of highly selective schools, the feedback we have often received is "follow your dreams", almost to heck with the scores. This is easier for them to say than it is for students to live based on the perceived pressure to show high signaling quality numbers, but I think it's worthy advice. It seems that admissions departments strive to be less formulaic (although there may be certain cutoffs). For example, I don't think that a highly selective university would necessarily reject a student not in the top 1% GPA if the rest of the application were compelling. A passionate and honest essay by Kevin about a desire to do great things in Micro Biology with supporting demonstrated activities and extracurricular studies may weight more than the 1% vs. top 5% (but probably not get a 50%er into Harvard).

On GPA weighting, this is an area where a guidance counselor letter of recommendation can be used effectively. If the recommendation stated that Kevin pursued a course in Micro Biology even knowing that it would damage his GPA, that would look very favorable. Guidance counselors can be sympathetic to this and effective to communicate unique academic records circumstances.

It seems that the constraint in finding great students (and for many of our successes) is not an issue with having inadequate human capital, but rather lacking the vision and motivation to follow our dreams. The top 1% will always apply to the best schools, but my sense is that great schools would rather have a top 5% student with a demonstrated passion to pursue their dreams rather than someone with high book smarts and human capital that was only focused on GPA. The key in successful college applications these days seems to be to share a portfolio to demonstrate the potential for future success as much as formulaic scores.

The choice for Kevin to take that Micro Biology class would be the one with more integrity to pursue his dreams and I'm sure that would have come out in other ways in the application. Great university admissions departments are not fooled by GPA pumping strategies, they strive to seek for other underlying qualities of future success. More often than not I think we all have a tenancy to do what we think will get us high signaling quality to others rather than take risks to pursue our dreams that often would have resulted in better ultimate success or at least educational failures that are more personally valuable than perceived external rewards.

The issue of "watering down" one's GPA by taking more classes is already being significantly addressed by colleges and high schools.

Most top colleges examine unweighted GPAs rather than weighted ones. Unweighted GPAs cannot be watered down by non honors classes, and have better predictive validity for college grades than weighted GPAs. One might be inclined to think that this provides incentives for taking easy classes, but the top schools are simply not going to take you seriously if you adopt this strategy (speaking from personal experience at a top liberal arts college and having seen the data on the average number of AP classes taken).

On the high school end, many high schools (including my own former school) have switched away from a weighted average system for class rank. Instead, they use a system where one's GPA for class rank purposes = 36 * (unweighted GPA) + .5 (number of honors classes taken) + 1(number of AP classes taken). The additive system prevents the possibility of having one's GPA watered down. Some high schools go further by adding additional points for taking extra classes beyond the number required for graduation, further encouraging the taking of additional classes regardless of their honor/AP status.

It surprises me how much my attitude to this post is "15 years from now, is it really going to matter that much what you did in high school to get into college?" AFAICT, academics are not that strongly related to long term career success, and that in the longer term, traits like conscientiousness and skills like working with others end up being more important. I wouldn't recommend to my child that they try to signal their worthiness to colleges and universities at the expense of actually acquiring skills.

Then again, I speak as someone in a field (nursing) where it really doesn't matter where you did your schooling; nobody cares. I get the impression that there are fields where it matters a bit more (like engineering) and fields where it might matter a lot more (like business, where most of the value of a prestigious college is in networking and building human capital anyway).

Caution in applying such a principle seems appropriate. I say this because I've long since lost track of how often I've seen on the Internet, "I lost all respect for X when they said [perfectly correct thing]."

Firstly, this post is awesome.

Secondly though, this post brushes on the topic of intuition as a useful tool, something I think far too many Logic-Based types throw out without considering the practicality of. It's better not to think of it as being an substitute for logical thinking, but rather as a quick and dirty backup, for when you don't have all the information.

Intuition can occur in up to two seconds, operates almost completely below conscious awareness, and begins effecting your body immediately. Here are some excerpts from Blink, a book by Malcolm Gladwell, in which he researches how intuition works, what abilities and drawbacks it has, and what biases can effect it's overall usefulness.

In front of you are four decks of cards, two of them red and the other two blue. Each card in those four decks either wins you a sum of money or costs you some money, and your job is to turn over cards from any the decks, one at a time, in such a way that maximizes your winnings.*

Ah, a perfect opportunity to be a Logical Thinker, using careful observation and reasoning to find the ideal pattern. What path does intuition take though?

What you don't know at the beginning however, is that the red decks are a minefield. The rewards are high, but when you lose on the red cards, you lose a lot. Actually, you can win only by taking cards from the blue decks, which offer a nice steady diet of $50 payouts and modest penalties. The question is how long will it take you to figure this out? After about fifty cards or so, people start to develop a hunch about what's going on. We don't know why we prefer the blue decks, but we're pretty sure at that point that they are a better bet. After turning about eighty cards, most of us have figured out the game and can explain exactly why the first two decks are a bad idea.

This is all standard enough, but what is more impressive is the fact that people started generating stress responses to the red decks by the tenth card.

That's right, palms began to sweat in reaction to the red decks almost immediately, naturally pushing people towards the blue decks before they could even understand why, or even recognize what they were doing.

In those moments, our brain uses two very different strategies to make sense of the situation. The first is the one we're most familiar with. It's the conscious strategy. We think about what we've learned, and eventually we come up with an answer. This strategy is logical and definitive. But it takes us eighty cards to get there. It's slow, and it needs a lot of information. There's a second strategy, though. It operates a lot more quickly. It starts to kick in after ten cards, and it's really smart, because it picks up the problem with the red decks almost immediately.

There are better examples of applied Intuition in Blink, but I've purposefully only used one of the earlier examples in the Amazon Sampler to respect the book. I'd recommend reading the whole thing though, especially if you're interested in understanding what it does while you're thinking things through.