Growing up Quaker meant not betting. When people would try to turn a disagreement into a bet I would just say "I don't bet". Should I still do that? The argument that a bet is a tax on BS is strong: bets are more expensive, on average, for people who are more ignorant on the issues they're betting on. This means that if someone is willing to bet to back up a statement we should take it more seriously. This is the idea behind prediction markets and the basis of futarchy (pdf). [1]

This is some reason to accept betting, but is it enough? Not believing in God doesn't mean rejecting everything I learned in a Quaker context. Religious advice comes from a social process involving generations of experience, and there's often something to it. While Quakerism is very decentralized and doesn't have an official statement of beliefs, regional organizations put out guides. What do they say about betting?

Baltimore, 1988:

We are faced at every hand with enticements to risk money in anticipation of disproportionate gain through gambling. Some governments employ gambling as a means of raising revenue, even presenting it as a civic virtue. The Religious Society of Friends continues to bear testimony against betting, gambling, lotteries, speculations or any other endeavor to receive material gain without equivalent exchange, believing that we owe an honest return for what we receive. Indulgence in games of chance blunts a proper sense of obligation.

New England, 1986:

Let us maintain integrity in word and deed. Holding to the simplicity of truth, let us keep free of oaths. Remember how widespread and diverse are the temptations to grow rich at the expense of others, and how apparently harmless indulgence often leads by degrees to wrong-doing. Let us avoid and discourage every kind of betting and gambling and commercial speculations of a gambling character.

There are two components of betting and gambling: deliberately increasing volatility, and making predictions. For example, consider three lotteries that cost $1 to play and pay $1000 if you win:

	odds of winning
A	1 in 10,000
B	1 in 1,000
C	1 in 100

If I buy a ticket in any of these lotteries I'll probably lose money but I have a small chance of coming away with much more money than I started. This increases the variance of my outcomes, and is generally not a good thing because of the declining marginal utility of money. [2] There's also a prediction component, where we're not just interested in volatility but also the expected value:

	odds of winning	expected value	chance of losing money
A	1 in 10,000	$0.10	99.99%
B	1 in 1,000	$1	99.9%
C	1 in 100	$10	99%

As you can see, while all three lotteries increase volatility, if I played lots of lotteries like A I'd probably lose a lot of money while if I played lots of lotteries like C I'd probably gain a lot of money.

In cases where the prediction is relatively simple, like in these lotteries, it's nearly valueless. The argument about "growing rich at the expense of others" makes some sense here: if I run a lottery like A then I'm pretty much just taking money from people who are bad at math. But what about in cases where the prediction isn't so simple?

Prediction markets are a good example of this. If the market isn't making the right prediction, you can make money by fixing it. If the market is set up to predict things that people want to know, then the people who make bets in this market are providing something of value: either they're making the market more accurate by betting in the right direction, or they're effectively paying other people to make the market more accurate by betting the wrong way. Quaker opposition to betting given above was based on the idea that you shouldn't try to get something for nothing, or "receive material gain without equivalent exchange" and that we "owe an honest return for what we receive", and that doesn't apply here.

With all this in mind, I'm going to start allowing myself to bet in cases where the prediction is valuable. While I'm not going to start playing roulette or bet on facts we could easily look up, I will be open to betting in cases where there's a substantive disagreement over a future event.

Update 2013-07-03: It's also surprising that the Quaker passages only talk about gambling as hurting other people ("the temptations to grow rich at the expense of others") and doesn't mention how most people who gamble lose money.

[1] There was recently some research showing that people give less biased answered when they have something at stake, but not that they give more accurate ones. In Partisan Bias in Factual Beliefs about Politics (pdf, 2013, n=795), the researchers got people to answer questions like:

In the 2008 Presidential Election, Barack Obama defeated his Republican challenger John McCain. In the nation as a whole, of all the votes cast for Obama and McCain, what percentage went to Obama?

Respondents were given a slider, which for this question went from 50% to 62% and started centered on 56%. On average Republican respondents pushed the slider down to 55.3% while Democratic respondents pushed it up to 56.5%. This difference dropped when respondents knew their chances of getting a $200 gift card were proportional to their number of correct answers. But:

We find that there is no difference between the control (flat fee) condition and the pay for correct condition in accuracy: The average distance from the truth across questions and treatments is .28 in both cases. Our earlier results show that offering incentives for correct responses substantially reduces partisan divergence. The analysis here suggests that convergence is, on average, no more likely to be toward the truth than away from it.

It sounds like people had some rough guess as to the true answer and then were adjusting from there in the more politically acceptable direction. But if their bias-caused adjustment tended to be smaller than their inaccuracy, and was equally likely to be in either direction, then we wouldn't actually expect mean accuracy to go up when bias is decreased. (Is this correct? I'm not that confident in the logic.)

[2] If I'm spending money on myself, $2K isn't twice as good as $1K.