Edit: This post is about a practical method for structuring a bet. It's not on how to extract information about people's true confidence levels based on the betting odds.
Bryan Caplan and Eliezer Yudkowsky figured out a way to place a meaningful bet on the end of the world[1]. Bryan described their simple approach in his April 2022 80,000 Hours podcast interview.
In brief, Bryan assigns a lower probability than Eliezer to the world ending by January 1, 2030. Of course, if the world ends by that date, Eliezer can't collect his winnings. So Bryan prepays Eliezer now, and Eliezer pays him back if he loses the bet.
This works for friendly bets. Bryan points out that they need to account for interest. To that, I'd add both risk and opportunity cost. Commenters have changed my mind, however, about whether we can really learn much about the participants' confidence levels from such a bet. I elaborate on this in the comments.
Here's the relevant part of the transcript, under "Bryan's Betting Record" starting at 1:48:19 in the podcast episode.
Bryan Caplan: Let’s see. Well, I’ve already done one huge [bet against the effective altruism community], and this is that machines are going to kill us — or at least do something terrible to us — in the medium term. So I literally have an end-of-the-world bet with Eliezer Yudkowsky.
Rob Wiblin: Oh wow. I didn’t know that.
Bryan Caplan: Yeah. Which many people believe cannot be made, but it’s super easy. The person who disbelieves in the end of the world just pays the money now. And then if the world does not end, the loser pays back with whatever the odds are.
Rob Wiblin: I can’t believe I didn’t think of that.
Bryan Caplan: Yeah. So Eliezer, we actually have a bet. It takes a little effort to understand the bet, because his view is so specific. He said, “Look, I want a bet on there will no longer be any human beings on the surface of the Earth on January 1, 2030.” I was willing to give him, like, “How about all of human extinction?” — “No, no, no, no, no. There could still be humans in mine shafts. That’s OK. But not the surface of the Earth.” And I’m like, “All right. If that’s such a big deal to you, fine, we’ll make it the surface of the Earth, whatever.” But yes.
Bryan Caplan: So anyway, we have a bet, where I don’t remember the exact odds. It might be just like two-to-one. And I prepaid, so implicitly there’s interest. So it’s not as good as it seems.
It's trivial to bet on the end of the world - it's called "taking a loan that you expect not to pay back". You "win" if anything happens that prevents your debt being collected - extinction, civilization or monetary collapse, personal death or bankruptcy. If you can find suckers to lend you at better rates because they're getting advertising value from it (like Bryan is), so much the better.
The problem is it's NOT trivial to bet on world survival, without accepting pretty bad odds (going interest rates) and without locking up capital you'd rather use elsewhere. edit: this isn't a big problem - survival is it's own payout for most of us. You ALREADY have your entire existence on that side of the line.
If dollars correspond 1:1 with utility, then I think you can simply adjust for the opportunity cost of lending money out as a loan. See my "toy model" in a comment response above. However, I don't think dollars correspond 1:1 with utility, and the act of betting has a potentially asymmetrical reputational effect regardless of whether the participants are right or wrong. We can still bet on the end of the world, but we shouldn't assume that the betting odds reflect the true confidence levels of the participants in the bet.
I still think bets are a piece of weak evidence about a person's true confidence in their claims. If Bryan refused to take this bet with Eliezer, I'd be somewhat more inclined to think he's blowing hot air. But I don't think that their 2:1 bet means that we can take Eliezer as putting 2:1 odds on the end of the world in 2030.
Edit: I take it back. Why would Eliezer take a higher-"interest" bet with Bryan when he could just take out ~unlimited money in a long-term loan at more favorable rates? I no longer think you can bet in a meaningful way on the end of the world.
Edit: This post is about a practical method for structuring a bet. It's not on how to extract information about people's true confidence levels based on the betting odds.
Bryan Caplan and Eliezer Yudkowsky figured out a way to place a meaningful bet on the end of the world[1]. Bryan described their simple approach in his April 2022 80,000 Hours podcast interview.
In brief, Bryan assigns a lower probability than Eliezer to the world ending by January 1, 2030. Of course, if the world ends by that date, Eliezer can't collect his winnings. So Bryan prepays Eliezer now, and Eliezer pays him back if he loses the bet.
This works for friendly bets. Bryan points out that they need to account for interest. To that, I'd add both risk and opportunity cost. Commenters have changed my mind, however, about whether we can really learn much about the participants' confidence levels from such a bet. I elaborate on this in the comments.
Here's the relevant part of the transcript, under "Bryan's Betting Record" starting at 1:48:19 in the podcast episode.
It's not in Bryan's public betting inventory at the time of publication of this post, but he describes it in more detail here.