Over time, I've noticed many examples of people making bets that don't make much sense from a subjective profit-maximizing point of view. Without naming the people involved, here are some examples:

1. A lends B some amount of USD to be paid back in seven years, with an effective interest rate of 15% per year on the loan. This is construed as a bet on AI timelines: B thinks there's a high chance the world will end in seven years and won't have to pay back the debt, or that AI will drive substantial economic growth which will make the repayment of the loan much easier.

2. A and B make the following bet: B reads a book authored by A. If B changes his opinion about some important issue as a consequence of reading this book, B pays A an unspecified sum X. Otherwise, A pays B a sum of 2X. The context was such that I think A had no reason to think B would be convinced by their book, even aside from the issue of perverse incentives created by the bet.

3. A bets B at 1:4 odds (in A's favor) that AI will drive substantial economic growth over the next two decades. The point is that A thinks such an event is more than 1/(1+4) = 20% likely, while B thinks it's less than 20% likely, so the bet is meant to have a positive expected value from the standpoint of both counterparties.

4. A agrees to buy a Bitcoin from B for $1 million in 90 days, as a way of betting that the price of BTC will exceed $1 million in 90 days.

All of these examples have strange features that don't make much sense if we think of them as purely expected profit-maximizing actions. To enumerate;

1. B can just as easily get a loan denominated in USD for much less than 15% per year in interest. There are liquidity constraints, of course, but they are likely significantly less binding in the ordinary lending market than they are in the "making bets with acquaintances" market. Likewise, A can simply arbitrage the bet against said lending market as commercial lending rates are currently far below 15% per year, so their accepting this bet doesn't give us any information about their beliefs.

2. The bet is structured in a rather strange way that creates perverse incentives on B's part: he has a reason not to be convinced by A's arguments even if he in fact finds them convincing because now it costs him money to admit to doing so. Moreover, A has no guarantee that B will not lie about being convinced, and the context of the bet was such that A really had no reason to think that B would find his arguments convincing.

3. A marginal dollar is worth significantly less in worlds where there's a lot of explosive growth. So even if I believed there's a 50% chance of substantial AI-driven economic growth in the next twenty years, from my point of view a bet at 1:4 odds favoring my counterparty that it's not going to happen is essentially like buying insurance against said growth not taking place. I'm happy to buy insurance even if it has a negative expected value, so my accepting the bet doesn't reveal much about my beliefs. In short, the prices are confounded by the marginal utility I would have in different states of the world in twenty years.

4. Same argument as (1): if A really believes BTC is likely to be worth more than $1 million in 90 days, just buying BTC and holding it for 90 days is a much better strategy from their point of view than entering this bet. Why would you pay $1 million for a Bitcoin when you can pay ~ $30k, which was the market price at the time of the bet?

I believe that the bets were made in all three cases regardless of these concerns because the bettors were optimizing for something other than expected profit: they were trying to signal.

What they were trying to signal can be different in different cases. One possibility is that bettors want to signal their commitment to a cause by publicly showing that they are willing to put their own money at risk: I think this is what was going on with (1), (3), and (4). Another possibility could be the public interest generated by the bet being worth more to one of the counterparties than the value at stake in the bet itself: this is probably the right explanation for (2), as A was able to exploit B's public platform to advertise their own book to a wide audience at a fairly small cost to themselves.

I believe the signaling motivation for betting has generally been underappreciated. Participants are in general optimizing for multiple objectives at the same time when they bet in public, and the solution to this optimization problem is often to not do what is optimal from the narrow perspective of expected profit maximization. The result is that the odds at which such bets are made give poor guidance about the beliefs of the bettors in question.

These difficulties can be overcome if participants agree to not make the terms of their bet public or to make themselves anonymous in some other way. In this case, the signaling motivations for betting disappear, as the world will not know about what bet you've agreed to, possibly aside from a trusted third party to serve as adjudicator of the bet.

Indeed, when I buy shares of some company or another, I don't have to disclose my position to the whole world: the transaction system on an exchange is anonymized. An ideal prediction market would probably work in the same way, and this seems like the better system from the vantage point of eliminating unwanted incentives that interfere with price discovery in a betting market.

In the absence of such a market, I'm still inclined to recommend that people should try to make more bets anonymously instead of announcing their bets to the public. Not doing so risks turning bets into (for instance) a status competition in which the party who can afford to put up the most money gets to be taken more seriously, and losing money just becomes a "business expense" that they are willing to bear in exchange for that.

I'm interested to hear people's thoughts on this subject - feel free to elaborate on what you think of this in the comments section.