A diachronic Dutch Book argument uses the fact that if you engage in a certain cognitive process, then there is a series of bets across different times that you will each find acceptable, but whose net consequence is that you lose money in every possibility. For instance, say that your current credence in p is 0.5, but you plan to have your credence in p tomorrow be 0.8. Now consider a bet that pays $1 if p, and nothing otherwise, and assume the marginal utility of money is constant enough. You’ll happily sell such a bet for 60 cents today. And you’ll happily buy it back tomorrow for 70 cents. So you’ll have lost 10 cents, whether the bet pays out or not. That’s bad, so you shouldn’t have arbitrary, and planned, credal jumps like that. A generalisation of this argument shows that any planned updating strategy that is not conditionalisation leads to sure losses, and, it is concluded from that, is bad.
But there’s something very odd about the argument here. There’s nothing wrong per se with a trading strategy that leads to a sure nominal loss. If there was, there would be something wrong with ever borrowing money at a positive interest rate. In the example above, you do end up with 10 cents less than you start with. But you also have the use of 60 cents for a day. Now 17% per day is probably a high price to pay for the use of that money. But we think having money to use is worth something. A non-zero liquidity preference is not irrational.
So what, exactly, is worse about the trading strategy the non-conditionaliser uses, and which leads to sure nominal loss than the trading strategy someone uses when they borrow money at a positive interest rate?
Part of the answer has to do with expected inflation, but presumably not all of it. Some people borrow money at what they take to be a positive real interest rate. And that can be, in some circumstances, rational.
Perhaps there is a simple explanation here, but it seems there is a very large argumentative gap in Diachronic Dutch Book arguments that isn’t there in Synchronic Dutch Book arguments.
Posted by Brian Weatherson in Uncategorized