The selection effect you mention only applies to offering bets, not accepting them. If Alice announces her betting odds and then Bob decides which side of the bet to take, Alice might be doing something irrational there (if she didn’t have a bid-ask spread), but we can still talk about dutch books from Bob’s perspective. If you want to eliminate the effect whereby Bob updates on the existence of Alice’s offer before making his decision, then replace Alice with an automated market maker (setup by someone who expects to lose money in exchange for outsourcing the probability estimate). Or assume some natural process with a naturally occurring payoff ratio that isn’t determined by the payoff frequencies nor by anyone’s state of knowledge.
The selection effect you mention only applies to offering bets, not accepting them. If Alice announces her betting odds and then Bob decides which side of the bet to take, Alice might be doing something irrational there (if she didn’t have a bid-ask spread), but we can still talk about dutch books from Bob’s perspective. If you want to eliminate the effect whereby Bob updates on the existence of Alice’s offer before making his decision, then replace Alice with an automated market maker (setup by someone who expects to lose money in exchange for outsourcing the probability estimate). Or assume some natural process with a naturally occurring payoff ratio that isn’t determined by the payoff frequencies nor by anyone’s state of knowledge.