Sure, you can fix unbounded downside risk by giving H a finite budget. You can fix the dogmatism by making H have an ϵ=1/3↑↑↑3 probability of tails.
If you and H have a chance to bet with each other before going to the bookies, then the bookie won’t be able to Dutch book the two of you because you will have already separated H and H’s money.
If you can’t bet with H directly for some reason, then a bookie can Dutch book you and H, by acting as a middle man and skimming off some money.
Sure, you can fix unbounded downside risk by giving H a finite budget. You can fix the dogmatism by making H have an ϵ=1/3↑↑↑3 probability of tails.
If you and H have a chance to bet with each other before going to the bookies, then the bookie won’t be able to Dutch book the two of you because you will have already separated H and H’s money.
If you can’t bet with H directly for some reason, then a bookie can Dutch book you and H, by acting as a middle man and skimming off some money.