If you weaken your will-to-wager assumption and effectively allow your agents to offer bid-ask spreads on bets (i'll buy bets on H for x, but sell them for y) then you get "Dutch book like" arguments that show that your beliefs conform to Dempster-Shafer belief functions, or Choquet capacities, depending on what other constraints you allow.

Or, if you allow that the world is non-classical – that the function that decides which propositions are true is not a classical logic valuation function – then you get similar results.

Other arguments for having probability theory be the right representation of belief include representation theorems of various kinds, Cox's theorem, going straight from qualitative probability orderings, gradational accuracy style arguments…