I don't have a solution for trading but betting can be fixed by parimutuel wagering. Since that form of betting and payout is entirely algorithmic (and not based on the event itself), it can be done safely and transparently in software.

For anyone not familiar, this style of betting (used in horse racing) pays out based on the relative amounts waged on the winners. The house takes a cut of the entire pool and (in theory) isn't interested in the outcome.