Only do markets on if there will be a community note.
This is kind of a dodge, but since this is mechanistic, no authority is needed. Either a community note ends up being displayed or it doesn't. If it does, resolve "Yes". Resolve "No" otherwise.
This would be good for dubious but hard to debunk claims. "Seems likely there will soon be a note next to this."
People can resolve their own forecasts and if disputed there is a vote. If there is a Community Notes-style consensus[1] for "Yes" or "No" it resolves that way. If not then the question gets delayed 6 months and attempts to resolve then. And over and over.
This way a single user couldn't delay resolution because there would still be consensus, but lacking consensus isn't game over, it just roles over.
I'm gonna describe this as requiring consensus where very similar views count for less. So you need support across twitter rather than just a lot of concentrated support (perhaps because others didn't see the question). I guess it's strictly more demanding that a majority.
Bitcoin Hivemind (nee Truthcoin) is the authority on doing this in a truly decentralized fashion. The original whitepaper is well worth a read. The fundamental insight: it's easier to coordinate on the truth than on something else; incentivizing defection to the truth works well.
Judges have reputation. If you judge against the consensus, you lose reputation, and the other (consensus) judges gain it. The amount you lose depends on the consensus: being the lone dissenter has a very small cost (mistakes have costs, but small ones), but being part of a near-majority is very costly. So if your conspiracy is almost but not quite winning, the gain from defecting against the conspiracy is very high.
Adaptations to a non-blockchain context should be fairly easy. In that case, you have a central algorithmic resolver that tracks reputation, but defers to its users for resolution of a particular market (and applies the reputation algorithm).
Kleros-like mechanism where a jury votes and you only get a reward if you vote the same way as consensus.
Or better, for Community Notes you could use CN algorithm itself (consensus of people across the political aisle)
I mean, the universal dispute resolution is violence, or the threat thereof. Typically this is encapsulated in governments, courts, and authorities, in order to make an escalation path that rarely comes down to actual violence.
For low-value wagers/markets, a less powerful authority generally suffices - a company or even individual running the market/site. The predictions can be written such that it's unlikely to be disputed, and to specify a dispute-resolution mechanism, but in the end the enforcement is by whoever is holding the money.
For algorithmically-determinable outcomes, it may be that a distributed/consensus mechanism could be used, so the "central authority" is actually "whoever has the most compute", and most of the time that authority won't bother to do anything nefarious.
Any system that doesn't have clear mechanisms for appeal of disputes, and specification of how a result will be decided and enforced is just a toy.
I've been chatting with some people about using Prediction Markets/Forecasts alongside Community Notes.
An initial suggestion is just to link to to forecasting sites really well. It's a good suggestion but I'm not gonna discuss that here.
Other suggestions revolve around a forecasting product on X/Community Notes face the following issue:
So:
What is your best suggestion for resolving a forecast without a central authority?
For clarity, a forecast has been written. People have forecasted on it, perhaps it's a prediction market where they have bought and sold shares, perhaps not. Now it needs to resolve to award either points or to allocate the value to "Yes" or "No" tokens. Perhaps people resolve their own markets, as manifold does. But someone disputes the resoution. What happens now?
Solutions can be deeply technical or wonky. I think a good one is very valuable here.
Polymarket uses some kind of "token holders decide" system and I think that's led to several awful resolutions, notably the Time Person of the Year one.