Define a user created asset that can be issued 1:1 by anyone putting up collateral in a specific bitasset.
Define the prediction criteria in the description of the asset.
Allow collateral to be freed by burning the issued asset.
That is all.
There is no need for a judge to settle the bet.
Now how does the game theory operate? The issued asset will trade based upon the markets belief that it someone will buy it back. Market participants will buy it back because they have collateral at stake. If it wasn't tied to a prediction criteria then the asset would sell at a price of 0.5 because that is the Nash Equilibrium price at which both parties break even.
Once you tie a prediction to it the Nash Equilibrium changes because the parties have a sense of "justice". If there are only two people and they are "honest bettors" then they would simply settle at the honest outcome.
If one of the players is a "sore looser" then they may demand 0.1 for a "false" outcome or only offer 0.9 for a "true" outcome. The ability of a "sore looser" to hold out depends upon the value the winner places on justice. If the winner is "hard core" he will simply hold out until the looser caves and agrees to settle honestly. If the winner is more practical he will offer the looser a financial incentive to settle at a reasonable price.
There is financial incentive for the looser to settle at any price above 0 or just slightly below 1, but no incentive for them to settle for nothing.
There is financial incentive for a winner to settle at less than full price so they can exit the market.
If there were only two players and both place a bet with dishonest intentions then they are in an "all or nothing" choice. If they settle then they break even, if they don't then they both lose.
If the market never closes and people are allowed to enter the Nash Equilibrium at any time then you end up with a market where people are betting on the price of justice.
Say an election ends and the winner is known. The best settlement offered by any loser is 60/40 which isn't particularly appealing to someone who won and was expecting something closer to 95/5. In this case the best settlement offered by any winner is 80/20. At this point in time speculators can bet on how long the sore looser will hold out and what price he will ultimately settle for. A speculator will take the 80/20 settlement and hold out for a 90/10 settlement.
Over time the market will discover the long-term price at which losers would rather get nothing than something and winners would rather get something than nothing. Once the market establishes this price then we can calibrate our prediction markets. Say the "long-term" settlement is 90/10, then a prediction value of .9 == 100% true and a prediction value of .1 == 100% false and everything can be scaled accordingly.
Because long-term settlement risk is being priced in from the start all markets will initially track in direction even if they don't track in magnitude until enough data is gathered to allow proper calibration.