We can make any query differentially private given a metric map (one that doesn’t increase any distance) from Message^100 to a space of possible query outputs. Set the probability mass of each query output to 0.99^(steps removed from the default answer). (Then normalize.)
For the identity metric map of a human just trying to read the sample list, this scrambles it entirely. The metric map image needs to branch less combinatorially for this not to happen.
One metric map image metric d(a,b) that comes to mind is one that bounds the utility cost of getting answer b instead of a. For example, we could ask the counterfactual humans to send back stock market prices, and try to calculate a trading policy that is profitable even if some forecasts are fake. And then, whoever is willing to assume the lowest UFAI probability wins the market! x(
We can make any query differentially private given a metric map (one that doesn’t increase any distance) from Message^100 to a space of possible query outputs. Set the probability mass of each query output to 0.99^(steps removed from the default answer). (Then normalize.)
For the identity metric map of a human just trying to read the sample list, this scrambles it entirely. The metric map image needs to branch less combinatorially for this not to happen.
One metric map image metric d(a,b) that comes to mind is one that bounds the utility cost of getting answer b instead of a. For example, we could ask the counterfactual humans to send back stock market prices, and try to calculate a trading policy that is profitable even if some forecasts are fake. And then, whoever is willing to assume the lowest UFAI probability wins the market! x(