[jlokier]

It is possible to perform "trustable" random number drawing by combining values from multiple third parties such that if any of them are fair, then the results are fair, with everyone publically able to verify the combining step.

That means all the third parties would have to be corrupt to corrupt the results. So if you can pick a diverse set of third parties such that everyone is likely to trust at least one of them, that will raise overall trust.

But you can do better than that.

You can also have people provide their own random input. In that case they will certainly trust themselves, and therefore can trust the results if they can verify the combination step.

And you can draw input from public sources that people can check for themselves, and have confidence is effectively random, in the sense that nobody can control the values. For example public blockchain hashes (as part of a combining scheme, not by themselves).

These sorts of schemes would give people absolute assurance that the drawn numbers are fair and uncorruptible, and they aren't difficult to implement.

(PM me if you'd like to discuss further. Email in profile.)

[labawi]

When designing a combining scheme, how do you avoid a last outcome wins situation?

If you get to choose or influence any of the inputs and (for the most part) know the others, you can influence the result. I.e. choose from a set of outcomes, or at least influence outcome probabilities.