What does "verifiably" mean for you? Are you talking about provable security?
First establish an upper bound, worst case scenario cost (as a function of time + resources) to fully reverse engineer the algorithm. Use that as the comparison benchmark, and if you can come up with a design that eliminates any reverse engineering efforts with fewer costs than worst-case, you've done it.
Here's where that breaks down: "ungameable" is not precise enough to establish worst-case bounds for, in the same way that we can establish worst-case bounds for breaking an MD5 hash (brute-force it - what does "brute-force it" mean for gaming a ranking algorithm, or reverse engineering more generally?). Other than that, were you to come up with such a measurement, it would almost assuredly increase the costs of reverse engineering to infeasibility by increasing the authorization controls in place and decreasing the usability requirements.
Well, probably not for such a broad description of "ungameable", but there is an entire research field dedicated to try and come up with such algorithms/systems: Mechanism design!
First establish an upper bound, worst case scenario cost (as a function of time + resources) to fully reverse engineer the algorithm. Use that as the comparison benchmark, and if you can come up with a design that eliminates any reverse engineering efforts with fewer costs than worst-case, you've done it.
Here's where that breaks down: "ungameable" is not precise enough to establish worst-case bounds for, in the same way that we can establish worst-case bounds for breaking an MD5 hash (brute-force it - what does "brute-force it" mean for gaming a ranking algorithm, or reverse engineering more generally?). Other than that, were you to come up with such a measurement, it would almost assuredly increase the costs of reverse engineering to infeasibility by increasing the authorization controls in place and decreasing the usability requirements.