Taking their characterization, a definition for relative intelligence is immediate--it writes itself
A definition, but not a concrete and practical way of determining the relative difference between two agents?
Come on, bring this into reality. We're mostly a bunch of coders here. Stop talking about ultrafilters, concepts that are complex and thus render those of us not familiar with them unable to understand what you're saying.
Answer the question.. How can you take two real agents and, in finite time with finite resources, and in a completely general way, compare their intelligences?
The answer might be "the paper doesn't get us any closer to that." So just say that. Otherwise you're being misleading, because you start out by presenting the problem in a simple way. Then you get complex when you answer it.
The paper isn't intended to be a manual for how to practically compare agents. It will indirectly help there, I hope, by making people realize that they're looking at an election problem, and that there's a big existing literature on that subject. So in the practical case, say you have 10 different benchmarks, and some agents perform better at some of them, and others perform better at others. You could approach the problem from scratch, but it would be helpful for you to realize "oh this is an election with 10 voters and people have been studying how to decide elections for hundreds of years, I probably shouldn't reinvent the wheel". For example, it might take you many ages to essentially rediscover the Condorcet paradox and you might put inordinate effort into futilely trying to "solve" that paradox. Or you could stand on the shoulders of giants and avoid all that! https://en.wikipedia.org/wiki/Condorcet_paradox
A definition, but not a concrete and practical way of determining the relative difference between two agents?
Come on, bring this into reality. We're mostly a bunch of coders here. Stop talking about ultrafilters, concepts that are complex and thus render those of us not familiar with them unable to understand what you're saying.
Answer the question.. How can you take two real agents and, in finite time with finite resources, and in a completely general way, compare their intelligences?
The answer might be "the paper doesn't get us any closer to that." So just say that. Otherwise you're being misleading, because you start out by presenting the problem in a simple way. Then you get complex when you answer it.