Starting assumptions: impact is measured on a per-belief basis, depends on scale, and is a relative measurement to prior expectation. (This is how I am interpreting the three reminders at the end of the post.)
To me, this sounds like a percent difference. The change between the new value observed and the old value expected (whether based in actual experience or imagined, i.e. accounting for some personal bias) is measured, then divided by the original quantity as a comparison to determine the magnitude of the difference relative to the original expectation.
My sentence: You can tell that something is a big deal to you by how surprising it feels.
While I agree that using percentages would make impact more comparable between agents and timesteps, it also leads to counterintuitive results (at least counterintuitive to me)
Consider a sequence of utilities at times 0, 1, 2 with U0=1 , U1=0.01 and U2=0 .
Now the drop from U1 to U2 would be more dramatic (decrease by 100%) compared to the drop from U0 to U1 (decrease by 99%) if we were using percentages. But I think the agent should ‘care more’ about the larger drop in absolute utility (i.e. spend more resources to prevent it from happening) and I suppose we might want to let impact correspond to something like ‘how much we care about this event happening’.
Starting assumptions: impact is measured on a per-belief basis, depends on scale, and is a relative measurement to prior expectation. (This is how I am interpreting the three reminders at the end of the post.)
To me, this sounds like a percent difference. The change between the new value observed and the old value expected (whether based in actual experience or imagined, i.e. accounting for some personal bias) is measured, then divided by the original quantity as a comparison to determine the magnitude of the difference relative to the original expectation.
My sentence: You can tell that something is a big deal to you by how surprising it feels.
While I agree that using percentages would make impact more comparable between agents and timesteps, it also leads to counterintuitive results (at least counterintuitive to me)
Consider a sequence of utilities at times 0, 1, 2 with U0=1 , U1=0.01 and U2=0 .
Now the drop from U1 to U2 would be more dramatic (decrease by 100%) compared to the drop from U0 to U1 (decrease by 99%) if we were using percentages. But I think the agent should ‘care more’ about the larger drop in absolute utility (i.e. spend more resources to prevent it from happening) and I suppose we might want to let impact correspond to something like ‘how much we care about this event happening’.
That would depend on whether things have a multiplicative effect on utility, or additive.