Another setting that seems natural and gives rise to multiplicative utility is if we are trying to cover as much of a space as possible, and we divide it dimension-wise into subspace, each tracked by a subagent. To get the total size covered, we multiply together the sizes covered within each subspace.
We can kinda shoehorn unequal weighing in here if we have each sub-agent track not just the fractional or absolute coverage of their subspace, but the per-dimension geometric average of their coverage.
For example, say we’re trying to cover a 3D cube that’s 10x10x10, with subagent A minding dimension 1 and subagent B minding dimensions 2 and 3. A particular outcome might involve A having 4⁄10 coverage and B having 81⁄100 coverage, for a total coverage of (4/10)*(81/100), which we could also phrase as (4/10)*(9/10)^2.
I’m not sure how to make uncertainty work correctly within each factor though.
Another setting that seems natural and gives rise to multiplicative utility is if we are trying to cover as much of a space as possible, and we divide it dimension-wise into subspace, each tracked by a subagent. To get the total size covered, we multiply together the sizes covered within each subspace.
We can kinda shoehorn unequal weighing in here if we have each sub-agent track not just the fractional or absolute coverage of their subspace, but the per-dimension geometric average of their coverage.
For example, say we’re trying to cover a 3D cube that’s 10x10x10, with subagent A minding dimension 1 and subagent B minding dimensions 2 and 3. A particular outcome might involve A having 4⁄10 coverage and B having 81⁄100 coverage, for a total coverage of (4/10)*(81/100), which we could also phrase as (4/10)*(9/10)^2.
I’m not sure how to make uncertainty work correctly within each factor though.