Lenses and frameworks

Different alignment proposals often seem hard to compare, but in the end try to achieve the same objective via different mathematical approaches and different terminology. But are these all comparable? Are some specializations of others? Or are some genuinely different? Many alignment approaches talk about states of the world and compare the value, utility, or reward of that state. Others try to prevent or prove impossible undesirable states. Others look at the system overall and establish properties or require empirical evidence. In this work, each alignment approach is mapped to an object and an assessment, then pairs of criteria are made comparable by finding a shared model where both can be determined and compared. Sometimes this leads to a one-to-one mapping between the two approaches. Sometimes, one approach is a specialization of the other. Sometimes, you can show that one criterion chooses differently from the other. Overall, there are four larger classes of alignment approaches: Scores, i.e., numeric utility or reward, relations and capacities, guarantees, and warrants, i.e., evidence. The map below shows the relations that were determined so far, using the toy worlds to make objectives pairwise comparable. Click to open the matching card or relation proof. Green combines two criteria through a named interface, in one correction-first reading. Red and orange are incompatibility inside a named situation class, with a boundary where both criteria can hold. Dotted red means one criterion cannot represent what the other needs, and enlarging it helps; dashed red means the two criteria choose differently from the same options; solid red means rigidity, where one criterion accepts only changes that do not matter to it. Orange is a shared resource that is zero-sum because the total is fixed.