I’ve been trying to think of social welfare functionals which meet all of Arrow’s conditions–––unrestricted domain, weak Pareto, independence of irrelevant utilities, and non-dictatorship (see this entry for definitions)–––plus (invariance with regard to) absolute-scale full-comparability (AFC).
Am I correct in thinking that any social welfare functional which meets all of Arrow’s conditions plus an informational condition with a weaker measurability assumption–––such as (invariance with regard to) ordinal-scale full-comparability (OFC)–––will also meet AFC? (For if there is full-comparability between all individuals’ absolute-scale-measured utility functions, then their rank orders of alternatives are comparable, so surely a functional such as maximin can be used. Please do correct me if I am wrong).
If the above reasoning is correct, then I can name several social welfare functionals which meet the conditions I am interested in, but none which are paradigmatic of these conditions (as maximin is of Arrow's conditions plus OFC). Therefore, I was wondering if there are any social welfare functionals which meet Arrow's conditions, but only AFC and no other informational condition?
Thanks for any help :)