We could distinguish between negotiations and aggregation solutions. Instead of looking for a result that, as the Kalai-Smorodinsky solution pretty much does, divides the difference between the different claims, we could try to bring the different rankings together into a general social choice. Arrow`s sentence and the problems associated with the rules of social choice cast doubt on any claim that a certain type of aggregation is merely rational: all have their flaws (Gaus 2008, chap. 5). Harsanyi (1977, Chapter 1 and 2; 1982) developed a contract theory similar to Rawls`s. It creates a veil of ignorance in which people do not know their identities under the contract and assumes that rational contractors will assume that they are just as likely to be a particular person. In addition, it argues that contractors can agree on people-to-people supply comparisons and will therefore choose a contract that will aggregate the supplier in the highest average (see also Muller 2003, chap. 26). It depends, of course, on the assumption that there is an undisputed metric that allows us to aggregate the usefulness functions of the parties. Binmore (2005) follows Harsanyi and Amartya Sen (2009, chap. 13) on the grounds that interpersonal comparisons can be made for aggregation purposes, at least in part. However, one of the problems with this approach is that interpersonal comparisons, if incomplete, will not be able to achieve a complete social order. As Sen points out, the result will be a maximum series of alternatives, where no alternative is dominated by another within the kit, but also where no particular alternative is optimal (Sen, 1997).
Instead of solving the problem of aggregation, interpersonal comparisons may only reduce the set of alternatives without being able to finalize the order of alternatives. There is a reading of the (first) hypothetical question “If the agreements if___ “, which, as has been suggested, is still, in a way, empirical.