An Impossibility Theorem in Population Axiology with Weak Ordering Assumptions
نویسندگان
چکیده
It has been known for quite a while now that the on-going project of constructing an acceptable population axiology has gloomy prospects. Already in Derek Parfit’s seminal contribution to the topic, an informal paradox was presented and later contributions have proved similar results.1 All of these contributions invoke, however, some version of a principle – the Mere Addition Principle – which is controversial.2 In Arrhenius (1998), I presented a theorem which didn’t invoke this controversial principle but replaced it with logically and intuitively weaker conditions. Still, however, one of the conditions in my theorem shares with these earlier results the presupposition that welfare can be measured on at least an interval scale.3 One can deny this and, as a matter of
منابع مشابه
Arithmetic Social Choice: Arrow’s Theorem and Single Peaked Preference
We construct an algebraic model of the social choice theory. First we give an arithmetic proof of Arrow’s Impossibility Theorem. Next we apply our algebraic method to single-peaked preference domain to establish two theorems. (i) A value of Arrovian social welfare function on single peaked preference domain is single-plateaued with at most two maximal elements. (ii) An ordering by majority voti...
متن کاملThe Hex Game Theorem and the Arrow Impossibility Theorem: the Case of Weak Orders
The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and t...
متن کاملExistence of a dictatorial subgroup in social choice with independent subgroup utility scales, an alternative proof
Social welfare orderings for different scales of individual utility measurement in distinct population subgroups are studied. In Khmelnitskaya and Weymark (2000), employing the continuous version of Arrow’s impossibility theorem, it was shown that for combinations of independent subgroups scales every corresponding social welfare ordering depends on the utilities of only one of the subgroups an...
متن کاملA topological approach to the Arrow impossibility theorem when individual preferences are weak orders
We will present a topological approach to the Arrow impossibility theorem of social choice theory that there exists no binary social choice rule (which we will call a social welfare function) which satisfies the conditions of transitivity, independence of irrelevant alternatives (IIA), Pareto principle and non-existence of dictator. Our research is in line with the studies of topological approa...
متن کاملOn the impossibility of complete Non-Interference in Paretian social judgements
We study a principle of ’Non-Interference’ in social welfare judgements. NonInterference captures aspects of liberal approaches (particularly aMillian approach) to social decision making. In its full generality, Non-Interference produces an impossibility result: together with Weak Pareto Optimality, it implies that a social welfare ordering must be dictatorial. However, interesting restricted v...
متن کامل