Limited Rights as Partial Veto and Sen’s Impossibility Theorem

The origin of the tremendous development of studies on rights and freedom within social choice theory and normative economics can be traced back to the famous short paper of Amartya Sen published in 1970 (Sen, 1970b); see also his book published the same year (Sen, 1970). In this paper, it is shown in the framework of aggregation procedures that there is a conflict between collective rationality (in terms of properties of choice functions or in terms of a transitivity-type of the social preference property — in fact, acyclicity of the asymmetric part of the social preference), Paretianism (a unanimity property) and some slight violation of neutrality (neutrality meaning that the names of options or social states are not to be taken into account) possibly combined with some slightly unequal distribution of power among individuals interpreted as an individual liberty property. Although, since then, rights have been considered within another paradigm, viz. game forms (see for instance Gärdenfors (1981, 2005), Gaertner, Pattanaik, and Suzumura (1992), Peleg (1998a,b) and Suzumura (2008)), and freedom has been mainly analyzed in the context of opportunity sets following the pioneering paper of Pattanaik and Xu (1990) (see also the survey by Barberà, Bossert, and Pattanaik (2004)), some authors (for instance Igersheim (2006) and Saari and Pétron (2006)) have recently revisited the foundational framework of Sen and Gibbard (1974) either by studying the informational structure of the aggregation procedure or by examining the consequences of taking a Cartesian structure to define the set of social states, consequences that take the form of a restriction of individual preferences. The purpose of this paper is different. I wish to formally study a weakening of the conditions associated with the notion of individual liberty. I have always considered that this condition was rather strong in Sen’s original paper. In fact, the condition is quite strong in the mathematical framework and only the interpretation, to my view, makes it not only acceptable but obvious. In his comments to a paper by Brunel (now Pétron) and Salles (1998), Hammond (1998) writes:

In the social choice rule approach …, local dictatorship becomes a desideratum, provided that the ‘localities’ are appropriate. Our feelings of revulsion should be reserved for non-local dictatorships, or local dictatorships affecting issues that should not be treated as personal.