The there exists a profile P' such that V (x, y; p) = --+ V(x, y; P') and V(x, y; P') E O(x, y). But then, by locality ofF, (x, y) E F( P). 1) is local. 1). The group w

Theorem 2. 8 was proved in [220] . 9 was stated in [7] , its proof here is due to [192] ; the other proof can be found in [6] . 1 Introduction In this Chapter we consider aggregation rules which transfonn individual binary relations (agents' preferences) into social binary relations (social preferences). Such rules were called in Chapter 1 as Social Decision Functions (briefly, SDFs). Chapter 3 consists of two parts. 10 deals with strongly local rules. These rules make the decision about the inclusion of a pair (x, y) into the social binary relation P depending only on the infonnation about inclusion ofthis very pair (x,y) in agents' preferences 15 Pi.

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