For each of the following societies state whether the preferences satisfy Sen's value restriction criterion, that is that for any three outcomes, all voters agree that at least on of the outcomes is not first, middle or last. If not, identify the tuple of preferences that violate value restricted preferences. Assuming that the voting rule is majority rule, are the group preferences in societies without value restricted preferences transitive or intransitive?

Society 1: 

yP1,  xP1,  zP1, w 

wP2 , yP2, XP2, z 

zP3, yP3 , wP3 , x 

Society 2: 

yP1, wP1, zP1, x 

wP2, xP2 , yP2, z 

zP3 , wP3 , yP3 , x 

Society 3: 

yP1, wP1, zP1 , x 

zP2, xP2, yP2, w 

zP3, YP3, WP3, z