  We study a class of preference domains that satisfies the familiar properties
of minimal richness, diversity and no-restoration. We show that a specific
preference restriction, hybridness, has been embedded in these domains so that
the preferences are single-peaked at the "extremes" and unrestricted in the
"middle". We also study the structure of strategy-proof and unanimous Random
Social Choice Functions on these domains. We show them to be special cases of
probabilistic fixed ballot rules (introduced by Ehlers, Peters, and Storcken
(2002)).
