  When aggregating preferences of agents via voting, two desirable goals are to
identify outcomes that are Pareto optimal and to incentivize agents to
participate in the voting process. We consider participation notions as
formalized by Brandl, Brandt, and Hofbauer (2015) and study how far efficiency
and participation are achievable by randomized social choice functions in
particular when agents' preferences are downward lexicographic (DL) or satisfy
stochastic dominance (SD). Our results include the followings ones: we prove
formal relations between the participation notions with respect to SD and DL
and we show that the maximal recursive rule satisfies very strong participation
with respect to both SD and DL.
