I am trying to confirm these following statements:
(1) If is convex, then if and , then .
(2) Suppose . If is convex, then for any , . Basically this is saying if is indifferent to , then one would prefer over . I am not sure why this is the case.
A preference relation is monotone if for any and such that for . It is strongly monotone if for all and for some implies that
Source: www.ksg.harvard.edu/nhm/notes2006/notes3.pdf