Lottery? Many make random choices (4,4)
I believe the answer is:
draw lots
'make random choices' is the definition.
(as in drawing lots to decide something)
'lottery? many' is the wordplay.
'lottery?' becomes 'draw' (I've seen this in other clues).
'many' becomes 'lots' (I've seen this before).
'draw'+'lots'='DRAW LOTS'
(Other definitions for draw lots that I've seen before include "Randomly decide" , "attract the crowd" , "Decide by chance" , "Decide which one" , "make random selection" .)