The documentation for mapreduce says that it is unspecified if the init key argument is used for non-empty collections. Since there is a single julia implementation leaving the behavior unspecified is bad. In general the init argument is a starting point that you want to combine with the rest. For example

sol = nlsolve(f!, initial_x)
 # mapreduce doesn't specify if `init` is used. Need to use reduce(..., map(...))
 if mapreduce(map(v -> v > 0, &,  sol.zero, init=converged(sol))
     return ...
 else
   ...
 end

Using the init argument to specify the result in case of an empty collection is a special case.