Arbitrarily

The winner was chosen arbitrarily.

From these remarks it will be seen that I look at the term species, as one arbitrarily given for the sake of convenience to a set of individuals closely resembling each other, and that it does not essentially differ from the term variety, which is given to less distinct and more fluctuating forms. The term variety, again, in comparison with mere individual differences, is also applied arbitrarily, and for mere convenience sake.

Studies of the viable blood cells with phase contrast microscopy showed peculiar cells that had numerous short villi and were arbitrarily called “hairy cells.”

The number or classes or potential offerers of satellite services should not be [limited] arbitrarily.

an arbitrarily large number