Sortition

The casting or drawing of lots; selection, choice, or determination by lot.
An act or instance of determining by lot.
And thus by extension: The ancient art of choosing members of government by lottery, as practised by the ancient Athenians and still in our modern jury system.

Derived from the Latin sortitio, from sortiri to cast lots.

The OED tells us the first recorded use in English was in 1597.