Which technique involves dividing a melody into short phrases that are shared among different voices?

The technique that involves dividing a melody into short phrases that are shared among different voices is known as hocket. This can be particularly effective in creating a sense of counterpoint and interplay between the voices. In hocket, the melody is fragmented, with each voice passing small sections of the melody back and forth, creating a collaborative effect as the different parts come together to form the whole musical idea. This technique is often used to enhance the texture and rhythm of the music, leading to dynamic and engaging arrangements.

Imitation, while it involves one voice repeating or echoing the melodic material of another, does not specifically involve dividing parts of the melody among voices in the same way that hocket does. Inversion refers to flipping melodies or harmonies, which is a different concept entirely. Harmonic generally refers to concepts related to chords and harmonization, rather than the division of melody among voices. These distinctions highlight why hocket is the correct choice for this question.