In his Matching Soulmates paper in the journal of Public Economic Theory, everyone is in a computer simulated dating pool, where thousands of digitally created daters rank each other. His algorithm picks "first‑order soulmates": pairs who choose each other in a stable matching. It removes them, and runs it again with those left, and you get second‑order soulmates, and so on.
When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.
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