fairness warps geometry

clustering algorithms are often presented as neutral, geometry-driven tools fitting data into neat groups.

but what happens when we demand "fairness"?

the hidden imbalance

here is a dataset of people.

when color-coded by a sensitive attribute (like efficiency or demographics), we see the natural geometric clusters are not balanced.

let's introduce a constraint: each cluster must contain at least a certain proportion (α) of each group.

try moving the slider.

as you increase fairness, watch the cost curve.

points are forced into clusters that are further away. the "natural" geometry is warped to satisfy the ethical constraint.

fairness is not a free lunch. it changes the solution space.

the question isn't just "is it fair?", but "what geometry do we accept?"