A pivotal event for a Boolean event in a collection of binary variables is the event that changing one designated variable changes whether the
Boolean event occurs. For an increasing event depending on finitely many independent
Bernoulli variables of common parameter 
, a coordinate is pivotal precisely when its two possible values
give different outcomes. Its pivotal status depends only on the other coordinates.
If 
counts pivotal coordinates, differentiation
of the product measure gives Russo's formula
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For a crossing in a percolation configuration, this counts sites or cells whose color flip changes the crossing. In Voronoi percolation, the tessellation is held fixed when testing pivotality, and an annealed expectation subsequently averages over both geometry and colors.
