Which social science finding says small groups of committed people shift a majority at about 25 per cent?

The tipping point in social convention. A 2018 experiment put groups online to agree a naming convention, let it settle, then introduced confederates who insisted on an alternative. Below about 25 per cent of the group they were absorbed and ignored; above it the whole group flipped, usually fast.

The mechanism is memory rather than persuasion. Participants weigh recent interactions, so once a minority is common enough that most people have met it several times lately, the alternative stops looking eccentric and starts looking like an option. The threshold moved with how much history people carried, which is the useful detail - it is not a magic number so much as a consequence of how long a convention takes to feel normal.

The finding gets cited well beyond what it supports. It is about arbitrary conventions in small online groups, not about revolutions or referenda, and attempts to read a fixed 3.5 per cent or 25 per cent rule onto political movements are doing something the experiment cannot license. It is nonetheless one of the cleaner demonstrations that social change can be non-linear - nothing, nothing, nothing, then everything.