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3. a small protest is both unlikely to effectuate change and...

# Question: a small protest is both unlikely to effectuate change and...

###### Question details

A small protest is both unlikely to effectuate change and provides less of the fulfilling feeling of being part of a large community. In other words, protesters produce positive externalities for other potential protesters. This has several implications for the dynamics of protests; most relevantly for present purposes, it means that protesting often has a "tipping point": if the protest crosses a certain threshold in size, it snowballs to become a large movement. If the protest is smaller than that threshold, conversely, it will tend to peter out.

As a simplified model of this, consider a society where each person thinks that choosing to protest involves costs – in time, effort, risk of arrest or injury, etc. – valued at $60. Each person thinks that if the number of people participating in a protest is p, the benefit of that protest is$p2 (that is, p squared). What would the tipping point be in this scenario? That is, how many others must people in this society think will protest before deciding it is worth joining the protest themselves?