Keep trying — you never know which conversation moves someone to action.
n → ∞ names a discipline, not a metaphor. Robert Axelrod's research on the evolution of cooperation found that simple reciprocity — cooperate first, then mirror what the other side does — outperforms every more complicated strategy in repeated interactions, and that the incentive to cooperate rises as the expectation of future interactions approaches infinity: the more likely two parties are to meet again, the more it pays each of them to cooperate now.[^1] Trust isn't won in a single encounter. It's built by acting as though there will always be a next one.
That is also the economic case for standing relationships. Ronald Coase's work on the theory of the firm showed that every one-off transaction pays, in full, the cost of establishing trust from zero — finding the other party, negotiating terms, verifying good faith.[^2] A durable relationship exists precisely because it amortizes that cost: once trust is built, every future interaction is cheaper than the last. Staying in the relationship isn't just persistence — it's the efficient path.
This shows up directly in how trust gets built between advocates and the people they serve. Ascanio Piomelli's work on collaborative lawyering describes trust between lawyer and client as something built through a sustained, non-hierarchical relationship — treating the client as the expert on their own life, not the recipient of the lawyer's expertise.[^3] Marshall Ganz's organizing research locates the same mechanism on the political side: political power is built one relationship at a time, through repeated, reciprocal one-on-one contact, not a single persuasive appeal.[^4]
The practical consequence: you cannot know which contact is the one that moves someone, because the tipping point belongs to the sequence, not to any single conversation in it. Keep the door open. Keep initiating contact in good faith. People cooperate back — not always on the first try, but reliably, if the relationship is allowed to run toward n → ∞.
[^1]: Axelrod, R., The Evolution of Cooperation (Basic Books, 1984).
[^2]: Coase, R.H., "The Nature of the Firm," Economica 4(16) (1937).
[^3]: Piomelli, A., "The Democratic Roots of Collaborative Lawyering," Clinical Law Review (2006).
[^4]: Ganz, M., Why David Sometimes Wins (Oxford University Press, 2009).