Who Rises When

It's tempting to think the distribution rules must decide how quickly a community reaches independence. Rules like: how the spillover is shared, whether the poorest or the middle earners are favored, how far a fast member may pull ahead. They mostly don't decide it. The finish line is set by how fast the businesses compound (see ROI is Destiny). The rules decide something else: who rises when.

That is not a small thing. It's the difference between two communities. One crosses the line all together. In the other, a lucky few finish early while the rest wait through a long tail. The date can be identical and the lived experience completely different.

Here is the same model run two ways (seed 12345). One uses strict lockstep — no member may climb past the community's frontier (max gap 0). The other lets members run up to three levels ahead (max gap 3). Each line is the share of members who have reached full coverage, over time.

The strict-lockstep wave rises late and then crosses almost vertically. Everyone lands within months of each other. The loose-gap wave starts its first graduations earlier. But it then stretches into a tail as the leaders wait for the stragglers, and it finishes later overall. Letting people run ahead doesn't speed the community up. It just spends the early capital on members who were already doing fine.

The logic is simple once you see it. Early capital is scarce. Every dollar sent to a member who is ahead is a dollar not sent to the member who is furthest behind. And it's the furthest-behind member who decides the graduation date, because the community only graduates when its last member is covered. Strict lockstep aims the scarce early capital exactly where it shortens the finish: at the back of the pack.

So the fairest rule and the fastest rule are the same rule. Holding everyone together isn't a moral tax on speed. It is the speed. A sweep across every gap tolerance confirms it. Max gap 0 graduates everyone soonest and keeps the tightest income spread the whole way.

This reframes what the distribution knobs are for. Take the spillover shape (favor the poorest, the middle, or the near-graduates), the allotment concentration, the cross-parliament split. None of these are levers for the finish date. They are levers for the character of the journey: how equal the climb feels year by year, who gets lifted first, how visible early progress is.

That's a healthy separation. A community can tune the feel of its middle years without ever gambling with the date everyone actually cares about. It can choose the encouragement of seeing some members reach milestones early, or the solidarity of everyone moving as one. Set the clock with ROI and the reinvest slice. Set the feel with the distribution rules.