A common beginning
Two good futures.
One beginning.
A wildlife crossing must be started before a survey tells us which habitat needs its guiding route: east or west. We can draw a good design for either answer. But can we begin both designs in the same way?
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When does flexibility earn its keep?
Every option must work for both possible requirements. We compare money and land separately; there is no hidden score that trades one against the other.
Later choices allowed
Keep the design behind the numbers.
A dot is a resource requirement. Select a complete choice to see its beginning, its later components and the arithmetic in each future.
A choice stays on the frontier if no other choice uses no more of either resource and strictly less of at least one. Equal totals can still have different designs.
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What changed?
A design is more than its best number.
The cheap east-only design and the cheap west-only design have different beginnings. Choosing each separately gives a reassuring answer to two separate questions. It does not give us a decision we can take before the survey.
The reserved junction costs more at the start, but retains both connection points. With a useful survey in time, we choose one matching guiding route later. If we discard that junction because it loses to a different specialist in each future, we lose the useful common beginning.
There is no general instruction here to “stay flexible.” A fixed compact crossing serves both requirements without using the survey. Increase the cost of the reserved junction and the fixed crossing can become better on both resources. Remove the long fence corridors and the compact site, and a timely survey can instead make the difference between a feasible plan and none in this catalogue.
The exact components and what connects to what
An exit is a connection type, not a quality score. A later component must find every exit it requires; it must then supply the route called for by the survey. “I” is the compact crossing’s integrated connection. Its routes are already paid for in the early price and footprint: zero later cost means no additional work, not free construction.
The early and later land footprints are assumed disjoint, so they add. Common bridge work is outside the comparison. The stated guide costs include installation and later mobilisation; only the reserved junction’s extra cost and the survey price vary. The two requirements have no assigned probabilities; animal behaviour is outside this model.
A closer look at the construction — worth the extra concentration
The order of the choices is the whole issue. First choose one early component. Then choose a later component for each observation the decision-maker can actually receive. If two futures still look the same, the later choice must be the same too.
For each such rule, connect the components and check both future requirements. Only then compare resources. This keeps the early component’s identity until we know whether it can support the whole plan.
In each future, money is early work + chosen later work + survey, if used. Land is early footprint + chosen later footprint. The displayed pair takes the largest money requirement and the largest land requirement across the two futures. It is a budget that covers either future, not their sum or an expected value. Those two maxima can come from different futures.
Allowing later choices includes the option of doing exactly the same thing whatever the survey says. Such a plan needs no survey here. The hindsight comparison relaxes the earlier commitment as well: it may install a different early crossing for each answer. It is useful as a benchmark, but requires information before construction starts.
This is exact enumeration of a small finite catalogue. It applies implementation and composition ideas from co-design. Read the method, assumptions and testable claims for its formal scope.
From the example to the research
A route into the idea.
You do not need these papers to use the example. They explain why we keep the implementation, its connections and the timing of choices visible.
- Start with implementations. Andrea Censi, A Mathematical Theory of Co-Design, §III, Definitions 10–12. A design has an identity, capabilities and resource needs; connected components must satisfy one another’s requirements.
- Keep shared choices when uncertainty arrives. Huang, Furter and Zardini, On Composable and Parametric Uncertainty in Systems Co-Design (2025), §III-D. Choosing after learning and committing beforehand are different queries.
- Make the timing explicit. Huang and Zardini, Distributional Uncertainty and Adaptive Decision-Making in System Co-design (August 2026), §IV-B and §V-D. This already develops staged choices and observations. Our contribution here is the small, inspectable demonstration.
The earlier Censi uncertainty paper bounds uncertain design problems; those bounds alone do not give a shared early commitment. Further source connections and the limits of this example.