Tensions in Practice: A second site need not add a second population¶
An invented network of collection points
An existing collection point is reachable by A and B under a fixed travel-time limit. Two candidate new points each have a two-person catchment: X reaches B and C; Y reaches C and D. Compare adding X or Y. Both add a site with two reachable people, but they add different numbers of previously uncovered people.
Offer another reachable option
Give some already-served users a second site.
Extend unique coverage
Bring previously unreachable users inside at least one site’s catchment.
Why these aims pull against each other
Overlapping reach can supply choice to an existing user, but that overlap does not count as a newly covered person. The union of reachable sets differs from the sum of site counts.
Choose an arrangement to see what changes and what remains difficult.
Compare the same rows across alternatives. Cells state explicit toy quantities, membership or permissions; colors do not supply additional meaning.
What this choice protects
What it costs
When it fits
Compare the arrangements
Add overlapping X
X reaches B and C, while the original site still reaches A and B.
| Existing | New site | Any site | |
|---|---|---|---|
| A | Yes | No | Yes |
| B | Yes | Yes | Yes |
| C | No | Yes | Yes |
| D | No | No | No |
- What it protects
- Gives B a second reachable location and adds C to total coverage.
- What it costs
- D remains outside; the two site counts sum to 4 but only 3 distinct people can reach a site.
- When it fits
- Plausible when giving B a second option has value beyond maximizing unique coverage.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
Add nonoverlapping Y
Y reaches C and D; the existing site still reaches A and B.
| Existing | New site | Any site | |
|---|---|---|---|
| A | Yes | No | Yes |
| B | Yes | No | Yes |
| C | No | Yes | Yes |
| D | No | Yes | Yes |
- What it protects
- Adds two previously uncovered people, giving 4 unique reachable users.
- What it costs
- No one gets a second reachable location; operating costs and suitability of Y remain to be assessed.
- When it fits
- Plausible when extending distinct-user reach is more valuable than local overlap and Y is otherwise feasible.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
What this illustration does—and does not—establish
The source establishes the structural tension; the concrete alternatives and their conditional costs are editorial synthesis. No arrangement is a universal recommendation.
- The toy sets are assumed results of a friction-weighted access calculation. Geographic distance alone does not establish them.
- Reachable does not mean willing, served or able to obtain capacity. A second reachable site is only a potential alternative, not guaranteed resilience.
Source entries
Access Catchment
Access catchment T 5 supplies the local tension. The setting, alternative arrangements, and stipulated consequences are editorial applications.
Single-Node Catchment versus Overlapping Catchments (scalar)
A node's catchment computed in isolation ignores that nearby nodes compete for and share the same population, so summing per-node catchments double-counts and overstates total coverage.