# Shared Routes, Individual Delay, and Fair Cost Allocation **Status:** An applied coordination problem and product-design proposal. **Edition:** English editorial reconstruction. Commercial names, local targeting, and rollout assignments are omitted. Numerical examples are illustrative, not current fares or financial advice. This branch is not presented as a consequence of the normative theory. ## 1. Cooperation must benefit the individual participant A shared journey can reduce total cost while imposing an unfair delay on one passenger. The objective should therefore account for each passenger's net benefit, not only occupancy, total distance, or aggregate savings. Pickup, dropoff, route order, service charges, capacity, and time preferences interact. ## 2. Transport charge and matching charge The proposal separates the actual transport cost from a matching-service charge. A candidate service charge is a fraction of the savings produced by a match: gross saving = estimated solo fare − allocated shared fare service charge = rate × gross saving net saving = gross saving − service charge A matching credit covers the matching charge, not automatically the transport fare. A proposed match should not silently consume credit before the relevant conditions are satisfied. These are candidate accounting rules, not a finding that one business model is optimal. ## 3. More passengers need not mean a larger percentage An illustrative policy lowers the percentage charged on each participant's saving as occupancy rises, while seeking sustainable total revenue. Whether both goals can be met depends on the actual savings and cost structure. The percentages remain experimental parameters. The underlying question is how to encourage higher utilization without reducing individual benefit. ## 4. Pickup detour is only part of the effect Adding a passenger changes both the pickup route and the later dropoff route. For an existing passenger i: additional time_i = arrival time_i on proposed route − arrival time_i on prior route A proposal producing delays of one, one, and eight minutes should not be described solely by its modest average. Maximum individual delay can matter as much as total delay. ## 5. Route order is part of the agreement Each passenger's pickup must precede that passenger's dropoff. Capacity must hold throughout the route. Different valid orders can produce different prices and arrival times. A short pickup diversion can create a substantial later dropoff diversion. The relevant computation evaluates the whole proposed sequence, not just geometric proximity to a line. ## 6. The symmetric-junction example Suppose two destinations A and B lie equally far in different directions from a junction X. The route X → A → X → B leaves B in the vehicle longer. But the extra travel is caused partly by serving A. Charging B for every additional occupied kilometer would confuse usage with responsibility. The example separates two quantities: - How long and how far a passenger occupies the vehicle. - How much extra travel that passenger's inclusion imposes on others. ## 7. Marginal cost and its limits One candidate compares total route cost C with the recomputed route excluding passenger i: marginal contribution_i = C − C_without_i This asks how much the participant changes the overall route rather than only how long they remain onboard. **Editorial qualification:** These marginal contributions do not automatically sum to C. They are candidate inputs to an allocation rule, not a complete budget-balanced solution. ## 8. Compensation for delay A proposed allocation combines a shared-use component, a participant's pickup/dropoff contribution, and compensation for delay imposed by others. The earlier dropoff need not always receive the lowest price. An alternative order might be offered at another price if participants prefer its time tradeoff. The open mechanism-design question is how to make those choices clear, feasible, and acceptable to everyone affected. ## 9. A map of joint opportunities The interface proposal includes available vehicles, occupied vehicles open to sharing, individual requests, and groups. A person can form a group before requesting a vehicle. The group then becomes one coordinated request with its own capacity and routing constraints. Approximate direction or route corridor can be visible before exact locations are necessary. Exact home addresses and destinations should not be public discovery metadata. ## 10. The offer as a reviewable object A useful offer exposes: - Seats and participants. - Pickup and dropoff effects. - Each affected passenger's added time. - Shared fare, service charge, and net saving. - The route order and acceptance conditions. A compact display of added time, net saving, and matching charge can help comparison. It should not conceal a large individual delay behind an average. A changed route or expired offer requires a corresponding state change, not an invisible revision of what was accepted. ## 11. Matching state and credit state Searching, proposal, acceptance, pickup, travel, completion, rejection, and cancellation are different states. A temporary hold and a finalized charge should also be distinguished. Cancellation needs an explicit rule for releasing holds or applying any separately agreed condition. These are proposed state semantics. No live transport or payment service is created by this publication. ## 12. Controlled evaluation A small controlled study could compare estimated and observed route changes, notification delay, location error, cancellation, disconnection, and stability under recalculation. Simulation can explore route orders and individual benefit before any deployment. No completed trial is claimed. ## 13. Open questions How should route cost be divided while preserving individual benefit and total cost recovery? How should time preferences influence order without hiding disadvantages? What information must be disclosed for meaningful consent? How should uncertainty in travel time affect an offer? What happens when a participant joins or leaves? Can compensation correct an unfair route without creating incentives to exaggerate delay sensitivity? This concrete setting makes tensions among efficiency, explanation, privacy, and consent inspectable without assuming one universal fairness formula.