What the Utility Score Is Really Ranking

What the Utility Score Is Really Ranking

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

What the Utility Score Is Really Ranking

A smart-city air-quality node must hand its pollution alert to the better carrier: a delivery vehicle that passes city hall 3 times a day scores U = 0.405, against 0.334 for a pedestrian who passes once a week — a 21% edge that the weights 0.6, 0.3, and 0.1 are meant to justify. This audit re-runs the weighted score at full precision and asks what that reassuringly exact number is really ranking.

Companion to the chapter DTN Social Routing — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is encounter predictability. The middle card applies this page's rule. The green card is carrier utility. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only encounter predictability, so the numeric fixture does not switch without explanation.

Encounter predictability changes carrier utility An input card leads through the rule utility = 0.6 x predictability + 0.105 fixed terms to the carrier utility result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. The chosen weight makes repeat encounters dominate the ranking while the other terms stay fixed.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 0.5 score.

  2. 2

    Name the relationship. utility = 0.6 x predictability + 0.105 fixed terms

  3. 3

    Substitute with units. 0.6 x 0.50 + 0.105 = 0.405

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change encounter predictability

Try Predict the direction of utility = 0.6 x predictability + 0.105 fixed terms. Test another encounter predictability, then compare carrier utility.

0.5 score
Chapter baseline
Carrier utility

Observe The chosen weight makes repeat encounters dominate the ranking while the other terms stay fixed. Reset encounter predictability to 0.5 and compare carrier utility.

Explain The chosen weight makes repeat encounters dominate the ranking while the other terms stay fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only encounter predictability moves here. Field effects named in the technical boundary stay fixed.

Ada: Social routing lives or dies on one comparison — is a candidate carrier a better bet than the node already holding the bundle? This chapter scores a delivery vehicle at U = 0.405 against a once-a-week pedestrian and calls it a 21% advantage. The weights (alpha = 0.6, beta = 0.3, gamma = 0.1) and the freshness and battery inputs (0.8 and 0.9) are the chapter’s own; let me re-run the score and keep full precision on the weekly rate.

  • Vehicle encounter rate: P_daily = 3 / 24 = 0.125 per hour.
  • Vehicle utility: 0.6 x 0.125 + 0.3 x 0.8 + 0.1 x 0.9 = 0.075 + 0.24 + 0.09 = 0.405.
  • Pedestrian encounter rate: P_weekly = 1 / 168 = 0.00595238 per hour (not the rounded 0.006).
  • Pedestrian utility: 0.6 x 0.00595238 + 0.24 + 0.09 = 0.00357143 + 0.33 = 0.333571.
  • Advantage: 0.405 / 0.333571 = 1.2141, i.e. 21.4% — the chapter’s “21%” rounded down slightly.

The audit confirms the ranking and sharpens the lesson: almost the entire gap comes from the encounter term (0.075 versus 0.0036), because the mobility and resource terms are identical for both carriers. A utility function only discriminates on the input that actually differs, so this forwarding decision rests entirely on the quality of the colocation estimate — not on the reassuring precision of the weighted sum.

Every number above is taken from the chapter’s own material and re-derived step by step.

TryChoose Check audit and calculate both relay utilities without rounding the weekly encounter-rate term.
ObserveThe vehicle scores 0.405 against 0.333571, producing a 21.4% ranking advantage.
ExplainThe weighted sum ranks the supplied encounter, freshness, and battery features; 0.405 is not a calibrated delivery probability.
Technical boundaries. The audit holds encounter rate, freshness, battery score, and weights fixed. It does not model correlated mobility, contact duration, buffer pressure, message expiry, route loops, social change, delivery history uncertainty, or sensitivity to weight choice.
Audit result

The full-precision ranking favours the vehicle, but a different weight set or mobility pattern can reverse that ordering.