Explores the case where the unweighted mean is reported directly to the
client, making the metric itself the source of satisfaction. Under this
model the entire paper's conclusion inverts: SPT genuinely maximizes
client satisfaction at zero marginal cost.
Analyzes this as a moral hazard / pooling equilibrium using game theory,
identifies three fragility conditions (client inspects own ticket,
competitor offers per-ticket SLAs, team internalizes the metric), and
maps the pattern across domains (education, healthcare, finance, software).
Concludes: the incentive exists, the equilibrium is real, and it holds
until it doesn't.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Corrections:
- Theorem 4: Restated from "maximizes slowdown inequality" (wrong) to
"uniquely assigns max completion time to largest task" (correct).
SPT actually compresses slowdown variance; harm is in absolute delay.
- Theorem 5: Completely rewritten. Old claim that LPT minimizes slowdown
variance was backwards (verified: tasks [1,5,10] give SPT var=0.06,
LPT var=42.2). New theorem correctly states SPT concentrates absolute
delay on the largest task.
- Theorem 10: Removed draft language ("Wait —"), corrected cross-term
analysis. Old claim that SPT is Pareto-dominated when p_H > 8p_L was
wrong (verified: n_H=2,n_L=2,p_H=10,p_L=1 gives D_SPT=275 < D_pri=283).
Replaced with correct WSJF exchange argument.
- IT example: Fixed PWCT arithmetic (9.225→10.2, 6.633→10.167). Added
honest discussion that aggregate PWCT fails to distinguish schedules;
per-priority-class metrics are needed.
- Section 5: Added caveat that Little's Law batch-case application is
not straightforward; clarified what Theorem 2 actually proves.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Sections 9-11: Prove that unweighted mean completion time becomes
adversarial under priority classification (Theorems 8-10), propose
PWCT/WSJF as alternatives with a worked IT service desk example,
and present honest counterarguments establishing the narrow conditions
under which the unweighted metric remains defensible.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Sections 7-8: Prove that optimizing unweighted mean completion time
maximizes slowdown inequality (Theorem 4), maximizes satisfaction
variance across clients (Theorem 5), provides zero throughput gain
(Theorem 6), and therefore simultaneously degrades client experience
while failing to improve productivity (Theorem 7).
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Mathematical proof that unweighted average task completion time
is gameable by scheduling policy (SPT), while work-weighted
completion time is schedule-invariant. Demonstrates that SPT's
apparent advantage is an artifact of the metric, not genuine
throughput improvement.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Mortdecai