Preference participants are never pooled into the primary W survival cohort.
Make the choice real.
Keep the estimate honest.
At seven residence milestones, a separately preregistered substudy offers a genuine choice: continue with the robot or take a randomized alternative study benefit. The choice is honored, nonresponse remains visible, and the resulting reservation value stays interval-censored and outside W.
Behavior, not praise.
Bounds, not guesses.
A binding offer reveals whether the participant's reservation value lies above or below that offer. It does not reveal an exact personal price.
One offer is drawn independently from the frozen benefit lattice at every reached milestone.
Keep means continued access; benefit means the alternative is delivered and robot access ends.
One binary choice reveals an interval, so the median is reported as a set—not an invented point.
Seven choices.
One longitudinal curve.
Every milestone reached by an eligible environment creates one due record. Silence is retained as nonresponse; an early benefit choice ends access and therefore ends future eligibility.
One choice gives
one inequality.
KEEP ROBOTR ≥ randomized offer
TAKE BENEFITR < randomized offer
At each milestone, the empirical median is published as the sharp interval [lower, upper). An unbounded upper endpoint remains ∞; zero completed choices remain null.Retain every choice.
Rebuild every bound.
The checker derives due milestones from exposure, validates randomization and binding outcomes, then reproduces all seven interval summaries.
It measures the offered benefit participants choose the robot over. It does not measure wealth-adjusted welfare, and it cannot compensate for rejection, burden, or unsafe behavior.
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