One Yes-or-No Note From Each Agency Could Fix Broken Aid Programs
When agencies don't share data, people fall through the cracks. New math shows a tiny fix.
When complementary resources are split across agencies that each see only their own coordinate of a person's needs, the paper shows local information alone can make even optimally coordinated policies arbitrarily inefficient — by a factor linear in the number of goods, and by a factor inverse in OPT with just three agencies. Measuring against a generous decentralized benchmark, the author finds a fix in "threshold referrals": an agency reports if its value lies below a public threshold, and a clearing rule uses only the joint reports. One threshold yields welfare of at least OPT/[4(1+ln(2/OPT))] with one bit per agency, and an equal-revenue family shows this log-loss is tight for a single threshold. A geometric threshold ladder improves this to a constant fraction of OPT with doubly-logarithmic messages: a staircase recovers OPT/8 with Θ(log log(1/OPT)) bits, which the paper shows is necessary within that class.
- When several agencies each hold one piece of someone's needs, using only their own information can waste almost all the potential benefit — even if everyone cooperates.
- The fix is tiny: each agency sends a single yes-or-no signal comparing a person's need to a public cutoff, and a large share of the lost value comes back.
- A slightly richer signal (a short 'staircase' of cutoffs, just a few bits per agency) recovers a guaranteed constant fraction of the best possible outcome.
Why It Matters
Better coordination between aid, health, and housing agencies — without anyone handing over your full personal file.