Market Design as Allocation Policy

Established The prize is a rule that hands out scarce public places without requiring anyone to lie about what they want, and it has already been collected at city scale. New York City ran roughly 100,000 high-school applicants a year through an uncoordinated process in which about 30,000 of them ended up in a school that appeared nowhere on their list. The deferred-acceptance clearinghouse adopted in 2003 cut that to about 3,000 in its first year, and raised the share placed in the main round from roughly half to 82 per cent.

Established The magnitude, in the units the field itself reports. Abdulkadiroglu, Agarwal and Pathak price the New York change at 10.62 miles of willingness to travel per student, standard error 0.64 miles, and locate the coordinated mechanism at about 80 per cent of an 18.96 mile range running from neighbourhood assignment to the utilitarian optimum. In kidney exchange the unit is transplants. The New England Program for Kidney Exchange, the first designed clearinghouse of its kind, produced 83 transplants in seven years from 2004; by 2019 well over 1,000 United States living-donor transplants a year came from exchange. Repairing the fragmentation still left in that market would add 200 to 440 transplants a year, 25 to 55 per cent of the then-current total, worth $220 million to $440 million annually.

Frontier Who gets the gain: the families who were never going to game the rule. The argument that carried Boston in 2005 was not efficiency but fairness — that a strategy-proof algorithm protects parents who do not strategise or who strategise badly — and the district’s own data showed both kinds in one applicant pool. The gain is redistributive before it is aggregate: it moves seats from households with good information to households without it, at roughly constant total seats.

Frontier The condition is the thing the field says least clearly: a matching mechanism reallocates access to places that already exist. Where the places differ little, reallocating them buys little. Angrist, Gray-Lobe, Idoux and Pathak find for Boston and New York that travel raises integration for the students who travel but has little or no effect on test scores or college attendance, because measured value-added differs so little between neighbourhood and choice schools. England’s 2008 statutory ban on immediate acceptance pushed every remaining local authority onto deferred acceptance and left low-income pupils at schools with lower value-added than before. The upside is real and it is bounded by supply, which is why the bottleneck list in section 5 opens on seats and organs rather than on algorithms.

Established A matching market is one where you cannot simply pay to get what you want, and both sides have to choose each other. Medical residencies, public school places, deceased-donor kidneys and army branch assignments share three features: the item is not sold at a market-clearing price, the recipient has preferences over which item they get, and the institution holding it has a claim ordering over who may receive it. Prices are absent by law, by ethics, or both — selling organs is illegal in the United States and almost everywhere else, and school seats are not auctioned. Something else must clear the market, and that something is an algorithm plus a priority rule.

Established The central object is the deferred-acceptance algorithm of Gale and Shapley, published in 1962 and independently in use since 1952. Applicants propose to their most-preferred institution; each institution holds the best applications received so far, up to capacity, and rejects the rest; rejected applicants propose again down their list until no proposal is rejected. Nothing is final until the end, which is what “deferred” means. The National Resident Matching Program reached the same algorithm a decade before the theorem, as an empirical fix called the Boston Pool modification, because the earlier Mullin–Stalnaker procedure penalised students who ranked a long shot first.

Established The property that made it a policy instrument is stability. A matching is stable when no applicant and no institution both prefer each other to what they got; in school assignment the same condition is called elimination of justified envy. Stability is what stops a clearinghouse being circumvented — a match that leaves blocking pairs on the table invites them to deal outside it, which is what unravelled every uncentralised medical market of the 1940s.

Established The second property is strategy-proofness for the proposing side, and it is a theorem rather than a design goal. Under applicant-proposing deferred acceptance no applicant can do better by submitting a list other than their true one. That is why the mechanism is legible: a district can tell parents to rank schools in the order they actually want them, and the statement is true.

Established The rule Boston replaced lacked that property, and its failure mode is specific rather than vague. The immediate-acceptance or “Boston” mechanism assigns every seat to students who ranked that school first, by priority, before looking at anyone’s second choice. A family that ranks an oversubscribed school first and misses loses its claim on its second choice too, because those seats are gone. The rational response is to rank a school you can actually get. The rule therefore prices information: families who understand it do better than families who do not, at identical true preferences.

Established The third mechanism in the family is top trading cycles, and the difference is about who owns a priority. Top trading cycles treats a priority as a property right that can be traded: a student with sibling priority at school A who prefers school B swaps with a student holding priority at B. It is Pareto efficient with respect to reported preferences and strategy-proof, but not stable, because a traded priority means somebody with a stronger claim was passed over.

Established You cannot have both, and the impossibility is proved rather than conjectured. Stability and Pareto efficiency with respect to student preferences are incompatible in general, so the designer chooses which to give up, and that choice is a political choice wearing formal clothes. This is the sense in which market design is allocation policy and not merely allocation software: the algorithm is where a district’s stated priorities become enforceable, and where conflicts between them become visible.

Established Gale and Shapley proved in 1962 that a stable matching always exists and that deferred acceptance finds one in finitely many steps. This is a constructive proof, not a simulation result, and it has not been disputed in sixty-four years. Among all stable matchings the algorithm returns the one most preferred by every member of the proposing side at once — the applicant-optimal stable matching.

Established Roth’s 1982 paper proved the positive incentive result and the impossibility that bounds it, in the same document. His Theorem 5 states that in the procedure which always yields the optimal stable outcome for one of the two sides, truthful revelation is a dominant strategy for all the agents in that set. His Theorem 3 states that no stable matching procedure for the general matching problem exists for which truthful revelation of preferences is a dominant strategy for all agents. Both are proofs. The second is why every deployed design must choose a side to protect, and why the unprotected side — hospitals, schools, programmes — keeps an incentive to misreport. Abdulkadiroglu and Andersson’s survey attributes the student-side result to Dubins and Freedman and to Roth, states the stability-versus-efficiency incompatibility by counterexample, and records the 2003 Abdulkadiroglu–Sonmez result that top trading cycles is Pareto efficient and strategy-proof but not stable. The design space is closed at the top.

Established The oldest deployment is the medical residency match, built to stop a market that had unravelled. By the 1940s American hospitals were making internship offers as early as a student’s second year of medical school, and offer deadlines had collapsed from ten days in 1945 to twelve hours in 1949, delivered by telegram and chased by telephone. Applicants had to answer before knowing what else might be offered. A clearinghouse using rank-order lists from both sides began operating for 1952 internships after a 1950 trial. The 1998 Roth–Peranson redesign, which handles couples and multi-year programme combinations, was described at the time as filling approximately 20,000 jobs a year.

Established That clearinghouse is now the largest it has ever been, and its 2026 figures are public. More than 53,000 applicants registered for the 2026 Main Residency Match, 48,050 certified a rank-order list, and more than 44,000 positions were offered across 6,809 certified programme tracks; 38,354 matched to first-year positions and 41,482 positions, 93.5 per cent, were filled. United States MD seniors matched at 93.5 per cent and DO seniors at 93.2 per cent, their highest on record; citizen international graduates at 70 per cent, also a record, and non-citizen international graduates at 56.4 per cent, the lowest in five years. A proved algorithm runs a national labour market once a year and the result is auditable.

Established New York City was the first school-choice redesign, and the problem it solved was congestion rather than strategy. Before 2003, roughly 100,000 eighth-graders applied to over 500 programmes, could rank five, and could receive multiple offers or none; only about half were placed in the main round, about a third were administratively assigned afterwards, and a number of schools appeared to conceal capacity from the central administration. Under the student-proposing deferred-acceptance design adopted for 2003–04, students ranked up to twelve programmes, over 70,000 matched to a school on their initial list, 7,600 more in a second round, and roughly 3,000 received none of their choices against about 30,000 the year before.

Established The measured welfare gain from that change is large by one metric in the paper and small by another in the same paper. Abdulkadiroglu, Agarwal and Pathak estimate the improvement in average student welfare between the uncoordinated and coordinated mechanisms at 10.62 miles of willingness to travel, standard error 0.64 miles. Against the 18.96 mile gap between neighbourhood assignment and the utilitarian optimum, the coordinated mechanism captures about 80 per cent, leaving 3.73 miles. The student-optimal stable matching would have added 0.11 miles, 0.6 per cent of the range; an ex-post Pareto-efficient matching 0.62 miles, 2.7 per cent. The brief on Institutional Design draws the uncomfortable general lesson: coordination did nearly all the work and algorithmic refinement did nearly none.

Established Boston is the case this brief is anchored to, and the anchor holds with one correction worth stating. Abdulkadiroglu, Pathak, Roth and Sonmez first met the Boston Public Schools planning team in October 2003; the School Committee opened a review that December; the superintendent announced in December 2004 that the algorithm would change; and on 20 July 2005 the Committee voted unanimously to adopt student-proposing deferred acceptance. The correction: the researchers’ own task-force recommendation was top trading cycles, and the district rejected it. Superintendent Thomas Payzant chose deferred acceptance because he did not want priorities, sibling priority above all, traded away, and judged that a trading mechanism would perpetuate the need or perceived need to game the system. The switch was a mechanism-design argument, but the district overruled the designers on which mechanism.

Established The empirical case against the old Boston rule is a set of discontinuities in the ranking data, and they are stark. At Lyndon Elementary 151 students ranked the school first and only 45 ranked it second; at Quincy the figures were 187 and 35. Among elementary applicants 53.4 per cent ranked an overdemanded school first and 35.7 per cent ranked one second, and of 202 unassigned elementary applicants 64 per cent could have received one of their stated choices simply by reordering their list. That is the signature of a rule that rewards information.

Frontier What the Boston analysis did not show is that the new rule would assign more students to their first choice, and on the district’s own data it would not have. Simulating all three mechanisms on the submitted 2001–02 lists under the null of no strategic behaviour, entering-kindergarten first-choice assignment was 77.9 per cent under the Boston mechanism, 73.7 per cent under deferred acceptance and 74.1 per cent under top trading cycles. Those lists were not truthful preferences, so the comparison is not a welfare comparison — but it was the only within-district comparison available at the time, and it pointed the other way.

Frontier The strongest evidence on whether the switch helped students is English, covers a national policy change, and is negative for the poorest families. An Act of Parliament banned the First Preference First criterion in 2008; 16 English local authorities using immediate acceptance were forced onto the equal-preference rule while 49 already using deferred acceptance were not, giving Terrier, Pathak and Ren a cross-market difference-in-differences design over 146 local authorities, 2,770 schools and 9.3 million students from 2002–03 to 2013–14. After the ban, low-socioeconomic-status students in treated authorities attended schools with value-added 0.8 percentage points lower relative to high-SES students, rising to 1.3 points in competitive authorities; their peers’ baseline achievement fell by 0.03 standard deviations, and by 0.072 in competitive authorities; and their enrolment at selective schools fell 2.6 points in competitive authorities. The authors’ explanation is mechanical: making the rule safe for truthful reporting encouraged high-SES parents to aim high, increasing competition at top schools and crowding low-SES students out.

Frontier That study also found no effect on the outcome a policymaker would most want to move, and states its own limits without prompting. Three years after enrolment, at Key Stage 3, there was no significant effect on the achievement gap. The authors have no individual data on reported preferences, cannot separate the mechanical effect of the algorithm change from changes in parental strategy, note that ranking lists were capped at three to six schools, and observe that England’s oversubscription rate of about 31 per cent is low by international standards.

Established Kidney exchange is the deployment where the mechanism unambiguously created transactions that did not previously exist. Roth, Sonmez and Unver proposed a clearinghouse in 2003 using a top trading cycles and chains mechanism, proving Pareto efficiency under one chain-selection rule and dominant-strategy incentive compatibility under others, against a United States baseline of over 55,000 patients on the cadaver waiting list, about 8,000 cadaveric and about 6,000 live-donor transplants a year, and roughly 3,400 waiting-list deaths. Their follow-up showed two- and three-way exchanges capture most of the available gain. Surgeons initially refused anything beyond two-pair exchanges because of operating-room simultaneity, so the first deployed design was deliberately smaller than the theory; the New England Program for Kidney Exchange produced 83 transplants in seven years.

Established The unlock was the non-simultaneous chain begun by a non-directed donor, and the growth figure is a hundredfold. Because a recipient in a chain receives before their donor gives, a broken chain harms nobody who has already donated, so chains need not be simultaneous. Rees and the Alliance for Paired Donation demonstrated this from 2007; by 2009 one chain had accomplished ten transplants across twenty surgeries, and chains of more than thirty followed. The NBER market design working group’s 2024 report states that research by its affiliates contributed to increasing paired-exchange transplants more than a hundredfold to over 1,000 annually, and Ashlagi and Roth record that well over 1,000 of the 2019 United States living-donor transplants resulted from exchange.

Frontier The designed kidney market is still badly fragmented, and that is measured. Agarwal, Ashlagi, Azevedo, Featherstone and Karaduman, using the full transplantation-network kidney-exchange dataset from 1 January 2008 to 4 December 2014 plus National Kidney Registry records, report that 62 per cent of kidney exchange transplants involve patients and donors from the same hospital, and that fixing these problems would generate between 200 to 440 additional transplants per year, 25 per cent to 55 per cent of the current total, corresponding to an economic value of between $220 million and $440 million annually.

Frontier Deceased-donor kidney allocation shows how far a well-run mechanism can sit from the outcome a planner would want. Agarwal, Hodgson and Somaini evaluate the United States deceased-donor system by life-years from transplantation rather than preference satisfaction, using patients who joined the waiting list between 1 January 2000 and 31 December 2010. The observed mechanism delivers an average of 9.29 life-years, 1.75 more than random assignment, against a maximum aggregate of 14.08. The gap is not incompetence: it is the tension between transplanting the sickest patients and transplanting those whose remaining lifespan would grow most.

Established The newest state deployment is military, and it shows the method working on an institution that is not a market at all. Greenberg, Pathak and Sonmez redesigned the United States Army’s cadet branching process, which assigns cadets to branches and can charge them extra years of service for priority. The rule in use for 2020 separated branch assignment from price determination, so cadets could be charged the higher price when they did not need it — nearly four times as often as under the older rule. The replacement lets cadets rank branch-price pairs directly and assigns both at once; the Army adopted it in autumn 2020 for the West Point class of 2021 and later for ROTC, covering roughly 70 per cent of newly commissioned officers, and the paper proves it is the unique rule satisfying five axioms drawn from the Army’s own stated objectives.

Frontier Adoption is wide, and the inventory matters because it is the evidence that this is policy rather than a seminar. Abdulkadiroglu and Andersson list deferred acceptance in Boston, New York City, Chicago, Denver, Indianapolis, Newark, Tulsa and Washington DC, and nationally or regionally in Chile, Finland, France, Ghana, Hungary, Ireland, Norway, Romania, Spain, Sweden, Taiwan, Tunisia and Turkey; top trading cycles in New Orleans’ Recovery School District from 2012 and in Oxelosund, Sweden; and immediate acceptance as abandoned in Boston and Chicago and forbidden by law in the United Kingdom. The same survey contains no systematic evaluation of whether adoption improved student outcomes, and its authors claim none.

Frontier The live question is not whether deferred acceptance is strategy-proof but whether strategy-proofness is worth what it costs. A strategy-proof rule collects true preferences; it does not collect intensity. Under immediate acceptance a family that cares enormously about one school can express that by taking a risk, and the resulting assignment can in principle be better in expected-utility terms for everyone before the lottery is drawn. Abdulkadiroglu, Che and Yasuda made this argument formally, and it is the main theoretical reason the profession does not treat the switch as settled policy. The English evidence is the same point arriving empirically.

Frontier Strategy-proofness only helps if participants know it, and the measured evidence is that many do not. Kapor, Neilson and Zimmerman surveyed New Haven school-choice participants and found subjective beliefs about admission chances with a mean absolute error of 37 percentage points, overestimation by about 8 points on average, 32 per cent of households listing a non-preferred school first, 48 per cent of revealed strategic applications qualifying as mistaken strategic behaviour, and only 20.6 per cent of respondents correctly understanding how ranking affects admission probability.

Frontier That same study contains the methodological warning the field has not absorbed. The authors find that switching to deferred acceptance improves welfare given the belief errors they observe — by about 3.9 miles of travel, 27 per cent of the mean baseline gain — but that an analyst assuming accurate beliefs would have reached the opposite conclusion, estimating a welfare loss of 1.8 miles. Two competent analyses of the same district, differing only in an assumption about beliefs, disagree about the sign.

Frontier The newer critique is that preferences are the wrong input, not merely the wrong measurement. Neal and Root argue that parents may not know enough about available options to form complete rankings at all, and propose policies to improve both knowledge and the quality of choices — work published as a chapter in 2026. Agte, Allende, Kapor, Neilson and Ochoa, in a paper revised in March 2026, find in Chile that parents do not know all schools, misperceive the quality ratings of schools they know and like, and underestimate how many schools exist; their model implies that cutting search costs without correcting beliefs can make outcomes worse.

Frontier If preferences do not track school effectiveness, optimising against preferences optimises the wrong objective. Abdulkadiroglu, Dur and Grigoryan design algorithms that maximise match quality subject to stability, reporting simulations with 20 schools and 1,000 students in which aggregate match quality runs about 40 per cent above deferred acceptance with random tie-breaking, against about 23 per cent for quality-based tie-breaking alone. That is a proposal, not a deployment, and it puts the normative question in the open: whose ranking is the mechanism supposed to satisfy?

Frontier Tie-breaking is an unresolved design question with real stakes and no empirical winner. Simulating deferred acceptance on 78,728 New York eighth-graders in 2006–07, a single tie-breaker assigned 32,105 students to their first choice and left 5,613 unassigned; multiple tie-breakers produced 2,256 fewer first-choice assignments and about 200 fewer unassigned. The distributions differ statistically but neither stochastically dominates the other, so the choice cannot be made on the data.

Frontier In kidney exchange the open frontier is time, not matching. Akbarpour, Combe, He, Hiller, Shimer and Tercieux propose an unpaired algorithm using memory of past giving as the medium of exchange, so a donation need not be reciprocated in the same clearing. On French data it reaches a 57 per cent match rate at an average 440-day wait against less than 34 per cent and more than 695 days for state-of-the-art algorithms, with the infeasible optimum only marginally better at 58 per cent and 425 days. Published 2025, not deployed.

Speculative The proposition that the whole apparatus generalises to any rationed public good is widely asserted and thinly evidenced. Public housing, refugee resettlement, foster care, daycare and disaster relief are all named as targets. The structural argument is sound — each has preferences, claims and no price — but the deployments are few, the evaluations fewer, and the settings differ in how contestable the priority order is.

Established Compute is not the bottleneck and has not been since the 1950s. Deferred acceptance runs in time polynomial in the number of applicants and the length of their lists; the 2026 residency match clears 48,050 certified lists against 44,344 positions in one batch. Nothing here is blocked by the cost of arithmetic, which distinguishes this subject sharply from almost every other in this corpus.

Established The binding constraint on the school side is the supply and variance of good schools. Angrist, Gray-Lobe, Idoux and Pathak attribute the absence of test-score and college-attendance effects from busing and choice in Boston and New York to minimal differences in value-added between neighbourhood and choice schools. If the variance in school quality is small, a perfect assignment and a random one produce similar outcomes, and no mechanism can manufacture variance.

Frontier The second school-side constraint is that choice changes house prices, which can undo the redistribution. Avery and Pathak model the general equilibrium and find that while choice compresses the gap between best and worst schools, housing prices adjust to the compressed distribution, both high- and low-income families face incentives to relocate, and the lowest-type residents may end up worse off than under neighbourhood assignment even when the worst schools improve.

Established On the organ side the constraint is biological and logistical before it is algorithmic. Crossmatch failures run above 35 per cent for highly sensitised patients at two of the three United States platforms; refusal rates run 20 to 35 per cent; and pools are structurally lopsided, with roughly 13 to 15 per cent over-demanded pairs against 42 to 43 per cent under-demanded pairs in 2012–14. A proposed match is a hypothesis about tissue compatibility and willingness, and a large fraction of those hypotheses fail.

Established Simultaneity was a hard operational constraint that had to be engineered around rather than optimised away. A two-pair exchange needs four operating rooms and four teams at once; a three-way needs six. Transplant centres customarily operate Tuesday to Thursday, and hospitals in different Medicare regions levy different charges, which had to be reconciled by inventing a standard acquisition charge. Under 2014 figures more than 60 per cent of United States kidney exchange transplants were internal to one hospital largely because of these frictions.

Frontier Congestion migrates rather than disappearing, and the residency match is where this is clearest. Electronic applications let candidates apply without limit while evaluation capacity stayed fixed; interviews were filled first-come first-served, privileging speed of reply over fit; travel added thousands of dollars to student debt; and programmes leaned on easily compared attributes such as first-licensing-exam scores. Signalling was introduced to ration attention, and in orthopaedic surgery the 30 permitted signals now act as a soft cap, with programme directors reporting they will not interview attractive applicants who did not signal.

Established The clearinghouse does not eliminate the residual market, it concentrates it. In 2026, 2,862 positions across 941 programmes went unfilled in the main match and 9,696 applicants went unmatched; the supplemental round placed 2,581 of those positions. Both figures rose against 2025.

Frontier The dependency that gates everything else is an agreed welfare metric, and there is not one. The candidates are willingness to travel in distance-equivalent utility, school value-added, peer composition, first-choice assignment rates, life-years from transplantation, and raw transplant counts. They disagree: on Boston’s data first-choice rates favoured the rule being abolished; on England’s data value-added favoured the rule being abolished; on New York’s data distance-equivalent utility favoured the reform strongly.

Established The methodological dependency that has been supplied is causal identification from the mechanism itself. Abdulkadiroglu, Angrist, Narita and Pathak showed that the lotteries embedded in deferred acceptance to break priority ties are themselves random assignment, and built estimators that recover school effects from assignment records covering far more students and schools than a standalone lottery study could. The mechanism generates its own evaluation instrument as a by-product, which is the single most useful thing market design has given education research.

Frontier Preference estimation from rank-order lists is solved in principle and contested in practice. Agarwal and Somaini survey the revealed-preference methods used to recover student preferences from choice data and are explicit that students do not always get their first choice, so standard demand estimation does not transfer. Every welfare number in this brief rests on one of these models.

Frontier Out-of-sample validation of those models exists and its verdict is qualified. Pathak and Shi used Boston’s 2013 Home-Based plan — three geographic zones replaced by address-specific menus, removing sixteen options and adding three for a typical kindergarten applicant — to score forecasts made before implementation. For one of two grades a simple ad hoc model did as well as the structural models; when actual applicant characteristics replaced forecast ones the structural models clearly won. The failure was in forecasting who would apply, not in modelling how they choose.

Frontier Long-horizon administrative linkage is the dependency nobody has satisfied for these switches. Evaluating a 2003 or 2005 reform on earnings, college completion or health means linking assignment records to tax, enrolment and health registries twenty years later, under privacy rules written for neither purpose. The cohorts exist; the linkage does not.

Speculative A dependency nobody has named is a theory of priority legitimacy. The theorems take the priority order as given. Where priorities come from — catchment, sibling, walk zone, examination, order-of-merit list, antibody sensitisation — determines who wins, and there is no formal literature on which priority orders a democratic body is entitled to impose. The brief on Institutional Design treats the adjacent question of whether rules can be engineered at all.

Frontier The decisive experiment is a long-horizon outcome comparison across a switch year, run on the lotteries the mechanism already embeds, with the welfare metric fixed and registered before the outcome data are opened. Boston switched in July 2005 and New York in 2003; England’s switch was forced on 16 local authorities in 2008. Each produced cohorts assigned under the old rule and cohorts assigned under the new one, and within each cohort the tie-breaking lotteries randomise seats among students of identical priority. The comparison that would settle the field’s central claim is therefore available in administrative data, and the reason it has settled nothing is that every analysis so far has chosen its welfare metric after seeing which way the data pointed.

Established The instrument the experiment needs already exists and is validated. The research-design-meets-market-design estimators recover causal school effects from assignment records by exploiting the tie-breaking lotteries, and they scale to whole districts rather than the handful of oversubscribed schools a standalone lottery study can reach.

Frontier What pre-registration would have to fix, in advance, is a short and contentious list. The primary outcome: value-added of school attended, peer achievement, distance travelled, first-choice assignment, or college completion at 25. The population: the whole cohort or the lowest-income decile, since the English result shows those give opposite signs. The comparison: switch-year discontinuity, cross-authority difference-in-differences, or within-cohort lottery contrast. And the sign that would count as failure, stated before the file is opened.

Frontier The English natural experiment is the closest thing to that design that has been run, and it was not pre-registered. A national statute forced the treatment, untreated authorities were a plausible control, the panel covers twelve years and 9.3 million students, and the result — low-SES students at lower-value-added schools after the switch, with no effect on the Key Stage 3 achievement gap — is the strongest single finding against the redesign consensus. Because the metric was chosen after the fact, a reader cannot tell how many metrics were examined.

Established A second, cheaper experiment runs every year and nobody reports it as one. Every district that changes its priority structure — Boston’s 2013 Home-Based plan, New York’s changes to screened admissions, Chicago’s selective-enrolment tiers — changes the input to a fixed algorithm and leaves a discontinuity in the same administrative record. Pathak and Shi showed such a change can be used to score forecasts made before it happened; that is a template, not a one-off.

Frontier The kidney analogue is a platform-level randomisation, and it is the one experiment here blocked for good reasons. Randomising hospitals into mandatory national-pool participation would test the 200-to-440-transplants estimate directly. It would also assign some patients to a less efficient clearinghouse, which no institutional review board would approve, so the counterfactual stays a structural estimate.

Frontier A staged rollout is the ethical substitute and has never been used for a matching reform. Districts adopt these systems all at once, on a date set by a school committee. Introducing a reform across a district’s zones in randomised order over three years would produce a stepped-wedge trial at no extra cost in seats; nobody has asked a board to phase a reform for the sake of measurement.

Speculative A field experiment on intensity would settle the one theoretical question the natural experiments cannot. The Abdulkadiroglu–Che–Yasuda argument is about ex-ante expected utility, which administrative outcomes do not observe. Eliciting cardinal valuations from real applicants before assignment, then scoring both mechanisms against those valuations, would test it; the elicitation is the hard part and no deployed system has attempted it.

Handwave The experiment most often proposed — simulate all mechanisms on submitted lists and pick the winner — cannot work, and the field knows it. Lists submitted under a manipulable rule are strategic reports, not preferences, so a simulation on them compares mechanisms on corrupted input. Boston’s own simulation illustrates the trap: it ranked the abolished mechanism first.

Established The result that would change this brief’s assessment fastest is a replication of the English finding under a pre-committed metric. If a second national switch reproduced the crowding-out of low-income students, the case for deferred acceptance would have to be restated as a fairness-of-process claim rather than an outcomes claim — which is, notably, the claim Boston actually made in 2005.

Frontier The horizon is not technical. The data exist, the estimators exist, the cohorts have aged twenty years. What does not exist is a funder willing to pay for an analysis whose metric is fixed before anyone knows the answer, or an agency willing to link assignment records to adult outcomes.

Established The engineering problem is an annual batch process with no second chance. A school or residency match runs once, on a fixed date, against a preference file that cannot be resubmitted, and binds tens of thousands of people for a year or more. There is no rollback, which is why deployed systems favour auditable simplicity over optimality: the design must be explicable to a school committee, defensible in litigation, and reproducible from the inputs.

Established Real systems are not textbook deferred acceptance, and the deviations are where the engineering lives. New York treats an educational-option programme as three programmes reflecting score bands, runs lottery schools on randomly generated preferences, handles specialised examination schools in a separate prior round, and runs a third round with a fresh random order for the unmatched. The residency match handles couples, whose presence means a stable matching is not guaranteed to exist, and finds one anyway; the Army mechanism assigns a branch and a price in the same pass.

Established Tie-breaking is an engineering decision with distributional consequences and no dominant answer. One lottery number per student, or one per student per school, changes who is assigned where, and the New York simulations show neither distribution dominates. Whichever is chosen must be published in advance and generated reproducibly, because the lottery is also the instrument the analysis in section 7 depends on.

Frontier Designed markets require maintenance, and Roth argues this is the normal condition rather than a failure. His analogy is a house: decades later some features no longer suit the inhabitants and others need updating because of changes outside. Every marketplace must solve thickness, congestion and safety repeatedly, and the solutions decay when technology, demography or law shifts. The residency match worked for forty years then broke on electronic applications; the economics job market, stabilised by signalling and a scramble from 2006, unravelled again in 2020–23 when video interviews made early offers cheap, prompting guidelines that invitations follow 1 December and offers stay open at least two weeks to 31 January.

Frontier The interface is now the frontier component, not the algorithm. Where the binding constraint is that families cannot rank what they have not heard of, the engineering task is search, comparison and quality display — territory shared with Civic Technology and, where the recommendation is machine-generated, with AI-Assisted Governance.

Speculative Nothing prevents a district running its match as a verifiable computation, and no district does. Publishing commitments to the lottery seed and the preference file before the run, plus a proof that the published assignment is the algorithm’s output on those inputs, would make manipulation detectable without revealing anyone’s list. This is standard cryptographic engineering, and its absence is a procurement fact rather than a technical one; the general problem belongs to Standards as Governance.

Established The sibling discipline is auction design, and it shares the field’s founding moment. The 1990s spectrum auctions and the residency match redesign are the two events market design dates itself from; the 2017 incentive auction, which bought spectrum rights back from television stations while selling them onward, is the most complex instance. Auctions solve allocation where money is permitted; matching solves it where money is not. The brief on Future Capital Markets carries the microstructure end of this.

Frontier Queueing and interconnection are the same problem in infrastructure clothing. An empirical analysis of the United States electricity interconnection queue finds that long queues raise waiting times, high interconnection costs drive withdrawals, and alternative queue rules with flat entry fees would increase completed capacity and cut emissions — a mechanism-design result about a process most people would call permitting.

Established Financial market design is where the failures are measured most precisely, and where the market does not fix itself. Latency-arbitrage races occur about once a minute per symbol in FTSE 100 stocks, account for roughly 20 per cent of trading volume, impose about a 0.5 basis point tax on trading and are worth on the order of $5 billion a year in global equity markets; a design eliminating them would cut liquidity costs by about 17 per cent. Budish, Lee and Shim then show why exchanges will not adopt it: they profit from selling speed. This is the sharpest counterexample to the assumption that better designs win on merit.

Frontier Rationing under emergency is the adjacent application with the most direct policy footprint. Pathak, Sonmez, Unver and Yenmez argue that reserve systems, which set aside proportions of a scarce resource for different claims, dominate priority-point systems for pandemic triage precisely because they do not force a single ranking over all units — letting a protocol honour instrumental value and equitable access at once rather than picking one.

Speculative The adjacency this brief would most like to see tested is intensity inside matching. Matching elicits ordinal preferences and discards intensity; Quadratic Mechanisms prices intensity and discards matching structure; Decision Markets in Governance prices outcomes. Nobody has run a hybrid at public scale, and the theory for one is incomplete.

Established The decision to change a mechanism is taken by a political body, and in Boston it overruled the economists. The School Committee voted on 20 July 2005; the superintendent, not the authors, chose deferred acceptance over the top trading cycles the task force had recommended, on the grounds that priorities should not be traded away and that a trading mechanism would be harder to explain. Any account of this field that presents the algorithm as the deliverable has the institutional relationship backwards.

Established Sonmez and Unver describe their own role in kidney and liver exchange as outsider critic rather than consultant, and say the distinction was decisive. Drawing on two decades in United States and Turkish clearinghouses, they argue that market design shaped institutions there through public criticism rather than paid advice, and generalise the approach as minimalist market design: translating an institution’s own objectives into axioms and deriving the unique rule that satisfies them. The Army branching reform and pandemic vaccine allocation are offered as instances.

Established The institutional prerequisite easiest to miss is a single authority that can compel a common deadline. New York’s pre-2003 failure was partly that schools concealed capacity from the central administration; the residency match works because participating programmes agree to be bound by the result. Without an authority able to bind both sides, a clearinghouse is a suggestion, and suggestions unravel.

Frontier Hospital-level incentives are an institutional problem the national kidney platforms have not solved. Agarwal and colleagues find that hospitals do not internalise their patients’ benefits from exchange and that platforms compensate them inadequately for contributing pairs, and conclude that capturing most of the available gains needs either a stronger participation mandate or new mechanisms plus reimbursement reform. They also note the market could support two to three national platforms near efficient scale, which is a regulatory question rather than a technical one.

Established Law is a hard boundary here in a way it is not on most engineering. Kidney exchange is legally prohibited in Germany and Brazil, practised with difficulty or not at all in China and India, and cross-border exchange remains rare despite the medical and financial logic — an Israel–United Arab Emirates exchange in 2021 stands out because it is unusual. Countries of around ten million people cannot reliably match hard cases domestically, which makes the legal barrier a mortality question.

Frontier The governance of a live mechanism is thinner than its design literature. There is a rich formal account of what a rule does and almost none of who may change it, on what notice, with what appeal. Districts alter priorities annually; the Army changed its branching rule in one cycle. The brief on Institutional Design owns the general question of whether such rules can be engineered; what this brief adds is that in matching the rule is already a statute in all but name.

Speculative There is no standing body anywhere that audits a deployed public matching mechanism. No jurisdiction this brief could find requires periodic independent review of an assignment algorithm the way it would require audit of an election or a pension fund. Given that these mechanisms allocate school places, medical careers and organs, that is an institutional gap rather than an oversight, and it is the kind of body Scientific Governance Models would have to specify.

Established The ethical argument that actually moved a school committee was about protecting the unsophisticated, not about efficiency. Boston’s superintendent argued that a strategy-proof algorithm levels the playing field by diminishing the harm done to parents who do not strategise or do not strategise well, and the supporting evidence was the coexistence of sophisticated and unsophisticated play in one applicant pool. This is a procedural-fairness claim, and it survives even if the outcome evidence stays mixed.

Frontier It is also a claim that can be true while the distributional result runs the other way. England’s switch made the rule safe for everyone and, on the measured evidence, moved low-income pupils to schools with lower value-added because truthful high-income families competed harder for the same top schools. Fair process and favourable distribution are separate goods, and the first does not imply the second.

Established Choosing stability over efficiency is choosing whose claim counts, and the choice is ethical rather than technical. Stability protects a priority holder from being passed over; Pareto efficiency lets priorities be traded for mutual gain. Boston chose the first and New Orleans’ Recovery School District the second. A sibling priority defended as a family-cohesion value cannot be traded; a sibling priority understood as an endowment can.

Frontier Reserve systems make the ethical pluralism explicit, which is their main virtue. Rather than compress instrumental value, equity and need into one ranking, a reserve system allocates shares to each claim and honours each within its share. During the 2020 pandemic some states prioritised frontline health workers on instrumental grounds while others declined on access grounds; reserves let both principles appear in one protocol without either silently dominating.

Frontier Repugnance is a measurable constraint on the design space, not a failure of public reasoning. Elias, Lacetera and Macis, surveying 2,666 Americans, found opinion split between those who oppose or support payment for kidneys regardless of consequences and about 18 per cent who would reconsider if payment substantially increased transplants; their companion choice experiment found the median respondent would support payment by a public agency for a six-percentage-point rise in annual kidney supply but demanded thirty points for private transactions. Identical efficiency, different verdicts, driven by fairness.

Frontier Designing against preferences raises a question the field has not answered. If parents systematically misperceive school quality, a mechanism maximising satisfaction of reported preferences maximises satisfaction of mistaken ones, and a mechanism overriding them substitutes the designer’s judgement. The match-quality proposals sit squarely in this dilemma and their authors say so.

Speculative The deepest ethical objection is that the mechanism launders a shortage. A well-run match makes the allocation of too few good schools or too few kidneys feel procedurally clean, which may reduce the political pressure that would otherwise build to create more of them. This brief found no study testing that, and states it as a hypothesis rather than a finding.

Established The durable civilizational fact is that a class of allocation decisions has moved from custom and queueing to designed, auditable procedure. Who gets a residency, a school place or a kidney is now set by a written rule that can be inspected, simulated and revised, in dozens of countries, for millions of people a year, and it happened in roughly twenty-five years.

Frontier It creates a new kind of constitutional text that nobody treats as one. A priority order encodes which claims a society recognises — residence, siblinghood, examination performance, order of merit, antibody sensitisation, service commitment — and a matching algorithm enforces it more consistently than any human process could. Constitutions get amendment procedures and courts. Assignment algorithms get an annual administrative update.

Frontier The scope of the method is bounded by the absence of a price, and that boundary is moral rather than technical. Where society permits payment, auctions do this work; where it forbids payment, matching does. The boundary moves: if attitudes to compensated donation shifted by the margins the survey evidence describes, part of kidney allocation would leave this field entirely.

Frontier The most likely civilizational failure mode is competence without direction. A jurisdiction can run an excellent match over a school system whose schools barely differ, and report first-choice rates rising while nothing about children’s lives changes. The English and Boston–New York evidence both point this way: a well-designed reallocation of an undifferentiated resource is a well-designed nothing.

Speculative The second failure mode is legitimacy transfer. When an allocation is produced by an algorithm with a theorem attached, objection becomes technically illiterate by construction, and the argument about priorities gets conducted as an argument about mechanisms. Whether this has happened anywhere is untested; that the incentive exists is clear from how the Boston debate was reported.

Speculative The strongest long-run case is that this is the template for allocating anything scarce and unpriceable. Refugee places, disaster housing, court-appointed counsel, vaccine doses and compute for public research each have preferences, claims and a legal or moral bar on payment. If the template holds, market design becomes a standing branch of public administration rather than a consulting speciality. Deployments outside education, medicine and the military remain thin enough that this stays a projection.

Handwave The claim that designed allocation raises aggregate social welfare at national scale is not supported by anything in this brief. Every credible estimate here is local — one city’s students, one country’s transplant pool — and the metrics do not aggregate. Anyone offering a national or global welfare figure for market design is extrapolating from the New York miles and should say so.

These horizons track two separate clocks: how fast the mechanisms spread, and how fast anyone learns whether they helped. The second is much slower, and nothing in this record suggests it is accelerating.

• 10 yr: Frontier The 2003–2008 switch cohorts reach their mid-thirties and adult administrative outcomes become linkable in principle; whether a pre-registered long-horizon comparison is run depends on funding rather than method, and the instrument described in section 7 already exists. Expect continued spread to new districts and countries, further reserve-system adoption in rationing protocols, and at least one more national natural experiment of the English kind. Kidney exchange consolidation toward two or three national platforms is the single change with the largest measured payoff available.
• 25 yr: Speculative Either the welfare question is settled by a small number of pre-committed studies and the field’s claim narrows to procedural fairness plus congestion relief, or it is not settled and adoption continues on the strength of the theorems alone. Applications outside education, medicine and the military — housing, refugee placement, caseload assignment — either accumulate evaluations or remain demonstrations; the administrative capacity catalogued alongside Future Civil Services is where that would show up first.
• 50 yr: Speculative If organ supply changes character — through the routes covered in Lab-Grown Organs and Ex-Vivo Organ Repair — the exchange problem shrinks toward irrelevance, which is the clearest illustration in this brief that a matching mechanism is a response to scarcity rather than a cure for it. School assignment has no equivalent exit.
• 100 / 250+ yr: Handwave Any claim that designed allocation becomes a permanent organ of government at that horizon is a claim about institutions two and a half centuries out. This brief attaches no probability to it and notes only that the residency match has now run annually for seventy-four years, the longest continuous record any mechanism in this family has.

• Depends on nothing on this map blocks building or running these mechanisms — the algorithms are sixty-four years old and the compute is trivial. What it waits on is evaluative rather than technical: whether engineered rules change outcomes at all is owned by Institutional Design, the measurement of school effectiveness that every welfare claim here rests on sits with Future Education Systems, and the administrative capacity to run an annual binding clearinghouse is the subject of Future Civil Services.
• Requires (not on this map) a long-horizon outcome study across a switch year whose welfare metric is registered before the data are opened, which is the one result that would move this brief. Legal authority to link assignment records to adult earnings, enrolment and health registries, without which the long horizon cannot be observed at all. A rule compelling hospitals into the national kidney pools, worth 200 to 440 transplants a year on the published estimate. A method for eliciting how much applicants care, not merely what they rank, since the strongest theoretical objection to deferred acceptance is about intensity and administrative data cannot see it. A standing audit body for live allocation algorithms, which no jurisdiction has. And more transplantable kidneys, because everything above redistributes a fixed pool.
• Enables credible impact evaluation of schools at district scale, because the tie-breaking lotteries are randomisation the district was going to perform anyway; a defensible allocation procedure for any resource that cannot be priced; and an explicit, inspectable statement of which claims a public body recognises, which is a precondition for arguing about them.
• Adjacent Quadratic Mechanisms, which prices the intensity this family discards; Decision Markets in Governance and Insurance as Regulator, the other two routes by which a formal instrument does a governing job; Standards as Governance for the verifiability of a published rule; Future Capital Markets for the auction and microstructure side; and Future Labour Markets, which inherits the residency match as its oldest worked example.

Established “Deferred acceptance is proved optimal, so switching to it must make students better off.” The theorem does not say that. What is proved is existence of a stable matching, applicant-optimality within that set, and strategy-proofness for the proposing side. None is a statement about educational outcomes, and the applicant-optimal stable matching can be Pareto-dominated by an unstable one — a gap the New York decomposition prices at 0.62 miles.

Established “Strategy-proof means strategy is gone.” It means one specific strategy is gone. Misreporting the order of your list no longer pays. Choosing where to live, which sibling to place first, which examination to sit and which programmes to signal all still pay, and the priority structure those actions target is untouched by the theorem.

Frontier “The algorithm decides who gets in.” The priority order decides; the algorithm enforces. Two districts running identical code with different priorities produce entirely different assignments. The substantive political argument is about catchment boundaries, sibling rules, walk zones and examination cutoffs, and it is routinely conducted as though it were about the algorithm.

Frontier “The old Boston mechanism was irrational.” It was manipulable, which is different, and on one metric it beat its replacement. Simulated on submitted lists, entering-kindergarten first-choice assignment was 77.9 per cent under the Boston rule against 73.7 per cent under deferred acceptance. Those lists are strategic reports, so the comparison does not establish welfare — but anyone claiming the old rule was simply worse should be able to say why that number does not count.

Frontier “A Nobel Prize settles it.” The 2012 prize was for the theory of stable allocations and the practice of market design, and the theory is not in dispute. What is in dispute is whether the deployments improved welfare for students, which is an econometric question the prize does not address. The strongest quasi-experimental evidence, from England’s 2008 ban, points the other way for low-income pupils.

Established “Centralised assignment is school choice.” They are separate decisions and the evidence separates them. New York’s measured gain came overwhelmingly from coordinating an existing choice process rather than from the algorithm chosen to run it: the coordinated mechanism captured about 80 per cent of the available range, and the student-optimal stable matching would have added 0.6 per cent of it.

Established “Kidney exchange solved the kidney shortage.” It did not come close, and the arithmetic is public. Exchange produces over 1,000 United States transplants a year against a waiting list that stood above 55,000 when the mechanism was proposed, and the best estimate of what fixing the market’s remaining fragmentation would add is 200 to 440 transplants a year. Exchange is a large improvement on a small base.

Speculative “Machine learning will produce better assignments than these algorithms.” There is nothing to learn that changes the result. Deferred acceptance already computes the applicant-optimal stable matching exactly; a learned model cannot beat an exact optimum on the same objective, and if it beats it on a different objective that is a change of policy, not of technology. A learned model could help upstream, predicting match quality, which is a different claim from replacing the mechanism.

Handwave “Any allocation problem can be handled this way.” The template is asserted far more often than tested. Public housing, refugee placement, foster care, disaster relief and compute allocation are all named as candidates; the evaluated deployments remain concentrated in schools, medical training, organs and one military assignment process.

Established “Once designed, a market stays fixed.” Every case in this brief needed repair. The residency match ran forty years then broke on electronic applications; the economics job market was stabilised in 2006 and unravelled again on video interviews between 2020 and 2023; kidney exchange needed non-simultaneous chains, standard acquisition charges and a participation fix; Boston changed its priority structure again in 2013. Maintenance is the normal state, not an exception.