Experimental Economics in the Tradition of John Kagel (video)

 In October there was an in-person celebration of John Kagel, which I was delighted to participate in, in Tucson, Arizona. (It was my first in-person conference since the beginning of the Covid pandemic, during a brief window of optimism.) Now it's been posted on YouTube by the hosts, at the Economic Science Lab of the University of Arizona:

Keynote lecture of Professor Alvin Roth at the Workshop in Honor of John Kagel, Tucson, Arizona, October 2021

My talk was called Experimental Economics in the Tradition of John Kagel, and I began by explaining this photograph, which has John in the middle.

I eventually focused on how the following experiment helped shape a good deal of practical market design:

Kagel, John H. and A.E. Roth, "The dynamics of reorganization in matching markets: A laboratory experiment motivated by a natural experiment," Quarterly Journal of Economics, February, 2000, 201-235.

And I concluded by giving John some unnecessary advice as he embarks on his tenth decade.

**********

You can see more from the 2021 North-American Economic Science Association Conference (including the above video) here.

Report from Dagstuhl: Matching Under Preferences: Theory and Practice, Edited by Haris Aziz, Péter Biró, Tamás Fleiner, and Bettina Klaus

 Matching theory was alive and well during the pandemic. Here's a report of the (partially in person) Dagstuhl Seminar, July 25–30, 2021 – http://www.dagstuhl.de/21301

Report from Dagstuhl Seminar: Matching Under Preferences: Theory and Practice, Edited by Haris Aziz, Péter Biró, Tamás Fleiner, and Bettina Klaus

"This report documents the program and the outcomes of Dagstuhl Seminar 21301 “Matching Under Preferences: Theory and Practice”. The seminar featured a mixture of technical scientific talks, survey talks, open problem presentations, working group sessions, five-minute contributions (“rump session”), and a panel discussion. This was the first Dagstuhl seminar that was dedicated to matching under preferences.    

...

"The seminar was conducted in a hybrid manner, with 15 participants attending the seminar physically from the Dagstuhl center and 34 participants attending online.

...

"The four main focus topics of the workshop were the following ones.

1. Matching markets with distributional constraints,

2. Probabilistic and Fractional Matching,

3. Matching in online and dynamic settings, and

4. Matching Markets and machine learning."

***********

As a sign of the times, this non-technical working group session caught my eye:

"4.1 Gender Terminology in Bipartite Stable Matching

Robert Bredereck (HU Berlin, DE) License Creative Commons BY 4.0 International license © Robert Bredereck

"Bipartite Stable Matching is classically presented as “Stable Marriage” with one side being men and the other side being women. Meant as illustration and not as proposal for real marriage, the many successful applications of the model are all in completely different domains. The classical terminology, however, can be easily misunderstood and becomes questionable at latest when one side behaves always passive while the other behaves always active, one site manipulates while the other is honest, there is external manipulation, or some couples are forced or forbidden.

"Participants of the seminar discussed the seriousness of these issues in particular in situations where people from outside the community are involved (teaching, grant proposals, etc.). To avoid misunderstanding many participants are using alternative terminologies:

"sportsmen ↔ sportswomen (mixed teams such as tennis)

"leaders ↔ followers (dancing)

"doctors ↔ hospitals

"student ↔ colleges

"workers ↔ companies

"workers ↔ apprentices

"mentors ↔ mentees

"While some of the alternatives even allow to keep using different grammatical gender for the two sides (and so allow to write easily comprehensible texts), other alternatives fit better with the manipulation setting. Some of these alternative terminologies are already established in more specialized or generalized settings of Stable Matching, but may still qualify for the illustration of Bipartite Stable Matching. Another possibility in use is to keep the marriage market terminology while clearly putting it into a historical context."

*****

I've used many of these terms when describing matching, but I wonder if "leaders" and "followers" in the context of dancing will solve the problem that this discussion of terminology is aimed at...

Better LAT than never: Living Apart Together for older romantic relations

 Marriage is not the only way that people can romantically partner, and of course young people are the pioneers in many new forms of household formation.  But here are two news stories that say Living Together Apart (LAT) relationships are growing among older and often previously married couples.

The NY Times has a story focusing on older couples:

Older Singles Have Found a New Way to Partner Up: Living Apart. Fearing that a romantic attachment in later life will lead to full-time caregiving, many couples are choosing commitment without sharing a home. By Francine Russo

"With greater longevity, the doubling of the divorce rate since the 1990s for people over 50 and evolving social norms, older people like Ms. Randall are increasingly re-partnering in various forms. Cohabitation, for example, is more often replacing remarriage following divorce or widowhood, said Susan L. Brown, a sociologist at Bowling Green State University in Ohio.

...

"As researchers study those who do partner, however, they find that increasing numbers are choosing a kind of relationship known as LAT (rhymes with cat), for “living apart together.” These are long-term committed romantic relationships without sharing (or intending to share) a home.

"“A big attraction of LAT is to avoid the potential responsibility of being a full-time caregiver,” said Ingrid Arnet Connidis, an emerita sociology professor at Western University in London, Ontario. “Women cared for their children, parents and spouse, and want to avoid getting into these traditional gender roles.”

"While researchers have not yet delved deeply into the demographics of those in LAT relationships, anecdotally it seems to be more prevalent among those at high enough socioeconomic levels to be able to maintain separate households. In general, there is evidence that wealthier people who are single later in life are more likely to re-partner."

*************

The WSJ has a story focusing on new couples in the midst of raising kids:

The Secret to These Successful Marriages? Living Apart. The number of married couples who live apart is small but growing. Here’s how they say the arrangement helps their families and their relationships   By Clare Ansberry

"Many couples who live apart have been married before and don’t want to uproot their children from homes, schools and friends, or can’t because of joint-custody arrangements.

...

"The number of married people living apart, which includes military couples, is still small but rose 4.8% in the last decade to 3.6 million, according to figures from the Census Bureau."

Online and Matching-Based Market Design (forthcoming in 2022), edited by Echenique, Immorlica, and Vazirani

 What to read in 2022? Here's a teaser...

Online and Matching-Based Market Design, forthcoming in 2022 from Cambridge University Press

Editors: Federico Echenique, Nicole Immorlica, Vijay V. Vazirani  

With a Foreword by Alvin E. Roth

The publisher's leaflet describes the book this way:

"The field of matching markets is, due to a unique confluence of circumstances, at the same time mature and yet in its infancy. Its birth goes back to the seminal 1962 paper of Gale and Shapley on stable matching. Over the decades, this field has become known for its highly successful applications, having economic as well as sociological impact. Its recent resurgence, with the revolutions of the Internet and mobile computing, has opened up altogether new avenues of research and novel, path-breaking applications. The distinctive feature of this book lies in treating this field in its true interdisciplinary spirit --- the field veritably sits at the intersection of economics, computer science, operations research and discrete mathematics, and this viewpoint has already led to a sequence of fundamental research results. Comprised of chapters written by over 50 top researchers, it still has the clarity, cohesiveness and organization of a textbook."

CONTRIBUTORS: Atila Abdulkadiroglu, Nikhil Agarwal, Samson Alva, Itai Ashlagi, Mariagiovanna Baccara, Gabriel Carroll, Hector Chade, Jiehua Chen, Yan Chen, Nikhil Devanur, Federico Echenique, Lars Ehlers, Matthew Elliott, Michal Feldman, Zhe Feng, Tamas Fleiner, Alfred Galichon, Renato Gomes, Aram Grigoryan, Guillaume Haeringer, Hanna Halaburda, John Hatfield, Zhiyi Huang, Nicole Immorlica, Ravi Jagadeesan, Philipp Kircher, Bettina Klaus, Robert Kleinberg, Scott Kominers, Soohyung Lee, Jacob Leshno, Shengwu Li, Irene Lo, Brendan Lucier, David Manlove, Aranyak Mehta, Paul Milgrom, Jamie Morgenstern, Thanh Nguyen, Alexandru Nichifor, Michael Ostrovsky, David Parkes, Alessandro Pavan, Marek Pycia, Aaron Roth, Bernard Salanie, Aleksandrs Slivkins, Paulo Somaini, Sai Srivatsa Ravindranath, Eduard Talamas, Alexander Teytelboym, Thorben Tröbst, Vijay Vazirani, Andrew Vogt, Rakesh Vohra, Alexander Westkamp, Leeat Yariv

The labor market that is the United States Marine Corps

 Armed forces around the world have some unique labor force problems, since by and large they do no lateral hiring...every senior officer was once a junior officer. (Doctors and lawyers are exceptions in the U.S. services--they can enter at a high rank without having spent years learning when and whom to salute...)  As we start to think about other specialties (e.g. cyber warriors, economic warriors), lateral hiring may become more important.  

A related problem faced by armed forces is retention: if all senior personnel have to be brought up through the system, it's especially costly to lose a (therefore) hard to replace, expensively trained operator.  Intelligent matching of people to positions is important for retention, particularly as they become more senior and have no further military service obligation (i.e. as their private sector opportunities become more salient).

The US Marines are thinking about this, and here's a recent report:

Talent Management 2030 November 2021, Department of the Navy, United States Marine Corps

Here are some highlighted snippets:

"The  core  objectives  of  all  modern  personnel  management  systems  are  to  recruit  individuals  with  the  right  talents,  match  those  talents  to  organizational  needs,  and  incentivize  the  most  talented and high performing individuals to remain with the organization"

"Our modern operational concepts and organizations cannot reach their full warfighting potential without a talent management system that recruits, develops, and retains the right Marines."

"Matching talents to duties maximizes performance."

"Incentives power the system."

"In this current era of heightened global competition, the Marine Corps requires a vehicle for rapidly recruiting mature, seasoned experts. We can no longer afford the cost in time – measured in years, and sometimes decades – to train and educate all our technical leaders, particularly given the extraordinary pace of technological change."

"We should have an open door for exceptionally talented Americans who wish to join the Marine Corps, allowing them to laterally enter at a rank appropriate to their education, experience, and ability."

"For Marines, a talent marketplace will increase available information about billet openings, improve transparency, and provide individuals with far greater influence over their future assignments."

"A talent management system relies on incentives, not coercion. While the needs of the Marine Corps are always paramount, we cannot afford to push the most talented young officers out the door after investing years in their leadership development, education, and training. "

**************

Earlier (including some obstacles to implementing effective talent marketplaces):

Tuesday, December 1, 2020

The labor market that is the military: a report from the National Academies of Science, Engineering, and Medicine

Marilda Sotomayor: a career in matching

 Pesquisa FAPESP has a good interview with Marilda Sotomayor, about her career in game theory, and matching theory in particular, and how she came to work with David Gale.  Google translate does a good job (except that it gives her the pronouns he and his...)

Marilda Sotomayor: Uma pensadora dos jogos, by Yuri Vasconcelos, Pesquisa FAPESP, Edition 309, nov. 2021

[GT: Marilda Sotomayor: A game thinker]

[With] Researcher and mathematician Alvin Roth, with whom he wrote a book in 1990

Matching refugees to countries by Jesús Fernández-Huertas Moraga and Martin Hagen

 From the IZA World of Labor:

Can market mechanisms solve the refugee crisis? The combination of tradable quotas and matching would benefit host countries as well as refugees  by Jesús Fernández-Huertas Moraga and Martin Hagen

"Ever since the major inflow of refugees (the “refugee crisis”) in 2015 and 2016, there has been heated debate about the appropriate distribution of refugees in the EU. Current policies revolve around mandatory quotas, which disregard the preferences of EU members and refugees alike. This problem can be addressed with two market mechanisms. First, tradable quotas minimize the cost of asylum provision for host countries. Second, a matching system gives refugees more discretion over where they are sheltered. While this proposal is theoretically appealing, it has yet to be tested in practice."

"A vivid demonstration of free riding was the EU's response to the upsurge in irregular migration in 2015 and 2016. In each of the two years, the EU registered more than one million asylum applicants, mostly from Syria, Afghanistan, and Iraq. Their main points of entry into the EU were Greece and Italy, whose reception facilities were quickly overwhelmed. Other EU members showed little willingness to help them out. As refugees tried to make their way toward Western and Northern Europe, several states reacted with border closures. Hungary, Slovenia, and Austria, among others, even erected fences to keep asylum seekers from entering their territories.

"To tackle the escalating situation, the European Commission launched the European Agenda on Migration in May 2015 [1]. One of its main components was an emergency mechanism to relocate 160,000 asylum seekers from Greece and Italy to the rest of the EU. A distribution key specified a quota of refugees for each EU member, based on measures of reception capacity (mainly GDP and population size). For each relocated person, the receiving country was financially compensated with €6,000 from the EU budget. Several Eastern European countries staunchly opposed the mandatory quotas but were overruled in the Council. Partly reflecting their reluctance, only about 35,000 refugees were eventually relocated.

...

"How the mechanism works in detail

"The proposal can be divided into three stages: an initial allocation of quotas, a market for these quotas, and a matching system.

"Stage 1: Initial allocation of quotas

...

"Stage 2: Quota trading

...

"Stage 3: Matching refugees to countries

...

"In the final decision adopted by the Council, the Parliament's proposal was redacted to a one-sided matching mechanism that gave countries the possibility to express their preferences over refugees but not vice versa. Both on paper and in practice, the matching procedure was rather ad-hoc. A more systematic approach that incorporates insights from matching theory can improve the outcomes for refugees and countries alike.

"As envisioned by the European Parliament, a two-sided matching mechanism would allow refugees to rank EU members from most preferred to least preferred. Conversely, countries would rank different types of refugees, stratified according to family ties, language skills, education levels, and so on. This information would be collected and fed into a centralized algorithm, which would return an assignment of refugees to countries."

Fuhito Kojima and I will discuss improving social welfare with matching theory in a Nikkei Business webinar this evening

Fuhito Kojima and I will participate in a Nikkei Business Zoom webinar on The Future of Management 2030, in English and Japanese (I think translation will be available).

 "Nikkei Business LIVE will hold a webinar entitled "The Future of Management 2030: Rebuilding Capitalism and Revitalizing Innovation" for three days from October 5th to 7th. 

Our discussion, on "Creating a better society by implementing matching theory" will be at 11AM tomorrow in Japan (which is 7PM this evening in California).

"Creating a better society by implementing matching theory in society"

"Auction theory that was in the limelight at the 2020 Nobel Prize in Economics. It is one of the theories representing the new field of microeconomics, "market design," which seeks to design a market in which traders can satisfy each other, rather than analyzing the existing market as in the past. The pioneer who won the Nobel Prize in Economics for "market design" is "matching theory" by Professor Alvin Roth and others. He talks with Professor Fuhito Kojima of the University of Tokyo Graduate School of Economics, who is a direct pupil and a former colleague at Stanford University, about the future brought about by the social implementation of economic theory." (via Google translate)

Matching theory in the September issue of Games and Economic Behavior

 The September 2021 issue of Games and Economic Behavior (Volume 129, Pages 1-590) has five papers on matching theory.

In the order in which they appear:

An improved bound to manipulation in large stable matches  by Gustavo Saraiva

https://doi.org/10.1016/j.geb.2021.05.005Get rights and content

Abstract: This paper builds on Kojima and Pathak (2009)'s result of vanishing manipulability in large stable mechanisms. We show that convergence toward truth-telling in stable mechanisms can be achieved much faster if colleges' preferences are independently drawn from an uniform distribution. Another novelty from our results is that they can be applied to competitive environments in which virtually all vacancies end up being filled. So this paper adds evidence to the fact that, though stable matching mechanisms are not entirely strategy-proof, in practice, when the number of participants in the market is sufficiently large, they can be treated as being effectively strategy-proof.

*************

How lotteries in school choice help to level the playing field by Christian Basteck, Bettina Klaus, Dorothea Kübler

https://doi.org/10.1016/j.geb.2021.05.010Get rights and content

Abstract: School authorities in the UK and the US advocate the use of lotteries to desegregate schools. We study a school choice mechanism employed in Berlin where a lottery quota is embedded in the immediate acceptance (IA) mechanism, and compare it to the deferred acceptance mechanism (DA) with a lottery quota. In both mechanisms, some seats are allocated based on academic achievement (e.g., grades), while seats in the lottery quota are allocated randomly. We find that, in theory, a lottery quota strengthens truth-telling in DA by eliminating non-truth-telling equilibria. Furthermore, the equilibrium outcome is stable for DA with a lottery but not for IA with a lottery. These predictions are borne out in the experiment. Moreover, the lottery quota leads to more diverse school populations in the experiment, as predicted. Students with the lowest grades profit more from the introduction of the lottery under IA than under DA.

**********

Substitutes and stability for many-to-many matching with contracts  by Keisuke Bando, Toshiyuki Hirai, Jun Zhang

https://doi.org/10.1016/j.geb.2021.07.002Get rights and content

Abstract:We examine the roles of (slightly weakened versions of) the observable substitutability condition and the observable substitutability across doctors condition of Hatfield et al. (2021) in many-to-many matching with contracts. We modify the standard cumulative offer algorithm to find stable outcomes and prove new results on the existence of stable outcomes. It is remarkable that size monotonicity at the offer-proposing side is essential for the existence result under observable substitutability across doctors.

*************

Slot-specific priorities with capacity transfers  by Michelle Avataneo and BertanTurhan

https://doi.org/10.1016/j.geb.2021.07.005

Abstract: In many real-world matching applications, there are restrictions for institutions either on priorities of their slots or on the transferability of unfilled slots over others (or both). Motivated by the need in such real-life matching problems, this paper formulates a family of practical choice rules, slot-specific priorities with capacity transfers (SSPwCT). These rules invoke both slot-specific priorities structure and transferability of vacant slots. We show that the cumulative offer mechanism (COM) is stable, strategy-proof and respects improvements with regards to SSPwCT choice rules. Transferring the capacity of one more unfilled slot, while all else is constant, leads to strategy-proof Pareto improvement of the COM. Following Kominers' (2020) formulation, we also provide comparative static results for expansion of branch capacity and addition of new contracts in the SSPwCT framework. Our results have implications for resource allocation problems with diversity considerations.

**************

Stability in sequential matching with incomplete information by Fanqi Shi

https://doi.org/10.1016/j.geb.2021.07.001Get rights and content

Abstract: I study a two-period matching model where one side of the market (e.g. workers) have an option to invest and delay matching in the first period. Investment increases each agent's matching surplus in the second period, by a magnitude of the worker's investment ability in the match pair. Assuming each worker's investment ability is her private information that unfolds in the second period, I define a notion of sequential stability, and show that the set of sequentially stable outcomes is a superset of the complete information stable outcomes. Moreover, with transferable utility, as long as the cost of delay coincides on the same side of the market, efficient investment occurs in any sequentially stable outcome. When every agent shares the same cost of delay, efficient investment also occurs in any sequentially stable outcome with non-transferable utility. My analysis suggests that efficient investment is a robust prediction in sequential matching markets.

Generalizing deferred acceptance in many to one matching with contracts, by Hatfield, Kominers and Westkamp in RESTUD

 Stability, Strategy-Proofness, and Cumulative Offer Mechanisms, by John William Hatfield, Scott Duke Kominers, Alexander Westkamp, The Review of Economic Studies, Volume 88, Issue 3, May 2021, Pages 1457–1502, https://doi.org/10.1093/restud/rdaa052

Abstract: We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulability via contractual terms—and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: if the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice.

Market design, redesigned (in startups and university labs)

Market design is evolving, and new ways of organizing it are being explored. 

In my post yesterday, I talked about the early work on school choice that Atila Abdulkadiroglu, Parag Pathak, Tayfun Sonmez and I did under the auspices of Boston schools Superintendent Tom Payzant. The market design by economists in Boston, as with the earlier successful effort in New York City, was conducted as part of our research work as professors.  Not a penny changed hands, and we all felt good about that.

But if there was a flaw in that working arrangement, it was that no contracts were signed, and so as staff turnover took place in school districts, and the individuals we had dealt with departed, the district's institutional memory eroded, and they didn't always remember to turn to us when difficulties arose that we could have helped them with. Partly to address that, and to have at least one person able to devote time to approaching school districts, Parag and Atila and I supported Neil Dorosin in founding the non-profit  Institute for Innovation in Public School Choice, which during its lifetime helped school choice in a number of American cities, including Denver, New Orleans, and Washington D.C.

Parag and Atila went on to be founding members of MIT's School Effectiveness and Inequality Intiative, which just this week was "relaunched" with a different team as MIT Blueprint Labs, which aims to build on MIT's strengths not just in school choice but in a much wider area of market design and policy analysis, and to be a lab with a large staff and extensive fundraising:

Launch announcement of MIT Blueprint Labs

Featuring

Professor Parag Pathak Faculty Director MIT SEII / Blueprint Labs Research spotlight: K-12 education

Professor Joshua Angrist Faculty Director MIT SEII / Blueprint Labs Research spotlight: Higher education and the workforce

Professor Nikhil Agarwal Faculty Director, Health Care MIT SEII / Blueprint Labs Research spotlight: Health care

Eryn Heying Executive Director MIT SEII / Blueprint Labs

****************

Update: and here's the Blueprint Labs new (announced Aug. 11) website: https://blueprintlabs.mit.edu/

***************

In a related development, Parag has cofounded a new for-profit Ed-tech startup called Avela, that plans to spread the technologies he's helped pioneer.  A for-profit firm has some funding, employment and investing opportunities that aren't available to non-profits or university labs, let alone to teams of professors organized informally. And as in the Blueprint Lab, they hope that the tools they will develop will be readily applicable to quite a broad range of matching markets and market designs.

***************

These various efforts look to me like design experiments themselves, in the search for sustainable ways of making market design a permanent part of not only the research that economists do, but of the practical effects we hope to foster.

Observing all this from the West Coast, and over several decades, I can't help noticing that these institutional changes have been accompanied by team changes, and shifting collaborations among market designers.  

There are also a growing number of different kinds of economists (and computer scientists, operations researchers and businesses) involved in designing and assessing markets, and market design has not only changed markets, but changed the way economists work, in many small and large ways.  Econometricians and development economists have led the way in organizing large labs, and market design may be heading in that direction as well. Big and small tech firms have also started to think of market design as among their core competencies, and as a discipline they should be hiring.

********************

Here in California, I'd be remiss if I didn't mention that my colleague Paul Milgrom has for a long time engaged in auction design through his for-profit company Auctionomics.

And Susan Athey is the faculty director of a big lab at Stanford using different technologies in other areas of market design:  the Golub Capital Social Impact Lab, which describes itself this way:

"We use digital technology and social science research to improve the effectiveness of leading social sector organizations.

"Based out of Stanford GSB, the lab is a research initiative of affiliated academics and staff, as well as researchers and students, who are passionate about conducting research that guides and improves the process of innovation.

"Research Approach

We collaborate with a wide range of organizations, from large firms to smaller startups, for-profits to nonprofits, and NGOs to governments, to conduct research. Then, we apply and disseminate our insights to achieve social impact at large scale."

NRMP Position Statement On The (In)Feasibility Of An Early Match

 There has been some suggestion that dividing the resident match into early and late matches might be a way to address the congestion in applications and interviews that has bedeviled the transition from medical school to residency in recent years.  The NRMP now has a statement pointing out that there are serious problems with that idea.

NRMP Position Statement On The Feasibility Of An Early Match

"For the past eighteen months the National Resident Matching Program® (NRMP®) has been working closely with other national medical education organizations to examine the current state of the transition to residency. Conversations have focused on mitigating burdens for both applicants and programs in the selection and recruitment process and addressing uncertainty in the future of the interview cycle.

...

"Among the proposed solutions to current challenges in the transition to residency are calls for an early match. Specifically, NRMP has been asked to implement the Early Result and Acceptance Program (ERAP) pilot program proposed for Obstetrics and Gynecology, created through American Medical Association’s Reimagining Residency Grant, “Transforming the UME to GME Transition: Right Resident, Right Program, Ready Day One”. The stated goals of the ERAP pilot are to allow applicants to engage in strategic decision-making, reduce burden on programs while hypothesizing that the change will result in holistic review, and reduce necessary applications and interviews. ERAP calls for an early match to begin in September 2022 for the 2023 Match cycle. ERAP permits applicants to apply to a maximum of three programs in the early match with programs including up to 50% of their positions if they choose to participate. This statement outlines NRMP’s concerns about the structure of the ERAP pilot program, the lack of evidence supporting the proposed changes to the Match, the implications of an early match for the matching process, and preliminary findings of modeling an early match being conducted by experts in market design and the matching algorithm.

"The NRMP has reviewed the ERAP pilot program with consideration for whether changes to the matching process have the potential to inadvertently disadvantage Match participants. It is through that lens NRMP remains concerned with the following aspects of the ERAP pilot:

"Although voluntary, applicants may feel pressured to participate in an early match where up to half the available positions in a specialty may fill before the Main Residency Match® opens.

"There exists no mechanism for demonstrating how an early match will make visible less competitive applicants and those underrepresented in medicine, which is hypothesized in the project document.

"The proposed limit of three applications per applicant could force applicants to make compromises not present in the Match today. ...While the ERAP investigation team hypothesized that the application limit will increase holistic review by programs, there are no mandates to ensure that programs conduct holistic review nor are there restrictions on the number of applications programs may accept, interviews they may offer, or applicants they may rank. With no objective evidence to support the hypothesis, we cannot conclude that the proposed application limit would increase holistic review of applications.

"There exists no mechanism for safeguarding an applicant’s failure to match in the early match from programs as they enter the Main Residency Match, which could result in the applicant being viewed as less competitive.

"In addition to concerns about disadvantaging applicants, NRMP is mindful of possible behavior changes resulting from changes to the Match process that could affect Match outcomes for all Match participants.

• "The structure of an early match does not allow for mixed-specialty couples ranking or multispecialty individual ranking, which may cause applicants to reconsider their specialty choices, fundamentally changing their career path.
• "Programs may have insufficient information (e.g., clinical evaluations, MSPE, LORs) to evaluate applicants fully and fairly in the early match.
• Programs may see a surge in non-traditional applicants as the early match provides three opportunities to enter training through either the early match, the Main Residency Match, or SOAP®. This may result in an increased number of applications or applicants who may otherwise not select the specialty.
• Not matching in the early match is likely to increase the number of applications per individual in the Main Residency Match, as applicants enter a matching cycle with only half of the positions remaining available. This may increase stress, cost, and could adversely affect the wellness of applicants.

...

"it is important to first outline the core concepts of the match as a stable “market”. The Match was established in 1952, to solve a “congestion” problem in medical residencies involving applications, offers, and acceptances. In a May 2021 pre-submission working paper, Itai Ashlagi, Ph.D. and Alvin Roth, Ph.D. describe the consequences of congestion as “unraveling” where programs initially responded to congestion by making “exploding offers” that prevented applicants from considering many programs because they were pressed to accept an early offer, before knowing whether an offer from a more preferred program might be forthcoming if they waited. The authors note that NRMP’s matching process, in its current form, has four distinct properties that are relevant to managing the problems of congestion and unraveling and maintaining a stable matching market. Specifically, the NRMP matching process

"1. Is Uncongested: participants make all decisions (on Rank Order Lists) in advance, so there is no delay in processing offers, rejections, and acceptances, which is done by the computerized Roth-Peranson algorithm.

"2. Defers acceptances: preferences of applicants and programs are not finalized until all preferences have been considered, thereby producing stable matching: i.e., matching in which there are no “blocking pairs” of applicants and programs not matched to one another but who both would prefer to be.

"3. Promotes true preferences: it is safe for participants to state their true preferences when they submit their Rank Order Lists (ROLs).

"4. Establishes a “thick” market: most residency programs in most specialties participate in the NRMP Match, which also allows for multi-specialty applications and couple matching (including for mixed-specialty couples).

"The authors opine that an early match such as the proposed ERAP pilot followed by the Main Residency Match would not share three of the four important properties of the Match:

"1. An early match would dilute the thick market: not all positions would be available at the same time (and further, it would not allow applicants to express multi-specialty preferences, nor would it accommodate mixed-specialty couples).

"2. early match would introduce complicated strategic decisions into the formulation of ROLs: it would no longer be safe for participants to submit ROLs straightforwardly corresponding to their preferences.

"3. An early match would not produce a stable matching: there would be mutually disappointed blocking pairs of mismatched applicants and programs. This would also make it less safe to report ROLs that straightforwardly corresponded to preferences."

Matching patients with effective therapists improves mental health coutcomes

 A recent paper in JAMA Psychiatry reveals that matching patients to therapists who are effective at treating their particular issues improves mental health outcomes. (This may allow you to update your priors on either matching or therapy...)

Effect of Matching Therapists to Patients vs Assignment as Usual on Adult Psychotherapy Outcomes: A Randomized Clinical Trial  by Michael J. Constantino, PhD1; James F. Boswell, PhD2; Alice E. Coyne, MS1; et alThomas P. Swales, PhD3; David R. Kraus, PhD, JAMA Psychiatry. Published online June 9, 2021. doi:10.1001/jamapsychiatry.2021.1221

"Question  Can assigning patients to therapists with empirically determined strengths in treating the patients’ specific mental health problem(s) (ie, measurement-based matching) improve the outcomes of naturalistic psychotherapy compared with case assignment as usual?

"Findings  In this 2-arm, double-blind randomized clinical trial including 48 therapists and 218 outpatients, measurement-based matching promoted significantly greater reductions in patients’ general symptomatic and functional impairment, global psychological distress, and domain-specific impairment on patients’ most elevated presenting problem over 16 weeks post intake.

"Meaning  In this study, mental health care was enhanced by prospectively assigning patients to empirically good-fitting therapists, which requires minimal disruptions within a mental health care system."

Redesigning the US Army's Branching Process, by Kyle Greenberg, Parag A. Pathak & Tayfun Sönmez,

 Here's a new NBER working paper that marks a significant step forward in matching soldiers to positions.

Mechanism Design meets Priority Design: Redesigning the US Army's Branching Process by Kyle Greenberg, Parag A. Pathak & Tayfun Sönmez, NBER WORKING PAPER 28911 DOI 10.3386/w28911,  June 2021

Army cadets obtain occupations through a centralized process. Three objectives – increasing retention, aligning talent, and enhancing trust – have guided reforms to this process since 2006. West Point’s mechanism for the Class of 2020 exacerbated challenges implementing Army policy aims. We formulate these desiderata as axioms and study their implications theoretically and with administrative data. We show that the Army’s objectives not only determine an allocation mechanism, but also a specific priority policy, a uniqueness result that integrates mechanism and priority design. These results led to a re-design of the mechanism, now adopted at both West Point and ROTC.

One of the unusual features of this paper is that the first author is both an economist and an Army officer, working in West Point's Office of Economic and Manpower Analysis:

"MAJ Greenberg is an Assistant Professor of Economics in the Department of Social Sciences and is OEMA’s Director of Long-Term Research. His primary areas of research are labor economics and public finance, with a focus on veteran employment, disability compensation, and military labor markets. Currently a Major in the U.S. Army, Kyle served tours in Iraq and Germany prior to teaching at the United States Military Academy. He earned a BS in Mathematics from the United States Military Academy in 2005 and a Ph.D. in Economics from the Massachusetts Institute of Technology in 2015."

*********

Here's a related earlier post, in which Major Greenberg discusses some of the design issues still facing the Army's assignment systems.

Monday, December 7, 2020

Officer assignment in the U.S. Army

Matching Teach For America Teachers to Schools, by Jonathan Davis

Some years ago Clayton Featherstone and I worked with Teach for America to design their process for matching new recruits to school districts.  Now here's a paper on the next step in the assignment process: matching teachers to particular schools.

Labor Market Design Can Improve Match Outcomes: Evidence from Matching Teach For America Teachers to Schools   by Jonathan M.V. Davis

Abstract: "I worked with Teach For America (TFA) to match high school teachers to schools in Chicago using the deferred acceptance algorithm (DA), while keeping its original mechanism unchanged for elementary teachers. Comparing actual matches under DA to simulated counterfactual matches suggests half of teachers strictly prefer their matches under DA and very few teachers are worse off. This improved matching yields longer-run benefits: matching with DA increased teachers retention through their two-year commitment to TFA by between 6 and 12 percent. This provides empirical support for the hypothesis that economic design can improve match outcomes in labor markets without negotiable wages. "

"Before I began working with TFA, interview day matches were determined by what I will refer to as the First Offer Mechanism (FO). This mechanism works as follows:

"Step 1. Complete round 1 interviews. After completing the round 1 interview, each school decides whether to make an offer to the teacher they interviewed. If given an offer, the teacher must accept it or exit Teach For America.

"Step 2 ≤ k ≤ K. Complete round k interviews involving unhired teachers. Each school decides whether to make an offer to the teacher they interviewed. If given an offer, the teacher must accept it or exit Teach For America.

...

"In fall 2013, I contacted TFA and suggested that they may benefit from replacing FO with DA. Given TFA’s policy that teachers accept their first offer and the organizational value that “TFA teachers go wherever they are needed”, the school position proposing version of DA was selected. In order to credibly identify the impact of the change, I worked with TFA to initially implement DA at its high school interview days for its 2014 cohort. This cohort was admitted to TFA in early 2014 and committed to teaching with TFA during the 2014-15 and 2015-16 school years. They continued using FO at the elementary interview days for this cohort."

Matching theorist wins high school science talent search

 Yunseo Choi will attend Harvard next year, planning to study math and econ (see video below).

Teen Scientists Win $1.8 Million at Virtual Regeneron Science Talent Search 2021 for Remarkable Research on Infinite Matching Algorithms, Machine Learning to Evaluate New Medicines and Water Filtration   $250,000 top award goes to Yunseo Choi in nation’s oldest and most prestigious STEM competition for high school seniors

"TARRYTOWN, N.Y. and WASHINGTON, D.C.  – Regeneron Pharmaceuticals, Inc. (NASDAQ: REGN) and Society for Science (the Society) announced that Yunseo Choi, 18, of Exeter, New Hampshire, won the $250,000 top award in the 2021 Regeneron Science Talent Search, the nation’s oldest and most prestigious science and math competition for high school seniors. Historically held in person in Washington, D.C., this is the second year in its 80-year history that the competition took place virtually to keep the finalists and their families safe during the ongoing pandemic. Forty finalists, including Yunseo, were honored tonight during a virtual winners’ award ceremony. More than $1.8 million was awarded to the finalists, who were evaluated based on their projects’ scientific rigor, their exceptional problem-solving abilities and their potential to become scientific leaders.

"Yunseo Choi won first place and $250,000 for her project where she played theoretical “match maker” for an infinite number of things or people. She studied matching algorithms that work for a finite number of couples and determined which important properties would still work for an infinite number of pairs. Matching theory has numerous real-life applications, including matching organ donors to recipients, assigning medical school applicants to rotations and pairing potential couples in dating apps."

HT: Scott Kominers

How do Zoom interviews change labor markets? Interview Hoarding by Manjunath and Morrill

 Suppose there were a pandemic that caused widespread lockdowns.  How might this influence the outcome of a labor market that was forced to switch from in-person, on-site interviews to remote interviews via Zoom or its equivalents?

Vikram Manjunath and Thayer Morrill take up the challenge, motivated by the case of the National Resident Matching Program, which matches new doctors to hospital residency programs. (Match Day is March 19 this year, so we may know some relevant things about how the pandemic influenced the Match not too long after.)

Interview Hoarding  by Vikram Manjunath and Thayer Morrill, February 22, 2021

Abstract: Many centralized matching markets are preceded by interviews between the participants. We study the impact on the final match of an increase to the number of interviews one side of the market can participate in. Our motivation is the match between residents and hospitals where, due to the COVID-19 pandemic, interviews for the 2020-21 season of the NRMP match have switched to a virtual format. This has drastically reduced the cost to applicants of accepting interview offers. However, the reduction in cost is not symmetric since applicants, not programs, bore most of the costs of in-person interviews. We show that if doctors are willing to accept more interviews but the hospitals do not increase the number of interviews they offer, no doctor will be better off and potentially many doctors will be harmed. This adverse consequence results from a mechanism we describe as interview hoarding. We prove this analytically and characterize optimal mitigation strategies for special cases. We use simulations to extend the insights from our analytical results to more general settings.

***********

Update: Manjunath, Vikram, and Thayer Morrill. "Interview hoarding." Theoretical Economics 18, no. 2 (2023): 503-527.

Deferred Acceptance with Compensation Chains by Piotr Dworzak

 Here's an interesting look at deferred acceptance algorithms, published online early in Operations Research 

Deferred Acceptance with Compensation Chains  by Piotr Dworczak 

Published Online:18 Feb 2021https://doi.org/10.1287/opre.2020.2042

Abstract: I introduce a class of algorithms called deferred acceptance with compensation chains (DACC). DACC algorithms generalize the Gale–Shapley algorithm by allowing both sides of the market to make offers. The main result is a characterization of the set of stable matchings: a matching is stable if and only if it is the outcome of a DACC algorithm. The proof of convergence of DACC algorithms uses a novel technique based on a construction of a potential function.

A proposed match for English professors, in the Chronicle of Higher Ed

 Here's a proposal for a centralized clearinghouse for new Ph.D.s in English.  It's a thought experiment, unconstrained by considerations of stability.

The Chronicle of Higher Ed 

Medical Residencies Use Automatic Matching. Professorships Should, Too.--A thought experiment in improving a dismal situation.  By Kim Adams

"What would a computerized match look like in faculty hiring? Let’s say that I am applying for a tenure-track assistant professor position in English. I would read job ads from universities and submit the requested application materials, just as I do now. The main difference would be timing. In order for a match to work, all the job ads would need to be posted by a given date, for example, September 1. It would work best if they were all posted in the same place, perhaps the website of the new Faculty Match Program. The application materials would likewise be due at a uniform time, let us say November 1.

...

"The algorithm would be designed to ensure a maximum distribution of candidates across openings. While the number of first round interview requests a candidate could receive would be unlimited, the number of campus visits would be limited to three. The process would prefer to provide each candidate with one campus visit before providing any candidates with a second. This would benefit both parties. A greater number of candidates would receive campus visits than in the current system. And the department conducting the search could rest assured that the candidates matched to their campus were actually interested in taking the job.

...

Colleges would then conduct campus visits and complete the hiring process as usual. Because of the imbalance of candidates and positions, the risk of unmatched candidates would be high (but that’s nothing new). The risk of unmatched positions is small, perhaps smaller than in the current system, under which searches not infrequently fail despite the superabundance of job candidates. Stable matches would mean fewer faculty members who go on the market after one or two years in a position, thereby decreasing the quantity of applications that search committees need to wade through in future cycles.

...

"The failure of the academic-job market is evident to all those involved. The madness of the market is subsuming the process of doctoral education. Without substantial changes, the doctoral degree will lose its value and the market will collapse. Collective action among graduate students and contingent faculty members can draw attention to these issues, but only the unified, cooperative action of deans and presidents can solve them.

Partial strategyproofness: Relaxing strategyproofness for the random assignment problem by Mennle and Seuken in JET

 Most market mechanisms that we encounter in practice aren't strategy proof, and many markets don't admit any strategyproof mechanisms, so we need to have a language to talk about how strategyproof a mechanism is or isn't.  There are a number of approaches to that, and here's a new one.

Partial strategyproofness: Relaxing strategyproofness for the random assignment problem

Timo Mennle  and Sven Seuken, Journal of Economic Theory, Volume 191, January 2021

Abstract: We present partial strategyproofness, a new, relaxed notion of strategyproofness for studying the incentive properties of non-strategyproof assignment mechanisms. Informally, a mechanism is partially strategyproof if it makes truthful reporting a dominant strategy for those agents whose preference intensities differ sufficiently between any two objects. We demonstrate that partial strategyproofness is axiomatically motivated and yields a parametric measure for “how strategyproof” an assignment mechanism is. We apply this new concept to derive novel insights about the incentive properties of the probabilistic serial mechanism and different variants of the Boston mechanism.