"Discreteness is the better part of value" (Vince Crawford)

 One of the themes of the conference celebrating Vince Crawford (in anticipation of his 75th birthday) is how two of his early famous papers (Crawford and Knoer, 1981 and Kelso and Crawford, 1982)  helped unify matching theory and the theory of markets and competitive equilibria, and thus began to bring matching theory into mainstream economics.

Vince remarked that the unification of matching with the rest of economics also brought discrete (as opposed to continuous) mathematics into the mainstream of economic theory.

He said he had come to realize that "Discreteness is the better part of value."*

*This is of course a play on the common English language expression "Discretion is the better part of valor," which has an indirect and complicated Shakespearean connection, but in common usage is meant to give advice like "Look before you leap."

The Professional Psychology Match and post-match scramble

 Here's an article that (among other things) describes the APPIC Match, and the more recently organized (and regularized) post-Match scramble for unfilled positions.

JenniferA.Erickson Cornish and Jeff Baker

"A Brief History of the Association of Psychology Postdoctoral and Internship Centers:  Trends and Directions for the Education and Training of Health Service Psychologists," Training and Education in Professional Psychology  

(2021,December20)  http://dx.doi.org/10.1037/tep0000401

Abstract: The Association of Psychology Postdoctoral and Internship Centers (APPIC) is the largest health service psychology education and training council in the U.S. and Canada, with approximately 787 internships, 238 postdoctoral programs, and 431 doctoral program associates. APPIC regularly interacts with the other major training councils over the entire developmental graduate sequence from doctoral education through postdoctoral fellowships. All psychology doctoral students in accredited clinical, counseling, and school programs are required to complete an internship in health service psychology, with a significant majority of those students (3,684 in 2021) obtaining those internships via the APPIC match. Although there is no current similar APPIC match for postdoctoral training, APPIC provides selection guidelines for such training and hosts a list of over 1,600 positions available each year. 

"A computerized national match began with the 1998–1999selection process (10 years after a less than successful trial led tothe board deciding to discontinue it) in which 2,923 students applied for 2,631 positions, and 83% were matched (Keilin, 2000). This match, overseen by NMS, used an algorithm based on the NationalResidency Match Program (Roth & Peranson, 1999) and was deemed a success in a subsequent survey, although applicants and directors of clinical training were more satisfied than internship training directors (Keilin, 2000). In 2010, due to the leadership of then chair Sharon Berry, Phase II of the match was launched. Phase II brought about significant changes since it allowed applicants additional time to review and apply to another program if unsuccessful in Phase I, gave internship programs additional time to review Phase II applicants in a more thorough manner, and removed much of the fairly chaotic process that was frantic for both applicants and training directors (some of whom had to replace their fax machines due to overload). The former clearinghouse became the PMVS in 2011. The PMVS currently does not include a match but rather lists postings of positions that are still available on the APPIC website, allowing candidates and sites to participate in an informal selection process as needed. The PMVS will become part of the AAPI process in 2022 and will bring some additional order for those programs that still have openings and for trainees who haveeither not matched or were recently able to participate in the match. In2012, the Nobel Prize for Economics was given for the Roth–Peranson Algorithm used in the match by NMS. The match became limited to students from doctoral programs accredited by the APA or Canadian Psychological Association (including those with a site visit scheduled) and in 2021 to APPIC member internship programs. Previously, nonmember programs could participate in the match with the development of“ Provisional” membership; all programs would now have undergone review by the APPIC membership committee prior to participating in the match.

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Some historical background:

Roth, A.E. and X. Xing, "Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists," Journal of Political Economy, 105, April 1997, 284-329.

Police assignments by seniority in Chicago

 Here's a recent NBER working paper reporting a study of the assignment of police officers in Chicago, where some officers can choose to transfer to newly vacant positions, with priority determined by seniority. The resulting allocation reveals that more senior officers move to assignments with lower levels of violent crime.

Police Officer Assignment and Neighborhood Crime  by Bocar Ba, Patrick Bayer, Nayoung Rim, Roman Rivera & Modibo Sidibé  WORKING PAPER 29243, DOI 10.3386/w29243,  September 2021

Abstract: We develop an empirical model of the mechanism used to assign police officers to Chicago districts and examine the efficiency and equity of alternative allocations. We document that the current bidding process, which grants priority based on seniority, results in the assignment of more experienced officers to less violent and high-income neighborhoods. Our empirical model combines estimates of heterogeneous officer preferences underlying the bidding process with causal estimates of the effects of officer experience on neighborhood crime. Equalizing officer seniority across districts would reduce violent crime rate by 4.6 percent and significantly decrease inequality in crime, discretionary arrests, and officer use of force across neighborhoods. Moreover, this assignment can be achieved in a revenue-neutral way while resulting in small welfare gains for police officers, implying that it is more equitable and efficient.