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Appendix D: Preference-Informed Matching in Job Assignment
Pages 223-238

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From page 223...
... Many of the current Air Force assignment procedures have grown out of the historical low-tech assignment tool consisting of a whiteboard covered with colored sticky notes, a long-standing system later augmented by spreadsheets. Often assignment teams worked with very little information about job requirements and candidate preferences.
From page 224...
... In each case, the Air Force would first establish job requirements and candidate qualifications to determine which candidates are qualified for which jobs. Preferences could then be solicited from candidates for the jobs for which they are qualified, and/or from hiring authorities for the qualified candidates.
From page 225...
... Under this system, the Air Force establishes a priority order either among the available jobs or among the available candidates. It also establishes which candidates are qualified to fill which job.
From page 226...
... . That is, lower priority jobs that have expressed preferences are allowed to choose first so long as qualified candidates remain for the higher priority jobs that find all qualified candidates equally desirable.
From page 227...
... , which suggests that the relevant Air Force goals could be met in a way that would increase the satisfaction of all the Airmen who are subject to assignment in this period. (Slightly modified forms of Pareto optimality work similarly; for example, we often want comparisons between two distributions of assignments to depend only on those Airman who get different assignments, and so the relevant comparison is whether some Airman can
From page 228...
... there are ways of breaking ties that make it possible to satisfy others' preferences more fully than if ties are broken arbitrarily. STABLE MATCHING Under stable matching systems, the Air Force establishes which candidates are qualified to fill which jobs, and elicits preferences from both candidates and hiring authorities (i.e., candidates are asked to rank jobs for which they are qualified, and hiring authorities are asked to rank qualified candidates, in order of preference)
From page 229...
... As described in Chapter 5, the Air Force's newly developed Talent Marketplace leverages a deferred acceptance algorithm as a preliminary step to improve the officer assignment ­ process.10 Candidate-Proposing Deferred Acceptance Algorithm The following should be read as the description of a computerized matching algorithm that takes as its inputs the preference lists (rank-order lists) submitted by Airmen over positions, and by hiring authorities over Airmen, after both hiring authorities and Airmen have had adequate time and information to formulate their preferences.
From page 230...
...  3 applies to P4, there are no rejections, the algorithm A ends with the matching A1-P1, A2-P2, A3-P4, A4-P3. Candidate-Proposing Deferred Acceptance Example Assignment Summary: A1:  ssigned to first choice, P1 (which was assigned its second A choice Airman)
From page 231...
... Benefits of Deferred Acceptance Algorithms DA algorithms use the information contained in the preferences of both candidates and hiring authorities, and they produce what are called stable matchings, which do not have "blocking pairs" (i.e., there is never a service member and Air Force job that would have both, mutually, preferred each other) or "justified envy" (in which a lower priority candidate receives a job preferred by a higher priority candidate with equal qualifications)
From page 232...
... Because of this, it is not clear that the form of stability produced by deferred acceptance algorithms is the best goal for an Air Force assignment system. Eliminating blocking pairs involving Airmen and alternative assignments within the Air Force comes at a cost, since a stable matching (i.e., one with no such blocking pairs)
From page 233...
... Constraints can include all the requirements (e.g., how many jobs need to be filled by what kinds of people) , while the objective function could measure, for example, satisfaction as expressed by rank-order lists or by some other measure of Air Force productivity.
From page 234...
... This compact formulation offers vast flexibility, which is good if used very carefully but can also present problems with interpretation and maintenance. Consider for example the objective function: Maximize the weighted sum (over all i, j)
From page 235...
... They tell us that big incentives to manipulate preferences in obvious ways should be avoided. For example: • Do not employ rules that penalize participants for submitting long preference lists.12 • Do not employ rules that penalize participants for failing to be as signed their first choice (e.g., rules that make it much less likely in 11 The committee did not find descriptions at this level of detail for the algorithm for officer specialty selection described in Chapter 4 of this report.
From page 236...
... That is, when a new procedure is introduced initially for some parts of the Air Force, data can be collected comparing the new experience with previous experience (e.g., do candidates list more assignments in their preference lists after some new information-sharing procedure) and with parts of the Air Force still using the prior procedures.
From page 237...
... One of the tasks facing the Air Force is to develop such institutions in parallel with the development of the Talent Marketplace.


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