The Complexity of Minimizing Envy in House Allocation

No abstract available

The Price of Equity with Binary Valuations and Few Agent Types

In fair division problems, the notion of price of fairness measures the loss in welfare due to a fairness constraint. Prior work on the price of fairness has focused primarily on envy-freeness up to one good (EF1) as the fairness constraint, and on the utilitarian and egalitarian welfare measures. Our work instead focuses on the price of equitability up to one good (EQ1) (which we term price of equity) and considers the broad class of generalized $p$-mean welfare measures (which includes utilitarian, egalitarian, and Nash welfare as special cases). We derive fine-grained bounds on the price of equity in terms of the number of agent types (i.e., the maximum number of agents with distinct valuations), which allows us to identify scenarios where the existing bounds in terms of the number of agents are overly pessimistic. Our work focuses on the setting with binary additive valuations, and obtains upper and lower bounds on the price of equity for $p$-mean welfare for all $p \leqslant 1$. For any fixed $p$, our bounds are tight up to constant factors. A useful insight of our work is to identify the structure of allocations that underlie the upper (respectively, the lower) bounds simultaneously for all $p$-mean welfare measures, thus providing a unified structural understanding of price of fairness in this setting. This structural understanding, in fact, extends to the more general class of binary submodular (or matroid rank) valuations. We also show that, unlike binary additive valuations, for binary submodular valuations the number of agent types does not provide bounds on the price of equity.Comment: A version of this work was accepted for presentation at 16th International Symposium on Algorithmic Game Theory (SAGT 2023

In Patient Department Services at a Private Super Specialty Hospital of a Metrocity

Introduction: A patient’s episode of care should be planned before his/her admission and should take account of the entire “journey” up to and after discharge from hospital. Patients and their care-giver should be partners in this planning. Pre-admission assessment should be a standard requirement for all elective admissions. The anticipated length of stay for elective admissions should be indicated as early as possible to facilitate scheduling. Discharge plans agreed between the hospital and a key worker in primary care, discharge planning that commences on day of admission. Objectives • To study the admission process. • To study the discharge process. Methodology: A cross-sectional study was conducted in a private super specialty hospital of a metrocity. A check list was prepared for various desks of the hospital such as admission desk, discharge desk, cash desk, billing desk, etc. Also, descriptive data was collected from various departments. Observation andResults: The various sources of admission to hospital were: direct admission, general OPD, emergency department and consultants’ clinic. Registers maintained at the Admission desk: Handover Book, Admitted Patient Register, Bed management Register, Announcement Register, OT Register, Briefing Register, Counselling Register. Discharge Process: On being advised discharge, the billing prepares the patient bill in two copies. Process of discharge is initiated after administration/ consultant advice. A detailed discharge summary covering investigation reports, treatments given and advice on discharge will be provided by the attending doctor and it will be given to the patient at the time of discharge. Charges for the full day on the day of admission are applicable irrespective of time of check in. Patient is discharged after the payment of the bill. Recommendations: There should be a hanging bold-written signage for insured patients, strict adherence to the visiting hour timings. More number of staff needs to be deployed in the billing department as because of staff crunch the billing gets delayed. Discharges must be pre-decided so that the nurses get sufficient time to prepare the patient file