Waitlist equity, when not everyone can wait a long time, by Afshin Nikzad and Philipp Strack

 Patients waiting for deceased donor kidneys are given priority in part by how long they have been on dialysis, while patients waiting for livers are prioritized according to how sick they are, sickest first.  When the wait is long, not everyone has an equal chance of surviving long enough to receive an organ. Here's a paper that suggests that service in random order (SIRO) has desirable equity properties. Efficiency depends on how patients' welfare and future prospects change while they wait.

Equity and Efficiency in Dynamic Matching: Extreme Waitlist Policies, by Afshin Nikzad and Philipp Strack, Management Science, forthcoming, Published Online:3 Oct 2023https://doi.org/10.1287/mnsc.2023.01212

Abstract: Waitlists are commonly used to allocate scarce resources, such as public housing or organs. Waitlist policies attempt to prioritize agents who wait longer by assigning them priority points (à la first come, first served). We show that such point systems can lead to severe inequality across the agents’ assignment probabilities unless they use randomization. In particular, deterministic point systems lead to a more unequal allocation than any other rule that prioritizes earlier arrivals, an axiom that ensures that agents who wait longer are treated (weakly) better. Among the policies abiding by this axiom, we show that service in random order (SIRO) leads to the most equal allocation. From a utilitarian perspective, we show that the planner faces no trade-off between equity and efficiency when the flow utility from waiting is nonnegative or negative and increasing over time. In these cases, SIRO is also the most efficient policy. However, when the flow cost of waiting increases over time, then the planner may face an efficiency–equity trade-off: SIRO remains the most equitable policy but may not be the most efficient one.

1. Introduction: Waitlists are a common way to allocate scarce resources, such as public housing,1 organs,2 or services such as call center support.3 There are many ways to decide who among the waiting agents receives an object once it becomes available. Some waitlists operate in a service-in-random-order (SIRO) manner and use lotteries to allocate objects to waiting agents, such as in the Diversity Immigrant Visa Program in the United States4 or Beijing’s license plate allocation.5 Many other waitlists follow designs akin to first come, first served (FCFS), in which whoever has waited for the longest time receives (priority points for) an object. For example, in the national kidney transplant waitlist in the United States, enrolled patients earn priority points for each day that they remain on the waitlist.6 Such rules ensure that an agent who waits longer is not treated worse than an agent with a shorter waiting time and otherwise identical characteristics.

"Prioritizing agents with longer waiting times, however, has a drawback: it implies that an agent with a longer lifetime, that is, an agent who can wait longer for an object, has a higher probability of receiving an object. This naturally leads to inequality in assignment probabilities across agents with varying lifetimes. For example, a first-come, first-served list would lead to many of the sickest patients never receiving an organ as they depart the system before having waited long enough to receive an organ. Such equity concerns, for example, play an important role in the context of organ allocations (Organ Procurement and Transplantation Network 2015). The high-level question we ask here is, what policy induces the least inequality among policies that give priority to agents who arrive earlier? Furthermore, is minimizing inequality aligned with the objective of a planner who maximizes the average of the agents’ utilities, or are there efficiency–equity trade-offs to be considered here?"