Making it easy to complain works best when officials also wait for many complaints before acting. A new game-theory model shows that for large populations, a system with a low cost of complaining and a high threshold for action always beats the alternatives at filtering out trivial gripes while catching real problems.
The paper is by Greg Leo and Jennifer Pate, economists at Loyola Marymount University. It was published online in the Journal of Public Economic Theory on December 23, 2024 (read the paper).
What New York’s 311 data show
The authors start with New York City’s 311 system, which began as a phone hotline in 2003 and added a web portal in 2009, text messages in 2011 and a mobile app in 2013. Between 2010 and 2022, annual complaints tripled from about one million to three million, while phone complaints stayed flat, suggesting the new digital channels drove the growth.
They looked closely at heat and hot water complaints, which landlords in New York are legally required to address. The category held almost 2 million entries from March 2014 to May 2023. About 33% were marked as duplicates, and 21% of issues, defined as a single address on a single date, drew more than one complaint.
About 26% of non-duplicate complaints led to a formal investigation by the city’s Department of Housing Preservation and Development. Single complaints rarely triggered one, while issues with many complaints usually did. The department publishes no rule, but it behaves as if it uses a threshold.
A volunteer’s dilemma with a quota
To explain this, Leo and Pate extend a classic game called the volunteer’s dilemma, in which each person hopes someone else will bear the cost of acting. In their “m-volunteer’s dilemma,” a problem gets fixed only if at least m people complain. Each resident weighs the effort of complaining against how likely their complaint is to tip the issue over the line.
The model shows why thresholds make sense. Complaining has value precisely because it costs something: people only bother when a problem is big enough. By setting the cost and the threshold together, an administrator can make it irrational to complain about small problems, without ever seeing how serious each problem really is. Lower the cost, and the threshold must rise to screen out the same trivial complaints.
For large groups, the authors solve the model with a mathematical tool called the Lambert-W function and prove their main result: low-cost, high-threshold policies are universally more efficient. They note real examples of the logic, such as the White House “We the People” petition site raising its response threshold from 5,000 to 25,000 to 100,000 signatures.
Beyond potholes and radiators
The authors list the model’s simplifications. It assumes people decide at the same time without seeing how many others have complained, which is not true on many petition sites, and it treats residents as alike in costs and benefits.
They see the same logic in fundraising. When matching funds depend on reaching a set number of donors, their results suggest a higher donor threshold paired with a lower minimum gift may raise the most.
Study Details:
- Title: Complainer’s Dilemma
- Authors: Greg Leo, Jennifer Pate
- Journal: Journal of Public Economic Theory
- Publication Date: December 23, 2024
- DOI: 10.1111/jpet.70011