Evidential vulnerability of religious beliefs in the context of petitionary prayers

Petitionary prayers—requests made to a deity for specific outcomes—are widely practiced across religious traditions. While their efficacy remains a subject of theological debate, they exhibit remarkable resilience to disconfirmation. In three pre-registered studies—a field study in China and two global surveys via Prolific (total n=1800)—we examined how religious believers (Christians, Muslims, local deity worshippers, and Hindus) update beliefs and behaviors in response to prayer successes or failures for both hypothetical co-religionists and themselves. Results indicate that belief updates generally follow a Bayesian pattern, with increases after prayer successes and decreases after failures, though with an asymmetry favoring belief reinforcement. Notably, participants from the Prolific sample exhibit sensitivity to the prior probability of prayed-for events, attributing greater belief increases to improbable outcomes. Muslims predict belief increases even after failed prayers, consistent with doctrines framing hardships as divine tests. Across traditions, believers estimate continued prayer regardless of past outcomes, with monotheists displaying stronger resilience. These findings illuminate the cognitive and cultural mechanisms that buffer religious beliefs against counter-evidence, contributing to debates on the evidential vulnerability of religious credence and its parallels with epistemically self-sealing belief systems.