We develop a theory that addresses the problem of the existence of stable vaccine allocations in a political economy. These are allocation policies that a political leader can enforce without losing their popularity. Our analysis distinguishes between contexts where vaccination has positive externalities and contexts where it does not. We show that a stable allocation may not exist if vaccine supply is sufficiently low relative to the number of individuals eligible to receive a dose. We then fully characterize the minimum number of vaccine doses that guarantees the existence of a stable vaccine allocation, regardless of society\u27s preference heterogeneity level. The minimum dose number depends only on a society\u27s influence structure or voting rule. When individuals have unequal voting rights, stable allocations favor those with greater voting power. We generalize our main characterization result to economies where spatial proximity between individuals varies and preferences are unselfish due to positive vaccine externalities. Applying the theory, we find that a political leader can enforce stable vaccine allocation policies that are minority-inclusive only when the supply of vaccines is sufficiently high
