The paper introduces a new method for multinomial inference using Dempster-Shafer (DS) theory, represented by partitioning the unit interval into unordered segments. The resulting DS posterior is characterized by a Dirichlet distribution, which simplifies numerical computation compared to the Simplex-DSM. The Dirichlet-DSM retains desirable properties such as symmetry, representation invariance, and embedding, while avoiding the computational complexities of the Simplex-DSM. The model is flexible in parameterization and can handle various testable assertions. The paper compares the Dirichlet-DSM to existing methods, including Bayesian and imprecise Dirichlet models, and illustrates its effectiveness through examples. The Dirichlet-DSM is shown to be computationally efficient and provides improved inference, particularly for observed categories, while weakening inference for unobserved categories.The paper introduces a new method for multinomial inference using Dempster-Shafer (DS) theory, represented by partitioning the unit interval into unordered segments. The resulting DS posterior is characterized by a Dirichlet distribution, which simplifies numerical computation compared to the Simplex-DSM. The Dirichlet-DSM retains desirable properties such as symmetry, representation invariance, and embedding, while avoiding the computational complexities of the Simplex-DSM. The model is flexible in parameterization and can handle various testable assertions. The paper compares the Dirichlet-DSM to existing methods, including Bayesian and imprecise Dirichlet models, and illustrates its effectiveness through examples. The Dirichlet-DSM is shown to be computationally efficient and provides improved inference, particularly for observed categories, while weakening inference for unobserved categories.