A new method for multinomial inference is proposed using Dempster-Shafer (DS) theory. The method represents cell probabilities as unordered segments on the unit interval and derives a DS posterior characterized by a Dirichlet distribution. This approach offers computational simplicity and desirable invariance properties, including symmetry and robustness to category permutations, refinements, and coarsenings. The model is flexible in parameterization and testable assertions, and posterior inference on relative probabilities depends only on the relevant cells. The Dirichlet-DSM is compared to existing methods and illustrated with examples. The model is computationally more efficient than alternatives and has desirable properties such as neutrality and representation invariance. The Dirichlet-DSM is shown to provide better inference for point assertions and constrained models compared to the Simplex-DSM. The paper also discusses the restricted permutation paradox and its resolution. The Dirichlet-DSM is shown to be vacuous with respect to unobserved categories, allowing for weaker inference on them while strengthening inference on observed categories. The model is applied to a trinomial example and a constrained multinomial model, demonstrating its effectiveness in inference. The Dirichlet-DSM is shown to be a fast learner, adapting quickly to new data and providing accurate inference. The model is also compared to the imprecise Dirichlet model (IDM), showing that it offers better inference for point assertions and constrained models. The paper concludes that the Dirichlet-DSM is a promising approach for multinomial inference with desirable properties and computational efficiency.A new method for multinomial inference is proposed using Dempster-Shafer (DS) theory. The method represents cell probabilities as unordered segments on the unit interval and derives a DS posterior characterized by a Dirichlet distribution. This approach offers computational simplicity and desirable invariance properties, including symmetry and robustness to category permutations, refinements, and coarsenings. The model is flexible in parameterization and testable assertions, and posterior inference on relative probabilities depends only on the relevant cells. The Dirichlet-DSM is compared to existing methods and illustrated with examples. The model is computationally more efficient than alternatives and has desirable properties such as neutrality and representation invariance. The Dirichlet-DSM is shown to provide better inference for point assertions and constrained models compared to the Simplex-DSM. The paper also discusses the restricted permutation paradox and its resolution. The Dirichlet-DSM is shown to be vacuous with respect to unobserved categories, allowing for weaker inference on them while strengthening inference on observed categories. The model is applied to a trinomial example and a constrained multinomial model, demonstrating its effectiveness in inference. The Dirichlet-DSM is shown to be a fast learner, adapting quickly to new data and providing accurate inference. The model is also compared to the imprecise Dirichlet model (IDM), showing that it offers better inference for point assertions and constrained models. The paper concludes that the Dirichlet-DSM is a promising approach for multinomial inference with desirable properties and computational efficiency.