This thesis explores the different mathematical frameworks that have been used in risk assessment, with an emphasis on Dempster-Shafer Evidence Theory and the applicability in cases of post seismic structural damage assessments and social vulnerability ranking. Evidence Theory allows the combination of multiple expert beliefs while considering uncertainties that are often inherent in such evaluations. In cases such as seismic hazards, for which structural vulnerability and structural damage are evaluated in a case-by-case scenario, subjective assessments are not only useful but necessary. The results of experimentation and survey distribution suggest that probability may not be the most natural framework in which to quantitatively incorporate the involved uncertainty. Ignorance and evidence-based assessments may be better represented using Evidence Theory.