Valuation by comparable sales and linear algebra

Summary Valuation by comparable sales is one of the most frequently used valuation methods. A considerable amount of experience has been codified regarding the principles to be used when selecting comparable sales. However the methodology utilizing the sales has not been seriously challenged, despite its imprecision, ambiguities and tautological structure. There is a need for a reconstruction which provides a sound algebraic and arithmetical framework, makes no additional data demands and acknowledges that any forecasting capability is secondary and intuitive. It is suggested that linear programming provides an acceptable methodology. A valuation is interpreted, in this context, as the maximum price a property can be valued at, consistent with its characteristics and the characteristics and sales prices of comparable properties. Additional algebraic criteria are imposed on the selection of comparables: consistency and independence. These contribute to the process of pricing property characteristics, so facilitating a valuation via the simplex algorithm. An interpretation, in valuation terms, is provided of various linear progamming phenomena, including degeneracy, alternative optima and unbounded solutions.