Improvement of the Sales Comparison Approach using Analytical Hierarchy Process and linear optimization: application and validation

The sales comparison adjustment grid within the market approach suffers from several flaws and drawbacks, one of the most conspicuous of which lies in the subjectivity - uncertainty, too, and even lack of reliability - affecting the weights of the comparables’ attributes. The literature has already focused on improving the sales comparison adjustment technique, but the approaches proposed so far - though promising - are usually inconvenient and too complex to be included in any appraisal. We propose to overcome the subjectivity issue by complementing the sales comparison adjustment grid with an automated weighting process based on the Analytic Hierarchy Process (AHP) and linear optimization. The solution suggested here aims to be easily replicable by practitioners and appraisers on a worksheet, without requiring expert knowledge of mathematics and statistics.The ranking of the comparables according to their sale price and the ranking of the same according to their attributes are elicited using pairwise comparison matrices, which are built by calculating the ratios of the prices and the ratios of the attributes’ values, respectively. Using ratios leads to pairwise comparison matrices that are, by definition, perfectly consistent. Nevertheless, while using ratios is straightforward for quantitative attributes, it also poses the issue of how the qualitative ones are coded and measured. The ranking of the comparables according to their sale price and according to their attributes are then matched by changing the attributes’ weights. The iterative search for the optimal weights employs the solvers available in common worksheets.Several tests are performed to validate the proposed model. Some of them use ordinary residential building units for sale both as the subject and as comparables. Once the subject is identified, ten or so other properties for sale are chosen in the same urban area as comparables; the comparison is primarily based on the information included in the online real estate advertisements. Other tests are conducted based on the appraisal reports the Italian Revenue Agency prepared for a set of peculiar publicly-owned buildings. As comparables, we use the same properties identified to that end in the appraisal reports mentioned above, and the comparison focuses on and is limited to the attributes considered there. The results suggest that complementing the sales comparison adjustment grid with a weighting system derived from the data itself leads to a fair appraisal of the property market value.