3.1.2. The Functional Form of Similarity

We give a specific functional form to the similarity function in Equations (3) and (4), where *x* and *y* denote two different problem vectors. We choose an inverse exponential function that uses weighted Euclidean distance between the elements of the circumstances to measure the similarity of situations. This choice has support from the psychology literature [33]. Specifically, the information that individuals encounter in past experiences and can observe in the current case are compared through the similarity function. The more similar the current case to the past case, the greater weight the past case is given in the formulation of utility. (We explore other functional forms of similarity and distance between information vectors in Section 7.2.).

$$S(\mathbf{x}, \mathbf{y}) \quad = \quad \frac{1}{\mathbf{e}^{d(\mathbf{x}, \mathbf{y})}} \tag{3}$$

$$\text{where } d(\mathbf{x}, \mathbf{y}) \quad = \sqrt{\sum\_{i=1}^{\#Dims} w\_i [(\mathbf{x}\_i - \mathbf{y}\_i)^2]} \tag{4}$$

for some weights *wi*.
