### Calculation of scores

Let us denote a list of variables to be used in the analysis by

*{x*_{1}, x_{2},
…., xi, …..,x_{v}}

and a priority list associated with them by

*{p*_{1}, p_{2},
….,p_{i}, …..,p_{v}}

The *Partial Order Relation* constructed on the basis of this
collection of variables,

*a **p b *for any cases *a* and *b*

is equivalent to the condition

*x*_{1}(a) *£ x*_{1}(b), x_{2}(a) *£ x*_{2}(b), ….,x_{v}(a)
*£ x*_{v}(b)

where *x*_{i}(a) and *x*_{i}(b) denote values of
the *i*^{th} variable for cases *a* and *b*
respectively.

When *comparing two cases*, the variables of highest priority (lowest
level value) are considered first. If they unambiguously determine the
relation, the comparison procedure ends. In the situation of equality, the
comparison is continued using variables of the next priority level.

This procedure is repeated until the relation is determined at one of the
priority levels, or the end of the variable list is reached.

For each case *a* from the analyzed set, the program calculates:

= the number of
cases strictly dominating the case *a*

*N(a)* = the number of
cases equivalent to the case *a*

= the number of
cases strictly dominated by the case *a*

and then one (or two) of the following scores:

where

*N *= total number of cases in the
analyzed set

*S *= the value of the scale factor,
i.e. the value specifying the range of the score computed (usually 100)