## 3 Results
### Limitations of This Approach
#### 3.1.4 Simple Pairwise Comparison  
The simple pairwise comparison technique for eliciting weights systematically considers all pairs of attributes in terms of which is more important. For each pairwise comparison, a point is assigned to the attribute that is considered more important. In the end, attribute weights are determined as the ratio of points assigned to each attribute divided by the total number of points distributed across all attributes. The simple pairwise comparison technique is comprised of the following two steps: (1) pairwise rank the attributes, and (2) calculate weights. Pairwise Step 1: Pairwise Rank the Attributes  
Given a set of \(N\) attributes, systematically compare pairs of attributes in terms of which one of the two is more important relative to small changes over its range. Of the pair, the one judged to be more important is assigned a point. The process is repeated until all \(N\)*\((N-1)/2\) pairs are evaluated. For example, consider the automobile purchase problem. Using the five criteria, there are 5*\((5-1)/2=10\) pairs to evaluate. The output from this pairwise ranking step might yield the following results:  
* [noitemsep]
* \(\bullet\): Purchase Price vs. Attractiveness: Purchase Price Wins;
* \(\bullet\): Purchase Price vs. Reliability: Purchase Price Wins;
* \(\bullet\): Purchase Price vs. Gas Mileage: Purchase Price Wins;
* \(\bullet\): Purchase Price vs. Safety Rating: Purchase Price Wins;
* \(\bullet\): Attractiveness vs. Reliability: Reliability Wins;
* \(\bullet\): Attractiveness vs. Gas Mileage: Attractiveness Wins;
* \(\bullet\): Attractiveness vs. Safety Rating: Safety Wins;
* \(\bullet\): Reliability vs. Gas Mileage: Reliability Wins;
* \(\bullet\): Reliability vs. Safety Rating: Reliability Wins;
* \(\bullet\): Gas Mileage vs. Safety Rating: Safety Wins;  
The point distribution obtained using these 10 comparisons is shown in Table 8.  
Note that the least important attribute in the above example has a score of zero points (as it won none of the pairwise comparisons). The resulting weight factor in this case will be zero unless some constant offset or systematic bias is applied to all scores. Such an offset or bias desensitizes the resulting weights of the attributes to changes in the points distributed to each via a pairwise ranking procedure--the greater the offset, the less sensitive the resulting weighting distribution will be to small changes in attribute scores. For example, if an offset of 2 points or 10 points is used, the revised score distributions shown in Table 9 would result. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviation** & **Criteria** & **Points** \\ \hline (P) & Purchase Price & 4 points \\ (R) & Reliability & 3 points \\ (S) & Safety & 2 points \\ (A) & Attractiveness & 1 point \\ (G) & Gas Mileage & 0 points \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Point calculation for pairwise method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Abbreviation** & **Criteria** & **Formula** & **Weight** \\ \hline (P) & Purchase Price & 4/10 & =0.4 \\ (R) & Reliability & 3/10 & =0.3 \\ (S) & Safety & 2/10 & =0.2 \\ (A) & Attractiveness & 1/10 & =0.1 \\ (G) & Gas Mileage & 0/10 & =0.0 \\  & Sum & 10 points & =1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Weights for pairwise method. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviation** & **Criteria** & **Points (2/10 Offset)** \\ \hline (P) & Purchase Price & 6 points/14 points \\ (R) & Reliability & 5 points/13 points \\ (S) & Safety & 4 points/12 points \\ (A) & Attractiveness & 3 point/11 points \\ (G) & Gas Mileage & 2 points/10 points \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Weights for pairwise method using offsets.