## 3 Results  
To see the effect of the outlined methodology, several examples will now be presented. First, the following general example visualizes the logic of the four-step procedure working with little market information. It deals with four product characteristics, hence four weights \(w_{j}\). Figure 1 contains between lines A and B four true weights of client 1 (the vertical side of the box is thought of as a numeric axis quantifying weights in this basic visualization). The quadruplet between lines B and C represents the true weights of client 2, and between lines C and D, there are true weights of clients 3 and 4. The four clients, in this elementary example, represent the segment of the market that bought the top-selling product. The product is a top seller thanks to these four clients. The entire box is considered to be a symbolic visualization of the step 1 space of weights (most of them not shown in the graph; in reality, the entire space would also not be a box), i.e., the set of all the many weights that, once inserted in the AHP formula, lead to the top-selling product having the highest AHP value. The set also contains the true and designated weights of the four clients. In practice, their location in the box is unknown. Two new product variants, V1 and V2, are considered. They constitute what the company is able to manufacture. Let us assume that for client 1, the new variant V1 would truly be the best one, given his/her weights and taking all the variants currently sold into account, while V2 would truly be the best for the two clients with weights between lines C and D. Now, following step 3 of the procedure, it is discovered that V1 is the best variant based on all the sets of weights lying in the region between lines A and B, which happens to capture the weights of client 1. In the case of variant V2, it turns out to be the best product for all the sets of weights located between lines C and D, this finding capturing clients 3 and 4. According to step 4, since the latter subregion of weights is greater than the former, the company makes the decision to start producing variant V2. This decision is correct because V2 is in reality preferred by more clients (two) than V1 (one client), or by a greater subset of the relevant market segment. But what is the point of this procedure when the true weights are unknown in practice? Because of the larger weight subspace (the case of V2), we can be more confident that there are clients in the relevant market segment for which the variant in question is the best (in the example, the larger subspace managed to capture both the clients). With small subspaces, that confidence is much smaller. Even though the V1 client was captured with the small subspace in the example, we are unaware of that in practice, and there is not much reason to trust such result--if the distribution of the true weights is rather even in the weight space, the small subspaces will at best capture fewer clients than the large subspaces (that's the case with V1, V2), or they will not capture any client--the V1 client did not have to be captured, so small subspaces are not of much use. We do not know in practice which of the two cases occur, but this is irrelevant because both of them are adverse. When the distribution of the true weights is uneven in the space, additional arguments presented in the second paragraph of the Section 4 apply, their main point being that when a large subspace is very large, as is the case in the example that follows, the character of the weight distribution should not be of much concern, and the large subspace should still be preferred. The following, more specific example works with three currently sold product variants assessed by three features. The first two features have the property that the higher they are, the better. The third has the opposite property; the lower, the better. Table 1 contains the levels of the three characteristics for each product variant.