Jack is going to propose to his long-time girlfriend Jill. He browsed three brands of diamond engagement rings on websites - Brand A, B, & C - and was trying to decide which brand to buy. The table below shows the attributes Jack has been considering and the ratings of how good each brand is on each attribute (6 = very good on this attribute; 1= not at all good on this attribute).

Jack wants to make a decision between Brand A and Brand C. He is using the additive difference model. Which brand will he choose?

Question

Jack is going to propose to his long-time girlfriend Jill. He browsed three brands of diamond engagement rings on websites - Brand A, B, & C - and was trying to decide which brand to buy. The table below shows the attributes Jack has been considering and the ratings of how good each brand is on each attribute (6 = very good on this attribute; 1= not at all good on this attribute).

Jack wants to make a decision between Brand A and Brand C. He is using the additive difference model. Which brand will he choose?

BlackTom AI · Accepted Answer

First, I restate the setup: Jack uses the additive difference model to compare Brand A and Brand C based on three evaluative criteria—Cost, Carat, and Design—with given importance weights for each criterion. The weights (importances) are 55 for Cost, 30 for Carat, and 15 for Design. Each brand has a rating (1 to 6) on each criterion.

Option by option analysis:
Option 1: Brand C
To evaluate Brand C, multiply each rating by the corresponding criterion’s importance and sum across criteria.
- Cost: Brand C rating 5 × Importance 55 = 275
- Carat: Brand C rating 3 × Importance 30 = 90
- Design: Brand C rating 6 × Importance 15 = 90
Total for Brand C = 275 + 90 + 90 = 455
This total can be compared to Brand A’s to determine which is preferred under the additive difference model. Since Brand C’s total is 455, it is tied with Brand A’s total (see below).

Option 2: Either is fine
For Brand A, compute similarly:
- Cost: 5 × 55 = 275
- Carat: 4 × 30 = 120
- Design: 4 × 15 = 60
Total for Brand A = 275 + 120 + 60 = 455
We already computed Brand C’s total as 455. Under the additive difference model, the decision rule is to choose the option with the higher total score; if the totals are equal, neither option strictly dominates the other.

Option 3: Brand A
As shown above, Brand A’s total is 455. It matches Brand C’s total, so Brand A does not outperform Brand C.

Option 4: He does not have enough information to make a decision.
All necessary information is indeed provided: the ratings for Cost, Carat, and Design for Brands A and C, plus their importance weights. Therefore, there is enough information to compare A and C under the additive difference model.

Summary of comparative calculation:
- Brand A total: 455
- Brand C total: 455
- The difference between A and C is 0, meaning neither brand strictly outperforms the other under this model.

Consequences:
Since A and C yield the same weighted sum, either could be chosen based on other preferences not captured by the given criteria, or additional tie-breaking rules could be applied. The key takeaway is that the additive difference model yields a tie for these two brands in this scenario.

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