Which method involves comparing brands based on the most important attributes until one remains?

The method that involves comparing brands based on the most important attributes until only one remains is the lexicographic method. This approach prioritizes attributes by importance and evaluates each brand against these attributes sequentially. The comparison continues until a brand can be identified that dominates the others across the most critical criteria.

In practical terms, if a consumer were determining which smartphone to purchase, they would first consider the most crucial feature to them — for instance, camera quality. They would compare all available brands based on this feature and eliminate those that don’t meet their standards. If multiple brands satisfy this criterion, they would then move on to the next most important attribute, such as battery life, and repeat the process. This continues until only one brand remains that excels across the prioritized attributes.

Other methods mentioned in the choices do not function in the same comparative manner. The average method typically involves calculating mean values which do not strictly compare attributes in a hierarchical manner. The compensatory method allows for trade-offs among various features, enabling brands to win on certain attributes at the expense of others, rather than strictly eliminating brands. Elimination by aspect would involve eliminating brands based on certain aspects but does not specifically prioritize them sequentially, hence differing from the lexicographic approach.