Final answer:
The Attenuation Model developed by Anne Treisman suggests that unattended information in the process of selective attention is weakened rather than completely blocked, allowing it to sometimes influence perception.
Step-by-step explanation:
The model of selective attention that suggests unattended information is weakened, but not completely blocked, is the Attenuation Model developed by Anne Treisman. Unlike Broadbent's Filter Model, which posits that unattended information is completely blocked from further processing, Treisman's model introduces the concept of an attenuator. The attenuator acts to reduce the strength of the unattended information, rather than eliminate it, allowing for the possibility that unprocessed information could still influence perception if it has a high enough threshold of importance or familiarity. This model better accounts for the occurrence of the Cocktail Party Effect, where a person can still perceive and respond to unattended messages, like hearing one's name in a noisy room, even when not consciously focusing on them.