Social judgment theory
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The Social Judgment theory of attitude change was proposed by Carl Hovland and Muzafer Sherif. The judgment theory attempts to explain how attitude change is influenced by judgmental processes.
In a study of weight perception, participants categorized several small weights by weight class based only on lifting each one in turn. A control group C categorized the weights roughly or evenly across six weight classes, while another group A was asked to lift a much heavier weight before each test weight. This group categorized most weights in the lowest weight class, with decreasing quantities in each successively higher weight class. The third group B lifted a weight only as heavy as the highest weight class before judging each other weight; this group categorized most weights into the highest weight class, with decreasing quantities in successively lower classes — the opposite result of group A, and contrary to predictions of the contrast effect. Hovland and Sherif called this effect, where things start to seem more like their context (the heavy weight), the assimilation effect.
In terms of anchoring and adjustment, when an anchor (the heavy weight) approaches the range of possible judgments (the six weight classes), the categorization or judgment shifts from contrast to assimilation.
When applied to social judgments, these effects show that the most effective position to advocate for changing another's attitude judgment is the most extreme position within that person's "latitude of acceptance," within which assimilation effects will make your position seem more like their own. Beyond this latitude lies the latitude of rejection, within which any position will be seen as more different from one's own due to contrast effects. ΣAE