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When Agreement Equals Knowledge: Equation 2

The second equation in the consensus model is the probability that two people, i and j, agree on the answer to a question. There are four ways for this to happen: (1) i and j both know the answer with probability d; (2) i knows the answer and j guesses correctly; (3) j knows the answer and i guesses correctly;and (4) neither i nor j know the answer but they make the same guess, which may or may not be the correct one. The combined probability here is:

which, as Borgatti and Carboni (2007:454) say, in a marvelous understatement, is “pleasingly analogous to’’ the first equation.

Assumptions of the Model

In other words, under certain conditions, ‘‘we can estimate the amount of knowledge of each person by knowing only the pattern of agreement among persons in the group’’ (Borgatti and Carboni 2007:455). Here are the conditions:

  • 1. Informants share a common culture and there is a culturally correct answer to any question you ask them. The culturally correct answer might be incorrect from an outsider’s perspective (as often happens when we compare folk knowledge about illnesses or plants or climate to scientific knowledge). Any variation you find among informants is the result of individual differences in their knowledge, not the result of being members of subcultures.
  • 2. Informants give their answers to your test questions independently of one another. Consensus analysis is not for focus-group data.
  • 3. All the questions in your test come from the same cultural domain and are more-or- less of equal difficulty. No fair asking about the uses of medicinal plants and the rules of kinship in the same test.
 
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