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5.2.1.4. Mental effort

Obviously, the more attributes are processed, the more mental effort has to be invested. Important attributes are decisive for a decision and if they are considered earlier, they may obliterate the need to consider other attributes and cost less mental effort. A complicating factor is that a decision-maker cannot be sure how much mental effort will be involved. He/she can only estimate expected mental effort based on his/her belief pjn that the attributes occupy certain states.

To illustrate, let three attributes and have A, B and C states, respectively (). Assume that the heuristic under consideration implies attribute search sequence . Let and denote the amount of the expected mental effort involved when processing attributeand, respectively, and letandrepresent the decision-maker's beliefs that the attributes are in the states with values va, vb and vc, respectively, such that, . The expected amount of mental effort is then defined as:

(5.15)

(5.16)

(5.17)

(5.18)

(5.19)

Eq. (5.17) tells that is inevitably fully involved since is processed first. For each possible state of, expected efforts are derived from two terms. First, the effort of processing is weighted by the probability of being in a particular state and , an identity function defined by Eq. (5.18).represents a judgment process, according to which a respondent examines the relationships between all subsequent overall values and the overall threshold . If all overall values are inactivated or activated, it means that the same decision or preference applies to all instances of that attribute and hence considering the attribute will not have any effect on the preference ordering or decision. In these cases, . In contrast, when , needs to be searched. According to the same logic, the second term relates to processingwhen at a state of is weighted by , the joint probability of being in the previous two attribute states, and is another identity function judging whether being against gives unanimous results.

 
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