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**1 - 3**of**3**### Inferring choice criteria with mixture IRT models: A demonstration using ad hoc and

"... goal-derived categories ..."

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### Concepts

, 2013

"... defined categories such as TRIANGLE and ODD NUMBER. Scalene triangles are often rejected as testimony reveals that when asked whether the house number 798 was even or odd, the poll worker responded: ‘‘Odd.’ ’ (Tracie Hunter v. Hamilton County Board of Elections, 2012). The remaining testimony follow ..."

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defined categories such as TRIANGLE and ODD NUMBER. Scalene triangles are often rejected as testimony reveals that when asked whether the house number 798 was even or odd, the poll worker responded: ‘‘Odd.’ ’ (Tracie Hunter v. Hamilton County Board of Elections, 2012). The remaining testimony follows: es. dd, you lo Q. And [if] there were more odds than even num would be an odd address? A. Yes. Although we can all agree with Hasen’s conclusion that ‘‘no one should lose the right to vote because a poll worker can’t tell an odd from an even number,’ ’ it is worth consid-ering whether such mistakes reveal something deeper

### Distributed representations Inference

, 2013

"... a b s t r a c t It is shown that educated adults routinely make errors in placing stimuli into familiar, well-defined categories such as TRIANGLE and ODD NUMBER. Scalene triangles are often rejected as instances of triangles and 798 is categorized by some as an odd number. These patterns are observe ..."

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a b s t r a c t It is shown that educated adults routinely make errors in placing stimuli into familiar, well-defined categories such as TRIANGLE and ODD NUMBER. Scalene triangles are often rejected as instances of triangles and 798 is categorized by some as an odd number. These patterns are observed both in timed and untimed tasks, hold for people who can fully express the necessary and sufficient conditions for category membership, and for individuals with varying levels of education. A sizeable minority of people believe that 400 is more even than 798 and that an equilateral triangle is the most ‘‘trianglest’ ’ of triangles. Such beliefs predict how people instantiate other categories with necessary and sufficient conditions, e.g., GRANDMOTHER. I argue that the distributed and graded nature of mental representations means that human algorithms, unlike conventional computer algorithms, only approxi-mate rule-based classification and never fully abstract from the specifics of the input. This input-sensitivity is critical to obtaining the kind of cognitive flexibility at which humans excel, but comes at the cost of generally poor abilities to perform context-free computa-tions. If human algorithms cannot be trusted to produce unfuzzy representations of odd numbers, triangles, and grandmothers, the idea that they can be trusted to do the heavy lifting of moment-to-moment cognition that is inherent in the metaphor of mind as digital computer still common in cognitive science, needs to be seriously reconsidered.