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Gigerenzer, G and Goldstein, D. (1996). Reasoning the Fast and Frugal Way: Models of Bounded Rationality. Cognitive Science 103(4), 650-666. 

@Article{GigerenzerGoldstein1996,
  author = 	 { Gigerenzer, Gerd  and Goldstein, Daniel  }
  title = 	 { Reasoning the Fast and Frugal Way: Models of Bounded Rationality},
  journal = 	 {Cognitive Science},
  year = 	 {1996},
  volume = 	 {103},
  number = 	 {4},
  pages = 	 {650-666}

}

Author of the summary: Danielle Coleman,2011, dcoleman@connect.carleton.ca

Summary
Humans and animals alike make inferences about the world under limited time and knowledge, but many models of rationality treat the mind as being able to compute these inferences with unlimited time, knowledge and computation might (similar to a Laplacean demon). Gerd Gigernzer and Daniel Goldstein from the Max Planck Institute for Psychology strongly oppose this Lapacean view of mind and strive to replace it with a more realistic, ‘satisfying’ algorithm based off of H.Simon’s bounded rationality (both cognitively and ecologically) called the “Take the Best” algorithm. They designed an inferential task based competition to compare the traditional “rational” Laplacean algorithm with the newer satisfying “Take the Best” algorithm.
The Task
Various two-alternative-choice tasks that occur in various contexts where inferences need to be made with limited time and knowledge. For example: Two different types of inferences can be made, one from knowledge retrieved from memory and the other from givens, they test both in the competition.
Theory
The cognitive algorithm Gigernzer and Goldstein propose is based off of the PPM theory, the Probabilistic Mental Model that assumes that inferences about unknown states of the world are based on probability cues.
Take the Best Algorithm
The "Take the Best" algorithm is a satisfying algorithm whose policy is “take the best and ignore the rest”. The “Take the Best” algorithm assumes a subjective rank order of cues according to their validity. The highest ranking cue is the best. The algorithm follows 5 steps in order to make an inference:
The Contest
The contest included “What German city has the largest population” out of a possible 83 cities. The model of the environment consisted of 9 ecological and the actual 9 X 83 cue values.
Contestants
Competitors include proper and improper linear models, in short the traditional “rational” algorithms - in which they all use complete searches and complete integration.
Contestant 1: Tallying
A simple integration algorithm that tallies all the positive cues from ‘a’ and b’ where if the summation of ‘a’ is greater than ‘b’ then choose ‘a’ or if ‘b’ is greater than ‘a’ choose ‘b’ and finally if ‘a’ and ‘b’ are equal then guess.
Contestant 2: Weighted Tallying
Weighted tallying is similar to contestant 1; only ‘a’ and ‘b’ are multiplied by their weighted ecological value. Where, if the summation of ‘a’ by ‘v’ is greater than ‘b’ by ‘v’ then choose ‘a’, if the summation of ‘b’ by ‘v’ is greater than ‘a’ by ‘v’ then choose ‘b’, if the summation of ‘a’ by ‘v’ and ‘b’ by ‘v’ is equal than guess.
Contestant 3: Unit- Weight Linear Model
Takes into account both positive and negative cue values during summation where if the summation of ‘a’ is greater than ‘b’ then choose ‘a’ or if ‘b’ is greater than ‘a’ choose ‘b’ and finally if ‘a’ and ‘b’ are equal then guess.
Contestant 4: Weighted Linear Model
Takes into account both the positive and negative cue values during summation and multiples by the ecological validity where, if the summation of ‘a’ by ‘v’ is greater than ‘b’ by ‘v’ then choose ‘a’, if the summation of ‘b’ by ‘v’ is greater than ‘a’ by ‘v’ then choose ‘b’, if the summation of ‘a’ by ‘v’ and ‘b’ by ‘v’ is equal than guess.
Contestant 5: Multiple Regression
Looks into the dependency between the cues, where the choices are multiplied by a certain value based on what they are.
Results
Because of the design of the “Take the Best” algorithm to only perform a limited search it reduces the time needed to search in memory dramatically. Depending on the amount of information the algorithm has, it only needs to search between 2 and 20 cues. The “Take the Best” algorithm drew as many correct inferences as any of the other algorithms, and more than most. The average results are as follows: As you can see “Take the Best” and Weighted Tallying averaged the same amount of correct interferences as the weighted tally and more than the others while the Unit-Weight Linear Model averaged the least.
A Note on the “Fast” Algorithms
Gigernzer and Goldstein wondered if this type of satisfying algorithm could be any faster than it already is because most inferences are made under very limited time. So, they tested the “Take the Last” algorithm and the “Minimalist” algorithm whose average score were .645 and .647 respectively. The “Take the Last” and the “Minimalist” algorithm averaged least amount of cues needed to look up, but sacrificed accuracy.
Final Words/Conclusion
In this article Gigernzer and Goldstein try to dispute the “fictional” Laplacean view of reasoning. The Laplacean Demon represents the idea that we can make inferences about the world under perfect circumstances – that we have unlimited time and knowledge coupled with the computational might to handle both. Obviously, that is not how our mind works or how it makes inferences because we just don’t have that kind of power –So, why must our algorithms represent this false view? Gigernzer and Goldstein propose that we use a ‘satisfying’ algorithm to better represent how we make inferences and to their surprised it made more correct inferences than most of the “rational” Laplacean algorithms.
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