On the relation between the Maximum Entropy Principle and the Principle of Least Effort

A customer loyalty formation model in electronic commerce

“…Principle of least effort theory expresses that human beings, animals and even well design machines like to choose the least effort to achieve the goal. Convenience is the important issue in this theory (Egghe and Lafouge, 2006). Fast and easy payment is the factor that has been considered based on this theory.…”

On the relation between the Maximum Entropy Principle and the principle of Least Effort: The continuous case

“…., m) the quantity of effort is defined asF = m r=1 E r · p r Ln(p r ). In Egghe and Lafouge (2006) we prove the following result, if we suppose p 1 , p 2 , . .…”

“…., p m is a decreasing sequence MEP and PLE are equivalent. In the conclusion to this article we provided a complete explanation of Zip's law (Egghe & Lafouge, 2006) or Lotka's law as a decreasing function.…”

“…In the production of words in a text, we express this regularity using the formalism of Zipf's law (see Section 4). In Egghe and Lafouge (2006) page 8, this hypothesis is formulated thus: the cost (effort) of using a word with i (i = 1, 2, 3 . .…”

“…In the second part, we mathematically demonstrate equivalence by introducing the concept of admissible effort function. Here, the mathematical proof is harder than in the discrete and finite case (Egghe & Lafouge, 2006), because the entropy (or the amount of effort) is not necessarily finished.…”