Who was the first to use Softmax to model decision making? Softmax is a mathematical function frequently used to model probabilistic choice between multiple alternatives associated with different values, e.g. two arms in a bandit task; See for example [1] and [2]. 

Where was this method first applied?

[1] Shteingart, Hanan, Tal Neiman, and Yonatan Loewenstein. "The role of first impression in operant learning." Journal of Experimental Psychology: General 142.2 (2013): 476.‏

[2] Egelman, David M., Christophe Person, and P. Read Montague. "A computational role for dopamine delivery in human decision-making." Journal of Cognitive Neuroscience 10.5 (1998): 623-630.
According to Sutton and Barto:


  The term soft-max for the action selection rule ... is due to Bridle (1990).
  This rule appears to have been first proposed by Luce (1959)