Can you create an action rule?

That rule option is only available in the new Responsive Forms 

I don't have the time to post about it now, but can make a write up later of how to accomplish this using the Classic Forms rule system. Just know that it requires javascript (as some people are put off by js. or simply cannot implement it in their own / client's environment). 

Any chance you could look at some code I've tried to cobble together to get something to work?  Essentially I'm picking a value from a list lookup.  I want that choice to populate another control (a single line of text) on the form.  Here is my control settings from the list lookup

Here is the settings from the Single Line of Text box control

Here is the code I've attempted to cobble together.  Yes, I'll admit I'm pretty horrible when it comes to Javascript.  Its been quite some time since I have even attempted to code JS.  Unfortunately, it is not like a bike and you do forget how to code it .  Basically the drop down doesn't populate the SLT box.  I've tried to insert different console.logs to try and follow what is getting captured, and it doesn't report back anything.  I can only assume I'm not capturing the correct value.  Any help here would be greatly appreciated.

function ReturnMySelection(source, arguments) {

var myselection = NWF$('#' + ddlPicker + ' option:selected');

var selectionText = myselection.text();

NWF$('#' + ddlSelection).val(selectionText);console.log(selectionText);

}

Something along the lines of this should work. 

note that I have changed your second function argument from the name 'arguments' to something else as the term 'arguments' is used natively by javascript 

function ReturnMySelection(validationSpan, validationObject) {

  var selectionText = NWF.RuntimeFunctions.parseLookup(validationObject.Value) || validationObject.Value;
  NWF$('#' + ddlSelection).val(selectionText).trigger("blur");
  console.log(selectionText);

}
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That worked.  Thank you.