Do chefs use customer feedback to improve dishes? I understand that chefs can gauge the quality of a dish by monitoring its popularity. However, suppose a chef wants to improve an existing recipe, how might he/she do that?

Will the chef rely on customer feedback? Suppose a customer says he likes the steak but thinks the sauce can be improved. How can a chef use that information?

Clarification - I want to understand if and how chefs might use customer feedback to improve dishes.

Suppose a chef surveys 100 customers. 60 of them say that the steak sauce need some improvement. Will the chef investigate further to improve his recipe? If so, how would he do it?

Also, suppose that the same 60 customers say that they prefer the steak sauce in another restaurant, will the chef go to the another restaurant to investigate?

I'm not senior enough to leave comment, so thanks to everyone that tries to help!
I'm only a semi-pro chef, but let's have a go at answering your question.

There are some people who have an actual impact when they provide feedback on one of my dishes. These are people I have cooked for more often and whose tastes are familiar to me. They will often function as a "test panel" when I want to try out a dish I'm considering for the menu of a commercial event I'm planning.

Should this test panel think my sauce needs more seasoning or more acidity, this would certainly cause me to adjust the recipe and/or process.

On the other hand, feedback from an individual guest whose tastes are unknown to me is pretty much meaningless. How would I be able to tell whether their likes and dislikes are anywhere near an average opinion? There those who will nearly always reach for the salt shaker when served a dish, even if to the average taste it is well seasoned.

So this hypothetical individual customer that features in your question seems pretty unlikely to cause a chef to change his recipe, unless of course the same feedback has been given before and a pattern emerges. In that case an individual customer can of course tip the scales in favor of a change.