Just to bring this in line with your revised question, this answer does talk about close votes because they are an integral part of how we handle questions that haven't met question-quality standards.
At the lower end (where, where it matters) and there is no overt mention of research, there is no helpful or reproducible way to determine the amount of effort that went into researching a question before it was asked:
Defining a problem accurately is hard if you don't know the system well. There are a dozen competing names for any given UI metaphor over the various desktops and that can make searching for the correct phrases a pretty tough thing. I still get it wrong.
Sharing useful information about past research is great (and asked for) but as above, plenty of people search and find nothing relevant. I wouldn't find a long list of failed search terms useful for answering the question.
So ultimately, there are no mandated expectations on users, only that their questions are on-topic and answerablein direct answer to the question, there are no mandated expectations for research, only that the questions are on-topic and answerable.
You probably have your own expectations for quality and you're free to vote how you like.
There used to be a research close reason on Stack Overflow. The expectations of reasonable research were so subjective that it caused a flood of close votes against the more simple questions. They had to pull it. Here's Shog9's take from back then:
See, the intent here was to handle the sorts of "here's my spec, please write code for me" questions that were already being closed - not expand closure to damn thousands of existing questions with good, useful answers.
Shog then posted a much wider question late last year about how we treat effort. There is some overlap with research so again, worth mentioning. Ignore arbitrary levels of research and focus onEffort is great but that's not what we actually want to measure. We care much more about the quality of the actual question.
So what you'reby extension, this "metric" you keep asking us to define herefor just isn't warranted ("a metric") is neithereven if it were possible or desirable). Again, just use the normal criteria you would for judging if it's a good question or notIt doesn't help us work out if something is a good, try not to get sucked into whatever the reasons behind asking iton-topic, and move onto the nextanswerable question; it's just a distraction.