Before reading my rather negative reaction to this suggestion, please bear in mind:
So, in short, I suggest to conduct an UXSE user research
But I think that your concrete suggestion of a user tooltip is not constructive, and overlooks some serious negative side effects of such a feature.
I would not like to see this data in the little tooltip. Data is great, but it should be placed where it has a purpose. Moreover, data shouldn't be placed where it leads to undesirable side effects.
People have a weird relation to KPIs (I'm using the business consulting term here on purpose). They read into them much more information than they actually contain. They imbue them with a lot of meaning. They start making moral judgments based on them ("What should I care about that idiot, he only has a UUII of 0.8, I can safely ignore him and it would even be OK to ridicule him"). They also change their behavior to optimize the KPIs into a direction they find desirable, regardless of how this differs from the behavior which would actually be optimal for the system's functioning.
If you wave the UUII in people's faces all the time, you'll get people doing whatever they can to make sure theirs is higher than that of the neighbour's. They will stop giving answers unless they think "this is sure to gather tons of votes". They will still have something to say though, so the lamentable tendency of "answers in comments" will grow, undermining the system and placing more burden on moderators. They will start going through old answers which did not get much attention, and deleting them. There will be tons of good answers which are entirely worth keeping, but got a score of 0 or one because the question is too obscure, because of the "fastest gun in the west" phenomenon, or whatever else. And this is just the most obvious consequence. I'm certain that hundreds of users with the time and motivation to game the system will come up with new and creative ways to increase this number without increasing the quality of their answers.
In short, such a feature will undermine the community aspect of the site and have negative impact on its main goal of providing a large quantity of high-quality answers to questions relevant for its users.
If all you want is to play around with the data and see if it tells you something interesting, that's cool. Stack Exchange gives us the tools to do so, and Kit Grose's answer produced a data set which seems to be good for this purpose. If you end up with interesting findings, you're welcome to share them with us.
In short: research is a great thing, please do it! You just have to keep in mind that some research methods are unsuitable for use because they interfere with the routine functioning of your subject. Choose a method without such side effects, and we will love seeing your results and be grateful for your contribution.