Sometimes multiple questions from one site could be chosen to show on the HNQ list.
This looks rather ugly, especially when this list is truncated to 5 or less questions - it feels as if the system tries to shove a particular site down your throat.
(for readers who may feel it's minor, a while ago a whole site was removed from HNQ after having pair of their questions repeat like that)
In order to estimate how frequently this is happening, I ran a little experiment. I picked a particular page that listed 5 questions in the sidebar and made a couple page reloads to observe how shuffling works.
16 cases of my 50 sampled reloads displayed me repeated sites. This seems a bit too many and I suggest taking measures for this to happen less often.
Another angle to look at this is a matter of consistency. System introduces specific limits for repeat sites in source hot list with the purpose to ensure broad representation of sites in SE network. This request proposes similar limitation and can be viewed as an effort to maintain intended variety to the part of source list that goes to sidebar and is supposed to be most viewed by end users.
One way that comes to mind, if we want to make it with minimal changes and risk, would be to "pre-select" a higher amount of questions, say, 5-10 more that we want to be displayed in the sidebar and, if it contains repeated sites, questions from that site could simply be removed from the list, up to the mentioned extra amount in the pre-selected list.
This is not quite waterproof but I would still expect a noticeable improvement over what we have now, especially in the cases where the final list is small and repetitions feel most annoying.