Alternative solution: Store presentation order in a string before presentation of first question
As a professional researcher in psychology I definietely subscribe to the notion that the current implementation of the randomization option lacks one central feature needed, i.e. that the very order of presentation for each response is logged. However, this is needed for subsequent item analyses (i.e. halo effects etc.)!

I therefore propse an alternative solution, namely, that for each group (or, indeed, across groups or all survey items?) the order of question presentation is determined before the first question is presented.

For example, this could easily be done by creating and writing to a long string field within the limesurvey[number] table which determines the order of presentation for each respondent. (Ideally, this should work for both randomized and nonrandom questions!!)

Then, for each group or question presented, the order can easily be determined by reading of the substrings of this field.

I agree. For psychological research this is critical. We need to know the presentation order for randomized questions.

Another situation where this would be needed. Imagine I want to present a set of randomized items, in separated screens. I want to ask two types of questions for each item in different screens (e.g. First answer Yes/No to a question, then tell me how confident you are in your response). As far as I see, there is no way to do this right now.

Storing the presentation order for the items would solve this type of problem.

getQuestionOrder : «Fill a question with the final order of question and/or group in any survey»

https://bugs.limesurvey.org/view.php?id=7486