There seems to be some debate whether the classical Delphi technique (i.e., qualitative questionnaire first round followed by quantitative survey rounds) is considered as qualitative, quantitative or mixed-methods approach. Any thoughts?
This could be considered to be an "exploratory sequential" mixed methods design, where the early rounds of qualitative data are used to develop the content for the later quantitative rounds. But most of the Delphis that I have seen involve relatively small Ns, so that it would be difficult to do anything but descriptive statistics with the quantitative data.
The basic Delphi Technique is qualitative as originally developed. However, you could use quantitative methods to analyze some of your results if your data points included quantitative data. If this were done, it would be a mixed method. Most likely, the quantitative methods would be descriptive rather than inferential as they would not involve random selection.
The Delphi technique (Hasson et al., 2000) is a qualitative method used, amongst other things, to elicit expert opinion - it replaces direct debate by a carefully designed program of sequential interrogations conducted by questionnaires interspersed with opinion feedback derived by computed consensus from the earlier parts of the process (Brown, 1968).
Any numerical data, such as description of the demographics of the participants and questionnaire response rates, is purely descriptive.
Brown, B.B.(1968), “DELPHI PROCESS: A Methodology Used for the
Elicitation of Opinions of Experts”, Santa Monica, CA, The Rand Corporation.
Hasson, F., Keeney, S. & McKenna, H.P. (2000), “Research guidelines for the Delphi survey technique”,Journal of Advanced Nursing, 15, 32(4) pp. 1008-15.
My understanding is that the classic three-round Delphi ends with seeking ratings on the items generated earlier, so that there often is a qualitative component.
Based on my understanding of Creswell (2012 & 2014), this enquiry can be encased into exploratory sequential design, in which qualitative themes guide extensive survey questionnaire! You may also see Dornyei (2007) for further clarification.