In literature there is no agreement about that. Many scholars support the idea that the conversion is neither logically acceptable nor reliable in practice. If you belong to the opposite team, in any case only self-valuation can give you the answer. A fairly “long scale” (at least 7 steps, but better 11 (0-10)) and a representative sample may lead to acceptable results (see: Van Praag, B., 2007, Perspectives from the Happiness Literature and the Role of New Instruments for Policy Analysis, 2007, IZA Discussion Paper No. 2568.). Nevertheless, I am not fully convinced that a subject answering 8 (a question such as “from 0 to 10 who happy are you?) means that s/he is double as happy as who answered 4. Best. Francesco

Note that some of the difficulties of ordinal data may not be a problem in a DEA model. But you need to think about how the data is used and coded. For example there are many papers looking at the performance of countries in the Olympics using DEA and address the question of how to cope with medal count data where the value of a silver medal is logically more than a bronze but less than a gold but how much better one is over another is contentious. This is most commonly modeled by having three transformed outputs (total medals, number of gold and silver medals, and gold medals) which is equivalent to having weights restrictions to enforce the ordinal positions.

Note that for an input variable you need to note that  having a zero in one of your input variable will exclude any unit which has a none zero for that input from being a peer. Also note that if you have the direct use of an ordinal variable as an input it is not likely to be valid even if you use VRS as the virtual unit will be often be constructed by combining lower and higher values of this variable in a linear combination. ie. if the input is a 5 point scale (0 very poor to 4 very good) a virtual unit compose of 50% of a unit  with V poor  and 50% of a unit with Very good could be used as the virtual peer for a unit with a score of 2 neither good or poor.

Seldom come across ordinal vs cardinal data on the conversion issue from ordinal to cardinal data,   But I do come across ordinal vs interval / ratio data in which I think they have the similar concept.  Many researchers / scholars only agreed converting from interval / ratio data to ordinal data e.g. exam mark of 49 (ratio data) can be classified into categories like A, B, C, D and E etc.(ordinal data) and not the other way round i.e. category E can't translate into specific mark.  The same applies to converting interval data to ordinal data.

However, some researchers do convert ordinal data (e.g. Likert Scale) to interval data through modifying their survey questionnaire i.e. converting Likert scale questionnaire (e.g. 1=Effective, 2=Some How Effective, 3=Moderately Effective, 4=Neutral, 5=Moderately Not Effective, 6=Some How Not Effective, 7=Not Effective) to Semantic Differential scale using Bipolar Adjectives (e.g. Effective1, 2, 3, 4, 5, 6, 7 Not Effective) so that parametric tests can be applied. The rationale claimed is that the intervals between the scale values can be treated as equal intervals, making it an interval scale which justified for parametric tests.  All the best to your research.

Kindly refer to:

Differences in the treatment of cardinal and ordinal data by Thomas E. Leonard in Journal of Chemical Education 1977 54 (7), 430

Yes, that's a very funny question! Have you consult and analyze the literature on "outranking"? That is a world in which you are still with a multidimensional vision (for example, the colors of the medals for each competitor) and a lot of players (the nations) ,and you will precise your preferences maps and will be conducted to something like  a ranking! See literature in The International journal of multicriteria decision.

Hi Maurice,

Do you have some specific article in mind in the International journal of multicriteria decision?

Can I suggest that you consider Wade D. Cook, Moshe Kress and Lawrence M. Seiford (1993) "On the Use of Ordinal Data in Data Envelopment Analysis"

The Journal of the Operational Research Society

Vol. 44, No. 2 (Feb., 1993), pp. 133-140 

And some of the 114 or so papers that subsequently refer to it according to Google!

The example in Cook et al's paper is using urgency as a input when urgency is classified on a 4 point scale from low-1 to high 4 and includes an example set of data with 31 DMU's

http://scholar.google.co.uk/scholar?cites=7505706567924761622&as_sdt=2005&sciodt=0,5&hl=en