Example of an Authorship list (with affiliations)
A mathematics or computer science researcher might also see the problem as one of choosing the proper representational data structure. The authorship order, no matter how determined, is a 1-dimensional queue (ordered list). Even though some publishers (such as PLoS) allow for footnotes (an inventory of author contributions), there is still little room for nuance.
The Academic Family Tree"
But is there a better way? Academic genealogies provide one potential answer. A typical genealogy can be thought of as a 1-dimensional order, from mentor to student. In reality, however, an academic have multiple mentors, influenced by a number of predecessors. The construction of academic family trees  is one step in this direction, turning the 1-dimensional graph into a 2-dimensional one.
Picture of the Authorship tree cover. COURTESY: "The Giving Tree" by Shel Silverstein
This is why Orthogonal Lab has just published a hybrid infographic/paper called the The Authorship Tree . This is a working document, so suggestions are welcome. The idea is to not only determine the relative scope of each contribution, but also to graphically represent the interrelationships between authors, ideas, and scope of the contributions.
As we can see from the example below, this includes not only our authors, but also people from the acknowledgements, funders, reviewers, authors of important papers/methods, and funders. While the ordering of branches along the stem suggests an authorship order, they are actually ranked according to their degree of contribution . To this end, there can be equivalent amounts of contribution, as well as inclusion of minor contributors not normally included in an authorship list.
Example of an authorship tree (derived from original 1-D author list).
 Cozzarelli, N.R. (2004). Responsible authorship of papers in PNAS. PNAS, 101(29), 10495.
 David, S.V. and Hayden, B.Y. (2012). Neurotree: A Collaborative, Graphical Database of the Academic Genealogy of Neuroscience. PLoS One, 7(10), e46608. doi:10.1371/journal.pone.0046608.
 Orthogonal Lab (2017). The Authorship Tree. Figshare, doi:10.6084/m9.figshare.4731913.
 For more on the point system convention, please see: Venkatraman, V. (2010). Conventions of Scientific Authorship. Science Issues and Perspectives, doi:10.1126/science.caredit.a1000039.