The issue with the definition of a social-political-cultural formation in its historical context – but possibly with any definition altogether – is the fact that we should treat it as a “statement” which assumes an underlying relation. A relation which a good number of attempts at a “classificatory” definition of “fascism” seem to leave entirely implicit, as if it were either obvious or irrelevant to the matter of classification.

It's quite unfortunate that I am neither well versed in methodological arguments, nor especially fond of investigations into “generic fascism”, but I'll do my best to illustrate what I mean.

From the perspective of an objective definition, an apple is merely an apple. And it is the exact same apple, whether it's sitting on the counter or still on the three, whether it's your apple or mine, whether you are offering it to a horse or a lion... If we consider the underlying relation though, the same apple becomes different things: it can be property, or nature, or food, or a piece of decoration, or a symbol of temptation, etc.

To make things slightly more complex, there is the fact that the relation we are examining isn't itself a static object: it depends on the historical context (both the original one and our own), as long as we wish to make this an historical investigation, but also on the intent of our investigation. This means that the scope of our “definition” - its narrowness or broadness – depends heavily on what we mean to examine.

An investigation of the relations between the growing fascist movement in Emilia-Romagna and the agrarian and industrial establishment during 1919-22 may find very little need for a broad definition of “generic fascism”, and could therefore be fully satisfied with an identification of fascism with Italian Fascism; conversely, an examination of the influence and legacy of “fascism” in a late XX Century environment probably needs a broader, more general, definition.

To be clear, in this example, it's not the definition alone which would change, but the underlying relation as well, and substantially, as the social, political and cultural environment of 1920 Emilia-Romagna would not be the same as, let's say, the social, political and cultural environment of post-unification Germany, or of the 1980s United States.

From my point of view – and here, and in the whole answer really, I'll have to be a bit sloppy with the details of where I am picking ideas from, since the whole issue of a methodological approach to Fascism is a subject of relative controversy on which I feel it's more proper to offer my personal perspective, rather than sticking unambiguously with this or that specific author, or attempt an encompassing examination which far exceeds my knowledge – there is no hard rule as to how one should form their definition, provided that it is self-consistent and mindful of the underlying relation. A broader, more general definition, allows for the inclusion of a larger number of phenomenons within the “fascist constellation” which would be otherwise left out as “incomplete”, “ancillary”, or “para-fascist” according to a narrower, more particular definition.

As to myself, given that I spend more time on certain specific traits of Italian Fascism, I am inclined to characterize “fascism” in a somewhat narrow sense, where two distinct but similar enough political formations came to exist in the inter-war period, with certain distinguishable traits, in a general cultural context which wasn't certainly exclusive of Italy and Germany, but which developed a “political-institutional” form only in those two instances.

This definition – I must insist – seems to work perfectly for what I am doing (as usually is for any amateur); but, while it is broader than the exclusiveness of Italian Fascism reclaimed by a certain sector of Italian historiography, it is probably already too narrow for someone who wishes to examine the evolution of, let's say, Portugal, or Spain, or Hungary during the 1920s and 1930s, adopting “generic fascism” as an interpretative tool.

As obvious as it may appear, the issue with any “generic fascism” definition – and especially with “compilatory” ones – is the fact that they operate in a constant friction with the underlying relation. For instance, the conceit of a fidelity to “tradition” and “traditional values”, of a defense of some form of “natural” or “cultural-heritage” order – which you suggest as a possible element of characterization – is certainly present in many political and social movements which have been linked to “generic fascism”. It is nonetheless an incredibly common, and broad one – characteristic of a large portion of the cultural-political discourse after the enlightenment and the French Revolution (and indeed even where a direct social-political connection with the Revolution is far from manifest). So that one should not be surprised in finding it present in many attempts at a “definition” of fascism (think for instance of the once very influential contribution by E. Nolte – which, to be fair, is quite more articulate than my brief summary can give credit for), as well as in seeing it progressively losing ground in favor of what I certainly believe to be a more accurate representation of the cultural side of the fascist phenomenon, which is that of a “renovation-restoration”, a “palingenesis” whose purpose is not to destroy the individual, society, hierarchy, property, culture, state; but instead to “restore” them, to return them to their natural, true form (either cultural, societal or racial). In this sense the elements of tradition do not represent “conservation” but need to be protected and restored to their fundamental status in so far as they represent the “true” character of the national collective, of the kin, of societal bonds – and the “revolution” goes against those forces which undermine (the liberal system), or openly threaten (Bolshevism) those characters. Therefore propriety, family, religion need to be protected not in so far as they are traditional elements per se - other traditional elements can be removed without any serious repercussions; their old age is not enough to prove their organic relation – but only in so far as they express the fundamental characters of the collective in its historical agency.

Which, still leaves us very much on the “cultural history” ground, and without addressing the specific forms of the underlying relation.

Notably, if we were to take tradition alone – and the “defense of tradition” in particular – our “cultural” definition of Fascism would have, somewhat controversially, to recognize (as is probably inevitable for a “cultural” definition) that fascism, as a cultural phenomenon, would be represented more properly by sociopolitical organism which are usually sidelined to the ranks of “para-fascism”, rather than by the Italian and German examples where the “transformative” and even “iconoclastic” inclinations were somewhat more prominent: organizations like the French Croix de Feu, certain nationalistic groups in post WW2 Japan, or – why not – the American Ku Klux Klan, would fit our bill of “defense of traditional values”, without bothering us with an examination of their existence and action as a government authority.

The addition of “authoritarianism” to our definition does – in my opinion – very little to improve it. Once we have defined “cats” as domesticated mammals, the information that they are “four-legged” doesn't really add anything to the substance of our definition, except for ruling out six-legged and eight-legged mammals. It probably serves us best to examine the possible causes of the adoption of authoritarian forms in fascist or para-fascist regimes – not last the fact that the state had to serve the ultimate purpose of embodying or concretely representing a collective which was, in itself, one, and one in its true and intimate connection; by which the consequence that the state had to operate as one and to encompass everything followed quite naturally.

Authoritarianism – broadly speaking – tends to have a more pragmatic approach to this sort of “community-building” and “collective-existing”, even if, again, there is no clear and obvious line to be drawn between “totalitarian” and “authoritarian” approaches.