I'm not a fan of defining personal lingo, I'm afraid. If you need a lengthy post to set up a personal definition, and folks have to read it in order to know what you're talking about, when to the rest of the world the exact same word means something rather different, I think that's bit of a communication failure on your part.
I'm not offering a personal definition. I'm offering up a hopefully definitive Aristotilean definition of the sometimes loosely defined and used slang term 'railroading'. If you feel that I have failed to define it properly, then by all means critique my definition. I believe I am using the term in the proper way based on the lexicographic information I've observed at EnWorld and elsewhere. I have used an Aristotilean definition rather than a nice short Socratic one, because I've not yet hit on a nice short Socratic one that isn't misunderstood.
The 'rest of the world' for all I know consists of you, because I have no special knowledge of how you use the term or whether your usage is in wide agreement with the core ideas I've observed the term being employed to reference.
I believe that I have been understood when I used the term on this thread. The one poster I have been in a direct dialogue with offers up that I'm using the term more broadly than he's used to using it, but he doesn't seem to quibble with my general idea. I submit that I'm using the term more narrowly than I've seen some use it, and with good reason.
I submit that the main reason for the disagreement is that many posters in addition to using the term as I've defined use the term 'railroading' very loosely and in an overlapping way to pejoratively mean, 'sorts of DMing I don't like', much as the term 'power gaming' is also used as a slur of player behavior. In consider this use of the term as a blanket insult to be a hinderance to understanding, and while my definition incorporates the notion of 'railroading' as an activity where by the DM disempowers the players and recognizes the pejorative intent of the term, it is a definition which avoids subjective analysis of actual railroading.
In other words, some posters would not call Shrodinger's Map a railroad if they felt it was fun, and other's would call it a railroad if they didn't. But a subjective definition is in fact a personal definition. In previous discussions this has led to utter chaos, and different posters have tried to define virtually anything and everything as railroading, for example offering up the claim that any linear adventure is a railroad. This sort of definition is in fact a personal definition and is nearly useless. (As can be seen from the definition, a linear adventure is only a railroad if you can't get off, and specifically if the DM is employing certain tricks and techniques of DM force that prevent you from getting off.) You or someone else may in fact feel that any linear adventure is a railroad, but that is merely an attempt to use a pejorative to state something is badwrongfun because they don't like linearity. If 'railroad' merely means 'linear but you know in a bad way', then its a pointless term.
"Please see my previous writings to understand what I'm talking about," is okay for formal talks by authorities - which this isn't.
This may not be formal, but I'd like to think that when it comes to gaming topics, we are the authorities.
I this case, it means what I think it means. If I take a small amount of heat from water, I get a cup of cold water. If I take a lot, I get solid ice. A matter of degree (kind of literally) leads to difference in outright physical qualities, not just quantitative difference in temperature.
Which is precisely where you analogy breaks down because unlike the state change that occurs in water, there is no objective point where we could say 'this isn't railroading' and 'this isn't' based on the quanitity of something observed. Games don't actually under go some physical and measurable state change based on exceeding some absolute and objective point in a scale of 'railroading' where a little isn't and a lot is.
Moreover, you are still getting it wrong. Ice and water are qualitative differences that relate to quantitative differences, but they aren't intrinsic aspects of the quantitative measurement of temperature. The quanitity and the quality still measure and describe different things. For example, there are quantitative differences between red light and blue light. But being 'red' or being 'blue' is not a quantitative difference, but a qualitative difference based not on the wavelength of light but how the human brain processes and perceives light. 'Blueness' and 'redness' exist independently of their quanitative measurements. This or that frequency of light is a quantitative difference, but blueness is a quality distinct and independent from the measurement.
Quantitative differences are those that can be measured. Qualitative differences are those humans "feel" as different. You can have both at the same time - it is often difficult to produce a qualitative difference *without* a quantitative one.
Be as that may a matter of degree is not a qualitative difference. Ice is not ice because it is cold (see a vacuum for instance), but because matter undergoes a state change (consuming or releasing energy independent of that necessary to cool or heat the matter). Yes, there are quantitative differences in this case between the two qualities, but qualities they remain nonetheless.
Matter of degree is not measurable in the case of 'railroading'. What would you have me measure? Either it is qualitative or it is wholly subjective. If it is wholly subjective, what is the point? Hense, you are probably the one using a personal definition and not me. I reject that the term means only no more than what Umbran believes to be railroading.