I think it would be interesting to rephrase the original poll. Instead of asking if a player wants the dm to fudge, I'd rather see the results of a poll like this:
Do you mind if your DM fudges to keep the game moving and to enhance the story?
Echoing Skyscraper here: Making the question biased toward painting "fudging" in as positive a light as possible would, of course, lead to more people being okay with it. Similarly, if we phrased it in some inherently negative way, I'm sure we'd see things leaning far in the other direction.
Admittedly, the original poll should have had more options than "yes," "almost never," and "never." Perhaps something like "frequently"/"occasionally"/"rarely"/"almost never"/"never"; while admittedly that still has issues of squishy frequency terms (some people might vote "occasionally" when they do it at least once a session on average, while others might consider "once or twice per campaign" to be "occasionally," and the difference between "rarely" and "never" is pretty big.)
It seems like a trust issue to me.
I guess trust is part of it--I really don't like being lied to, and see a vast gulf between "I don't tell you every fact up front, you have to learn or experience some of it yourself" and "I do things which I intentionally prevent you from learning and will go out of my way to deceive or even lie to make sure you never learn." But I also see it as...sort of a crutch, if that makes sense. It's a crutch for the players, cushioning them against the actual consequences of their actions, even when those consequences are
purely the result of poorly-managed risk. And it's a crutch for the DM, either to avoid admitting that a mistake was made, or to avoid going to the effort of learning other ways to resolve the problems at hand. Because I have yet to hear a
single example where fudging was the
only solution to the problem--again, given that I define fudging as either modifying a stat after it's "been used in play," modifying the *kind* of result produced by a roll (e.g. monster dies, and can't fight -> monster lives and continues to fight,
not monster dies, and can't fight -> monster is knocked unconscious, and can't fight), or giving the players true/accurate information (complete or partial) only to turn around and make that information false/inaccurate at a later point.
If players trust the DM and enjoy the game experience, they'll be more likely to accept DM fudging if it happens.
Alternatively, the players trust the DM and enjoy the experience, because they know the DM will neither deceive them nor pretend the game works a way it doesn't.
On the other hand, for many players, knowing that the DM will fudge, cheapens the experience because they feel that they have less control.
Control has never had anything to do with it, for me. I can't learn from my mistakes--even the mistake of poorly managing risk--if those mistakes are whisked away when they would cause harm. I can't learn from my successes--even the success of getting lucky--if the benefits of actual good luck are removed (monster doesn't die when someone gets a lucky hit that should kill it), and I think I receive good luck when I didn't. That's not a control issue; it's a skill issue. By playing the game, building up a body of experience of what works and doesn't, what's risky and what's not, etc. I learn how to play well; but I can't do that if the body of experience contains manufactured data, aka fudging.
I can definitely see both sides of the issue.
Well, if there actually are people who feel that other side of the issue you discussed, great. But it would seem to me that you are under the mistaken understanding that there are
only two sides to this issue. Yes, we can group answers, more or less, as "pro-fudging" or "anti-fudging," but that's a bit like grouping, say, religious traditions on whether they're pro-monotheism or anti-monotheism. You'll end up with weird stuff like atheists and polytheists being "anti-monotheist," and thus "the same" despite being fundamentally different (similarly, you'd end up with a portion of maltheists "on the same side" as Christians, despite their radical differences).
Personally, I'd enjoy playing with a DM that could fudge unobtrusively when it makes the game more interesting (or saves a PC from a stupid or undeserving death).
Alright, here's a question then: Would you prefer a DM that fudged unobtrusively to satisfactorily address those problems, or one who addressed them satisfactorily without any fudging at all (obtrusive or not)?
As a DM, I fudge very little, especially because all of my games are run on Fantasy Grounds and the encounters are pre-set. The urge to fudge often comes when I DM 2-3 PC parties and I don't adjust an adventure for less PCs. Likewise, the urge to fudge is also stronger when I DM for 6-7 PCs and the encounters/situations are not scaled for such a large party. I guess, it is more like making adjustments on the fly.
I've got no problem with adjusting an adventure before the fact, nor with adjusting future encounters "on the fly" (so long as the players haven't got an ironclad reason to expect specific encounters in a specific way, e.g. an accurate and recent copy of the guard duty roster for the castle they're infiltrating). I see your "urge to fudge" in either case as more accurately an urge to ensure that the adventure is an appropriate challenge for the party in question, and I believe the distinctly superior answer to that urge is to change the challenge itself, rather than interfering with the resolution system once the encounters/situations actually "begin."
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As for the lumping together of results: it's going to be controversial no matter what you do. Leave them separate. Don't lump. Just don't do it.
Not that the percentages actually matter in any meaningful sense. Volunteer sample, can edit or retract vote later on, the possibility of sockpuppets, the unrepresentative nature.... Statistically, you can't claim a damn thing from either one, unless you restrict yourself to JUST the people who voted, which is obviously not very useful. But I've said all this a bajillion times before, so I doubt it will have any meaningful effect on attempting to "analyze" this stuff.