I've not come across any sort of formal use of the term, though most folks seem to understand what I'm nattering on about when I make use of the expression. The "Tinker Bell Doctrine" or "Tinker Bell Theology" or "Tinkerbell effect" is a term I utilize when I encounter a peculiar, if pervasive, perspective when it comes to the nature of the gods. The origin of the term denotes the character Tinkerbell, originating in the works of J.M Barrie and most popularly, the 1953 Disney animated film, "Peter Pan", and in particular that the more an individual (or group) believes in something, the more potent it becomes. This is a concept which, while not necessarily a major strain in theological thought, is none the less pervasive, especially in fictionalized representations of mythic beings.
There are a number of fictional works where this approach to deities can be observed, ranging from stories by Douglas Adams, to Neil Gaiman, to the show "Supernatural". Jason, at the Wildhunt blog, has already explored some of the problematic aspects of the practical application to gods some of us actually still worship (in the case of the later); it is one reason why I dislike the show and despite the protestations of my wife and others, will not "give a chance". I'll touch on this in a little more detail later on.
I wanted to touch on and explore in a little more depth the approach Gaiman in particular takes. I really, really like the fiction of Neil Gaiman. I am at a loss to name any other recent author who so thoroughly "gets" what many refer to as "mythical thinking". The love the man has for mythology, in and of itself, permeates all of his works. Coupled with the understanding that myth is a framework, a lens through which to understand our experiences, to provide meaning to those experiences, is a thoroughly refreshing approach, normally only found haunting academic approaches to the subject itself.
Having gotten my fanboy gushing out of the way, Gaiman does make substantial use of "Tinker Bell Theology", smatteringly throughout his "Sandman" graphic novel series, but centrally in his novel "American Gods". In particular, his framing of the origins and extent of deities in particular (sometimes conflated with genius loci, sometimes not) fully adopts this perspective. The basic framework outlining the "life" of a god or goddess is as follows.
1. Humans have something they begin to believe in strongly.
2. This belief manifests itself in a physical form.
3. This form will follow the humans who believe in it, or another localized form will do the same.
4. The level of offerings/sacrifices/ influence directly correlates to the potency of the god/ goddess.
5. As the level of devotion wanes, so too does the god.
In conclusion, the mitigating factor in the existence of a deity is the extent in which Humans actively/inactively believe in them. The more people who believe, the stronger the deity is.
While this creates an interesting framing of the origins and nature of gods, and certainly works as a plot device in a number of fictional universes, it is at its core, incompatible with a truly polytheistic approach to theology. Pantheistic, Panentheistic, Monistic, even perhaps so called "soft polytheism", but not polytheism in and of itself.
I personally think such a theological approach to the gods is an almost textbook definition of self-importance and solipsism. That we create the gods, that they are beholden to us, that they need our worship to sustain them speaks far more to the ascendency and dominance of monotheistic thinking, than to the actual nature of the gods, from a polytheistic world view.
If the gods are little more than thought projections, delusions of a fevered mind or mass imagining, then what value do they have, really? How can these mere mental (and later physical) constructs, or idols, hope to compete with the supreme being, with the "author of creation"? In a word, they can not; they are literally straw(god)men, built up specifically so they can be torn down by the obvious truth which can only be found through the worship of the "One true God". Monotheists, while trying to explain away the historic context of the struggle monotheistic systems had in dealing with contemporary polytheism, will argue that references to "gods" do not refer to deities aside from their own, but the metaphorical idols of the human condition: money, greed, power, lust, etc. In the same breath, the gods of our ancestors are explained away as at best base superstition and at worst demon worship. The gods of polytheism necessarily have to be imaginary friends or hallucinatory monsters, because they do not fit anywhere else.
While I can appreciate the more sympathetic approaches in some of the other theistic frameworks I listed above, they all tend to have one thing in common; they reduce the existence, the nature of the gods, as being sourced to the human mind. The gods become archetypes of human endeavour, they become names of power, they become explanations of natural phenomena to a primitive people, they are relegated to a bygone era, they are shelved in storybooks, and they are proclaimed to be dead (especially when compared to the "living" god of monotheism). Is it any wonder, then, that people will often look askance at those of us who mention that we not only "believe" in these gods, but that we actively worship them?
This turns back to one of my major criticisms with the show "Supernatural", and also why I balk at it, but give Gaiman a pass. The narrative framing of the series is from a monotheistic theological perspective; gods when they do show up, are little more than glorified monsters and readily dispatched by the recurring heroes/villains. Living in a culture steeped and saturated with the superiority of monotheism, I'd rather spend my time in fictional universes more sympathetic to my own view of theology. While Gaiman does us similar framing, and is just as guilty of utilizing 'Tinker Bell theology", he applies it equally across the board. For those of you who like me have the 10th anniversary edition of "American Gods" and have read the Apocrypha, you'll understand what I'm getting at. For those who have not, suffice to say that Jesus is "stretched", just a little bit, not unlike an aged Bilbo Baggins. Gaiman gets a pass for having a good grasp of the myths his characters are sourced from, and not just using them as magical (and recognizable) names, to be disposed of at will for plot convenience. In addition, his sympathies lie with mythic thinking, and not mythic name dropping.
I am firmly of the perspective that the gods are both real and external to us. They do not require our worship, nor do they require our belief in order to exist. At least not anymore than I require your belief to exist. Subjectivity is fine and good, and context is always relevant, but one needs to have a grounding in what is, so as to not fall into the trap of solipsism. Why then worship the gods, if they do not need our worship to sustain themselves?
Because it is better to live in harmony with the gods than to be in opposition to them.
Because they enrich our lives and provide us with models and guidance to follow.
Because they offer to us a connection to something far greater than ourselves.
Because their worship establishes a connection with those who came before us.
Because they, and their stories, provide us with meaning and purpose.
I believe in the gods, because they believe in me.