Tiddy Smith last year published an interesting article, "The Common Consent Argument for the Existence of Nature Spirits", in which he argued that a common consent argument for theism fails for reasons that nonetheless don't rule out the success of a common consent argument for nature spirits. The article doesn't seem to be easily available online, but there's a nice nontechnical summary of some features of it here. Perry Hendricks had a recent response, "How to Debunk Animism" (DOCX).
Strictly speaking, neither Smith nor Hendricks gets common consent arguments quite right; they both misunderstand them as being arguments from at least nearly universal belief that X exists to its being probably true that X exists; this has not been how people putting forward common consent arguments have generally understood them. In general, common consent draws on the fact that one's fellow beings are rational beings, and that while individuals can be led astray from individual quirks, the tendency of reason can more easily be discerned by looking at the whole population of reasoners, to the extent that it is possible to do so. (I've discussed some of this point here: I, II.) Common consent arguments in general are also not arguments that the conclusion is probably true, but (in weak forms) that it is reasonable and (in strong forms) that it is so reasonable as to be at least morally certain.
In any case, Smith rejects the probabilistic argument from widespread agreement for theism (which would be a more accurate label for the argument considered, and which I will abbreviate as PAWA-Theism) on the grounds that (A) agreement for theism is imposed, although Smith seems often to confuse coercive imposition with cultural diffusion and education, all of which are very different things, and (B) agreement for theism does not arise independently in each individual or each subpopulation. (Both the confusion of imposition with diffusion and the concern with independence would in and of themselves be evidence that Smith is not actually working with real common consent arguments, which are always about the greater power of human reason when it is not merely individual reason but common reason.) Neither of these problems arise if we consider a PAWA for animism. There is excellent evidence that animism arises or at least is found in 'separate knowledge communities' that are very isolated from each other and not under any identifiable regime of coercion. So, if (A) and (B) are problems for PAWA-Theism, they are not so for PAWA-Animism.
Hendricks considers whether countervailing considerations can 'neutralize' this argument even if one takes its premises (i.e., that there is such widespread agreement among independent communities and that such widespread agreement makes the agreed-upon probably true) as true. He attempts to argue this on the basis of a 'problem of animistic hiddenness'. This is based on "the current widespread lack of belief in nature spirits". While this is based on comments by Smith himself, however, it, I think, is already a weakness in Hendricks's argument. First, part of the problem is an ambiguity never really properly eliminated by Smith over the meaning of 'animism', which can just mean belief in nature spirits of some kind, but can also mean a religious position in opposition to theism, in which one believes in nature spirits and not God. It is in fact quite common for there to be theists who do believe in some nature spirits; we wouldn't usually call them 'animists' but 'theists', but believing in God does not automatically mean one disbelieves the existence of nature spirits. (Indeed, historically, most theists have probably also believed in nature spirits of some kind.) Second, while bare animism is rare, and no doubt belief in nature spirits is relatively rare in academic circles, it's simply false to say that belief in nature spirits is unpopular. It varies in how specific and detailed the articulation of it is -- Icelanders have very specific ideas about how elves work, for instance, whereas (outside Native American communities) Americans who believe in nature spirits might not get any more specific than the generic belief in some kind of spirit of the land or waters. This is important because Hendricks wants to build his counter-argument on the basis that animism is not widespread at all times. But while it's true that bare animism is not widespread, belief in nature spirits of some kind has, in fact, been widespread at all times, and is widespread in our own.
Thus Hendricks's argument fails completely, although in fairness it's partly because of confusions introduced into the discussion by Smith. The disagreement in any case is somewhat pointless, because the question of animism vs. non-animism is too specific for this kind of argument. Most people have no idea what animism is, and thus are not actually believing 'animism' even if they are animists -- it's an extrinsic description. This is one reason why putting it in terms of nature spirits is better than putting it in terms of animism. But even this is not really adequate, because the real argument should be at a level more general. Hume was exactly right that the right level of analysis is the generic "invisible intelligent power", which may be nature spirits (like the animists Smith has in mind), or ghosts (like those for which the Mohists argued), or gods, or any number of other things. If we're simply trying to establish existence, we don't want to already be prejudging whether they should be kami or gods or elves or vengeful ghosts or what have you; we need to allow for the possibility that people could be right about their existence but misinterpret the details of their nature (e.g., by confusing one kind of spirit with another); and in this argument we'd need to consider the matter at a generic level that is suitable for discussing widespread agreements. Hume's 'invisible intelligent power' (IIP) meets these quite well. So, if we are considering PAWA's, the best one to consider is PAWA-IIP:
(1) Near enough everyone, both across nations and across eras, agrees that there are IIPs of some kind.
(2) Whatever near enough everyone agrees is probably true.
(3) Therefore, it is probable that there are IIPs of some kind.
As a PAWA, this is of course not a demonstrative argument (and also not a real consensus gentium argument, as it stands), but none of the problems for PAWAs considered by Smith and Hendricks apply to it: (A) and (B) are not problems for it, for much the same reason they are not problems for PAWA-Animism; and Hendricks's unpopularity problem is not a problem for it, because in fact belief in IIPs of some kind has always been extremely popular at all times, and still is today. Premise (1) is far more plausible for IIPs than for anything more specific (that there are kinds of intelligent causes other than living human beings is one of the most common beliefs in the world); so the only question that would be relevant would be whether (2) is actually true, either in general (i.e. whether there are reasons to accept it as a general guideline) or in this kind of case (i.e., whether there are any relevant defeaters). Which is perhaps as it should be.