Matthew Braddock has an interesting paper, Resuscitating the Common Consent Argument for Theism (PDF). As I noted in discussing Tiddy Smith's "The Comment Consent Argument for Nature Spirits" and Perry Hendricks's response, "How to Debunk Animism", these sorts of arguments are not, in fact, common consent arguments, but probabilistic arguments from widespread agreement (PAWA). He actually gives two PAWA arguments. The first is:
(1) There is widespread belief in a High God.
(2) Common Consent Principle (CCP): Widespread belief that p is defeasible evidence that p.
(3) Thus, widespread belief in a High God is defeasible evidence that a High God exists. [From 1 and 2]
(4) There are no undercutting defeaters of this evidence.
(5) Thus, widespread belief in a High God is good evidence that a High God exists. [From 3 and 4]
(6) Thus, widespread belief in a High God is good evidence for theism (which asserts there is a High God) over metaphysical naturalism (which asserts there are no supernatural agents).
An obvious issue is what exactly we count as a 'widespread belief'. Braddock has an interesting set of arguments arguing that about 90% of the world believes in some Supreme Being or primary deity of some kind. I confess myself very skeptical that it is quite so high, but it's easier to get within reach of that estimate that one might think -- Christianity and Islam alone get you around half the world, even being fairly conservative; many forms of Hinduism, despite being polytheistic, take there to be supreme deity of some kind; Sikhims and Judaism of course also count; a very large portion of the very large number of small religions would also count; and, as Braddock points, out a significant portion of those who are not definitely affiliated with any particular religion would also count. Braddock also argues that you can get similarly high figures both looking to the historical past and to the foreseeable future, so the 'widespread' here is very widespread indeed.
With respect to premise (4), Braddock considers three possible lines by which one might reject this: the expertise objection (the dissenting minority is better placed to know), the debunking objection (we have an alternative explanation for the widespread belief in this case that disrupts its connection to truth), and the independence objection (the belief's being widespread is not the relevant kind for CCP because there is not enough independent acceptance of it). Of the three, the independence objection is the most complicated and difficult to answer -- indeed, my own view is that it is why the traditional common consent arguments, despite some difficulties, are often superior to PAWAs, because traditional common consent arguments commit to a specific means or set of means for why the belief occurs (nature and/or reason, usually) and thus are not putting direct evidential weight on numbers but on the hypercumulative character of the evidence available to the entire human race. Braddock himself converges on something like this in his response to the independence objection, using the results of cognitive science of religion and empirical surveys that show that people can and do give a wide variety of reasons for why they believe in God. But these responses essentially mean that the nerve of the argument is not the widespread belief but what lies behind it.
The second PAWA is this:
(7) There is widespread belief in a High God.
(8) Widespread belief in a High God is more surprising given naturalism than theism.
(9) Thus, widespread belief in a High God is evidence for theism over naturalism.
This part of the paper is much weaker. I think, despite the profligacy and confidence with which contemporary philosophers make such judgments, it is in fact impossible to assess claims like premise (8). For one thing, there is actually no 'naturalism' and 'theism'; these labels designate very large and diverse families of very different views, and tweaking details can radically throw things in a different direction. For instance, on which position is widespread belief in a High God more surprising, a naturalism that has an explanation of theism as a part of our tendency to interact with our world socially or a a theism that holds that God is trying to keep His existence secret except to a select few? Even to begin assessing an argument like this, we would need to have done some work establishing what the best forms of naturalism and the best forms of theism; there are at least enough poorly thought out versions of positions in the world, that we would need to be able to focus on the more tenable versions.
