Alright. I'm happy enough being a Mormon with proof that only makes you right somewhere around 90% of the time. Cough up.
Resetting confidence levels is a dangerous game for any person to play with their beliefs. You've said I can set it wherever I like. Fine, I choose to set it such that greater than or equal to fifty one percent confidence will be knowledge of some degree, rather than faith.
Do you see the consequences here? I've just reduced the chance that any aspect of your canon and testimony is actually correct to the odds of a coin flip. If you accept those boundaries, then you can't use the book of Mormon or divine testimony or anything like that as something any more substantial than a coin flip to guide your decisions or beliefs. It's essentially admitting that you'd be just as well off using a gambler's dice to guide your life.
There's a tension in fiddling with confidence levels like this. Between meaning and proof. If you want an empty faith – then that's very easy to have without obligating yourself to any sort of evidence, but it's not clear there's anything there to believe in. However, if you want to preserve that sort of meaning then you've got to select confidence levels in excess of fifty percent and retain those as faith and that obligates you to some sort of proof.
And, by the by: this all works whether or not you're a pure Bayesian. Axioms are true simply by virtue of the rules of the system. They are true in every possible world where the system in which they're constructed can be made to apply. To the truth state of an axiom it doesn't matter whether god will provide testimony or not.
If you think knowledge only comes from axioms - (or is built purely on axioms) - then in offering some prediction as being fulfilled you're not being asked for anything that would qualify as knowledge. It's not even clear under such a construction that you're being asked for anything that would qualify as evidence of a particular axiom.
Of course the minute you start saying that the evidence does matter to the truth states it ceases to be an axiom; for all that the formula may itself contain or wrest on axioms.
Put it this way, if you think that there is a 1% probability (e.g. you are convinced it is bogus) that I am right in stating that if taken seriously God will answer prayers as from the scriptures I provided and this is enough to get you to try out what they say then that was sufficient faith in that instance. Clearly at 1% probability you shouldn't be doing anything else that comes with believing in the Book of Mormon or being LDS (at least that doesn't already coincide with what you think of as being right).
If you follow through and get evidence to boost...
(Disclaimer: This post is sympathetic to a certain subset of theists. I am not myself a theist, nor have I ever been one. I do not intend to justify all varieties of theism, nor do I intend to justify much in the way of common theistic behavior.)
I'm not adopted. You all believe me, right? How do you think I came by this information, that you're confident in my statement? The obvious and correct answer is that my parents told me so1. Why do I believe them? Well, they would be in a position to know the answer, and they have been generally honest and sincere in their statements to me. A false belief on the subject could be hazardous to me, if I report inaccurate family history to physicians, and I believe that my parents have my safety in mind. I know of the existence of adopted people; the possibility isn't completely absent from my mind - but I believe quite confidently that I am not among those people, because my parents say otherwise.
Now let's consider another example. I have a friend who plans to name her first daughter Wednesday. Wednesday will also not be adopted, but that isn't the part of the example that is important: Wednesday will grow up in Provo, Utah, in a Mormon family in a Mormon community with Mormon friends, classmates, and neighbors, attending an LDS church every week and reading scripture and participating in church activities. It is overwhelmingly likely that she will believe the doctrines of the LDS church, because not only her parents, but virtually everyone she knows will reinforce these beliefs in her. Given the particular nuances of Mormonism as opposed to other forms of Christianity, Wednesday will also be regularly informed that several of these people are in a position to have special knowledge on the subject via direct prayer-derived evidence2 - in much the same way that her parents will have special knowledge of her non-adopted status via direct experience when she wasn't in a state suitable to notice or remember the events. Also, a false belief on the subject could have all kinds of bad consequences - if the Muslims are right, for instance, no doubt Hell awaits Wednesday and her family - so if she also correctly assumes that her parents have her best interests at heart, she'll assume they would do their best to give her accurate information.
Atheism tends to be treated as an open-and-shut case here and in other intellectually sophisticated venues, but is that fair? What about Wednesday? What would have to happen to her to get her to give up those beliefs? Well, for starters, she'd have to dramatically change her opinion of her family. Her parents care enough about honesty that they are already planning not to deceive her about Santa Claus - should she believe that they're liars? They're both college-educated, clever people, who read a lot and think carefully about (some) things - should she believe that they're fools? They've traveled around the world and have friends like me who are, vocally, non-Mormons and even non-Christians - should she believe that her parents have not been exposed to other ideas?
Would giving up her religion help Wednesday win? I don't think her family would outright reject her for it, but it would definitely strain those valued relationships, and some of the aforementioned friends, classmates, and neighbors would certainly react badly. It doesn't seem that it would make her any richer, happier, more successful - especially if she carries on living in Utah3. (I reject out of hand the idea that she should deconvert in the closet and systematically lie to everyone she knows.) It would make her right. And that would be all it would do - if she were lucky.
Is it really essential that, as a community, we exclude or dismiss or reflexively criticize theists who are good at partitioning, who like and are good at rational reasoning in every other sphere - and who just have higher priorities than being right? I have priorities that I'd probably put ahead of being right, too; I'm just not in a position where I really have to choose between "keeping my friends and being right", "feeling at home and being right", "eating this week and being right". That's my luck, not my cleverness, at work.
When Wednesday has been born and has learned to read, it would be nice if there were a place for her here.
1I have other evidence - I have inherited some physical characteristics from my parents and have seen my birth certificate - but the point is that this is something I would take their word for even if I didn't take after them very strongly and had never seen the documentation.
2Mormons believe in direct revelation, and they also believe that priesthood authorities are entitled to receive revelations for those over whom they have said authority (e.g. fathers for their children, husbands for their wives, etc.).
3I have lived in Salt Lake City, and during this time was, as always, openly an atheist. Everyone was tolerant of me, but I do not think it improved my situation in any way.