Suppose Heavenly Father wishes to convey some important information to us that will be useful to our salvation. Now we know that He can communicate with us but that He limits that communication to be based on faith (ours or those around us). Thus, getting answers from God involves a cost in terms of faith and effort (see D&C Section 9). Starting from this point, one can write down a simple model of prophetic guidance that lets us understand what we observe:
Assume everyone wishes to know some value T (if it helps, pretend it is the exact percentage of tithing we are to pay). We can receive an estimate of this value but our estimate is “noisy” in that it is error-laden. Thus we get information Y with Y = T + e, and e is the error. If e is big (negative or positive), then our estimate Y is not very close to T. If e is 0 then we are fine. But we don’t know e or T, we only have Y.
Case 1: Robinson Crusoe
If we are the only person available, we go with Y=T, since we don’t really have anything else to go on. This isn’t great if e can be very big, but it is all we have.
Case 2: Dark Ages
Suppose there are many of us, each with a different estimate of T. Thus we each have a different Y. If we think that on average, our errors cancel out (so that e is as often too low as too high), we can average our Y’s and call that the best guess T. Then we all do that. We may all be very wrong if, in fact, the e’s don’t “cancel out” (average to 0). But that is all we can do. This is one of the many justifications for democracy– it aggregates information. This view also gets you things like the Iowa Electronic Markets.
Case 3: The Restoration
Suppose we are in Case 2, but some person (call this person a prophet) is known to draw e’s close to 0 (so that Y is always or typically close to T). We should take advantage of this fact. This could happen in one of two ways:
A) Suppose we believe our Y contains separate valuable information that the prophet’s Y does not. Thus we would wish to average our Y’s together, though we may wish to give more weight to the prophet. There is a nice little mathematical formula for how to do this, but basically it amounts to giving more weight to people who have high-quality draws. In this model, since one never actually believes the prophet to be exactly right, one always modifies the advice by one’s own information. One believes some combination of one’s own Y and the prophetic Y (you can add in other people’s Y as well). This will give you the best available guess.
B) On the other hand, it may be that we have basically no good information once one accounts for the prophet’s statement. Thus the only reason we get a different Y than the prophet is because we have trouble “getting the signal” and so have a noisy measure of T. In this case, we should totally ignore our Y, and assume T equals the Y revealed by the prophet. This may be the case if the prophet is also aggregating together information to determine the Y he tells you.
Note 1: Case 3 requires us to decide about how close the prophet typically is to the truth, and whether or not we have separate information that the prophet is not privy to. But even those who ignore their own Y and just follow the prophet are not assuming infallibility, far from it! Case 3B makes no claims about prophetic infallibility (though that would be fine), only that the prophetic statement includes all the useful information available to you. Personally, I think that Case 3B is a pretty good guess of where we stand on relation to information stated in General Conference.
Note 2: God authorizes servants so that we know who has the good information.
Note 3: How good our Y is is likely to be a function of our own efforts at prayer, obedience, etc. It may be that, in our current mortal state, it is easier to verify a truth than to receive one. Thus it may be low cost to take the prophet’s Y to the Lord and ask if this is the best available one. It may be much easier to get an answer to that query than to receive a high-quality Y from one’s own efforts. Thus we confirm the prophetic counsel as part of the process of confirming the prophet’s standing as the best available information.
Note 4: If each person has a different correct T, this presents a problem for general revelation. In this case, the Church may take no stand because there is no one one correct answer that is worth giving. It also may go to localities and offer advice specific to that location (stake conference). Or one’s best counsel may come from a local “prophet” (bishop or head of family) that has a better signal than you. Lastly, it may be that our individual guesses are so off that it is better for the prophet to give a universal guess that is perfect for no one but is better than what we’d do individually. See the first few verses of Section 89 where we get a revelation that is geared to the weakest among us, but was then applied to all.
Now there are other reasons to obey counsel than the one given above. This is not a Grand Universal Theory of Prophets. It is just a little model that may give some insight to what we observe.