Historians are fond of saying "history has no predictive value," a statement that is about 80 per cent true. If history had no predictive value, there'd be no point in studying it. After all, apart from a few delusional compulsive gamblers, nobody studies old winning lottery numbers because they have absolutely no predictive value even if they may have won millions for the lucky ticket holders. We do study history because we can glean some predictions out of it. The U.S. got involved in the former Yugoslavia very reluctantly because history shows clearly that occupying Yugoslavia may be easy, but subduing it may be another matter altogether.
Multiple Factors
To return to the crime question, it is distinctly possible that all the proposed causes for the drop in crime are correct. It may well be that deterrence and removing criminals from circulation, legalization of abortion, outlawing of leaded gasoline and the end of the Baby Boom all acted jointly to lower crime rates. An additional complication when multiple factors are involved is synergy - two agents acting together have a stronger effect than the sum of their individual effects. So it's entirely possible that statistical tests of any of the proposed causes in isolation might be inconclusive, but all four acting together could have a powerful effect.
Motives For Advancing Hypotheses
Some of the hypotheses for the drop in crime rates were not advanced with the purest of motives. Although the motives of someone for holding an idea never - repeat, never - constitute evidence, they can raise red flags. Motives can alert you to the potential for hidden fallacies, selective use of data, maybe even outright fakery. You are never justified in rejecting an idea solely because of the motives of the person presenting it, but you are entitled to give intense scrutiny to the evidence and logic.
The baby boom hypothesis is probably the most innocent. Since young adult males dominate the crime statistics, a natural approach is to ask what happened when they were children. In a quick scan of history twenty years before the crime rates bagan to fall, the end of the Baby Boom leaps out. So it's a simple and sensible hypothesis. One way to evaluate it would be to see if crime rates track population growth with a time lage of about 20 years. But major population dips and rises are rare, and there are many other factors that could affect the results. On the other hand, this explanation might supply a ready rationalization to someone who is ideologically predisposed to reject any of the other hypotheses.
The legalization of abortion would also leap out at anyone looking for significant societal events from the early 1970's. But this hypothesis has a powerful appeal to anyone looking for an argument in favor of abortion.
The hypothesis that tougher sentencing has had a deterrent effect makes sense, but also has a powerful ideological appeal to social conservatives.
The leaded gas hypothesis is also fairly innocent. The researchers noted that leaded gas was phased out in the 1970's, were intrigued enough to look at crime statistics from other countries, and found a widespread correlation. But this hypothesis might appeal to people who want an alternative to some other proposed cause. Opponents of tough criminal laws might latch onto this explanation to argue that it's a viable alternative to the deterrent hypothesis, and opponents of abortion might seize on it to discredit the abortion hypothesis. And it's a wonderful argument for environmentalists.
So, apart from genuine conviction, people can embrace hypotheses either because they support what they want to believe, or offer an alternative to something they don't want to believe. Thus we have the complication that people can believe the right things for the wrong reasons.
Motives For Rejecting Hypotheses
Most of the debate over the drop in crime rates seems to have had less to do with advancing an explanation than finding reasons not to accept some proposed explanation. People who otherwise aren't concerned with why crime rates fell become very concerned when the drop is credited to some cause they reject. The motives for rejecting hypotheses, apart from genuine conviction, mirror those for acceptance: people either don't want to believe the hypothesis or want to believe some alternative.
In science, the motivation issue tends to be settled by the bystanders who don't have a deep emotional investment, but who do have a vested interest in their own disciplines. I don't care one way or the other how astronomers sort out the Big Bang, dark energy, and the like. I would start to care if they came up with something that radically revised the age of the earth. They in turn don't care how far back we can trace plate tectonics, but they'd get very interested indeed if we recalculated the age of the earth and doubled it. That would play havoc with their models of stellar evolution. So regardless how vehemently an outsider like H.C. Arp argues that galaxy red shifts don't always correlate with distance, I will trust the astronomers to sort it out, as long as their conclusions are useful, or at least harmless, to my own field.
An important group of bystanders are scientists in the pipeline as undergraduates, graduates, and junior scientists. They may be intrigued by and dabble in some of the off-brand theories, but they don't have the emotional attachment that the originators of those theories, or defenders of the status quo, have. So when conflicting evidence comes along, they take it with a lot more equanimity. They tend to gravitate to the position best supported by the evidence, so the alternatives either linger on as marginal theories or eventually die out.
Conclusion
It may never be possible to resolve exactly why crime rates in the United States dropped in the early 1990's. Even if there is really only one correct explanation, there may be no way to establish its correctness using any known methods. There may be many equally valid ways to interpret the evidence. "Valid" here doesn't mean as seen by some hypothetical omniscient observer. "Valid" means that using the best available evidence and the best available reasoning and analysis, there may still be mutually incompatible explanations that fit the data equally well. It's like watching replays of a controversial football play. Some angles suggest that a receiver had control of the football when he hit the ground, others don't, and two equally skilled referees might differ on the call they make. And even though, on the whole, football referees make remarkably good decisions, even the best available evidence and training doesn't guarantee there won't be occasional errors.
The Nature of Gods (or Other Beings)
Note that the word "god" (capitalized or not) has not been mentioned since the introductory section. Everything since then has been about the problems of proof when evidence is ambiguous, theoretical frameworks are lacking, and there may be several interpretations that explain the data equally well.
The only question about a god that is meaningful or interesting is whether or not there is a god who interacts with the universe. Pantheism, the idea that the sum total of everything that exists is a god, is trivial. Deism, the idea that a god created the universe but does not interact with it, is of no imaginable interest or relevance.
In practical terms, deciding the existence of a god amounts to testing for the existence of some rational and extremely powerful supra-human being or beings. Whether it's a single infinitely powerful deity, a number of finite but still powerful supernatural beings, or a powerful natural alien civilization, the practical problems of evidence are the same. Whether or not a god exists may not be testable by scientific methods, but there are very similar questions that science certainly can address. Suppose, instead of asking whether there exists an infinite, omnipotent deity acting by supernatural means, we ask if there is some very powerful intelligent Entity interacting with our planet. The Entity need not be infinite or omnipotent, merely far more powerful than we are. The Entity need not act supernaturally, but merely by means of natural laws we have not yet discovered, or technology we have not yet developed. To free ourselves from any distractions imposed by the supernatural, let's consider the hypothesis of a purely natural, but extremely powerful and knowledgeable Entity.
What's the Entity's agenda? It could be malevolent or sadistic, seeking to harm us or cause prolonged suffering rather than destroying us outright. That might be a plausible explanation for war, famine, and disease. Or it could be dispassionate, watching to see how long we can avoid destroying ourselves. But let's consider only the possibilities that the Entity is benign and actively trying to help us. Furthermore, it is knowledgeable enough about human psychology and the workings of our planet that clumsiness or ignorance are not an issue. If it had tried to prevent World War II, for example, it would not have inadvertently triggered some worse alternative history. It would not, say, have gotten Hitler into art school only to have Stalin conquer Europe. And remember, this Entity is not a deity; it is merely a very intelligent and very powerful, but 100 per cent natural, being.