An election, however imperfect, is a scientific process. It is an attempt to gather factual, empirical evidence about which candidate the people prefer. Instead of guessing or trusting instinct or listening to whoever shouts the loudest, we do our best to measure who is most popular. Like any measurement, our results are only as good as our accuracy. Accuracy is affected by errors, which are called "error variance." If we are trying to say there is a difference between two things, for example cancer rates for people who ingest mercury and people who do not, we compare numbers. We announce that there is a difference only if the numerical difference between the two groups is greater than the error variance. This is called "statistical significance."
If a seeming difference between two groups fails to meet this standard, we cannot assert that the two groups are different. We say that the results are "statistically insignificant." Alternately, we say the difference may have occurred by chance. This is because chance, or factors outside of the experimenter’s control, could tip this small difference in one direction one time and in the other direction another.
In the case of an election, as an empirical method, the same mathematical principles apply. When we obtain a difference of 42 votes out of 2.6 million, this doesn’t mean that the number 42 is significant, either statistically or otherwise. It means we don’t know who would have won if our measurements were perfectly accurate. The only thing we are sure of is that the seeming difference between the two candidates is smaller than all of the errors we have made in gathering votes and adding them up.
If we could get rid of our errors, we might find that there is a real, albeit small difference between the two groups. In science, this is what repeated experiments attempt to do. In election science, this is what recounts attempt to do. By them, we reduce the error variance in order to measure more accurately. Think about a man balancing a checkbook. He wants to know if he has enough in the account to pay off his credit card or if he needs to wait. He adds twice to be sure and gets different numbers each time. Now he doesn’t know if the first number was correct, or the second, or another number altogether. He knows that somewhere, somehow he is making mistakes. So, he adds again (and again, if need be), catching errors, until his tallies converge on a single number. A recount is similar, although more complex. Someone adding a checkbook can add enough times to obtain a certain result. This is not possible with an election, but we can come close.
Historically, hand counts are considered more accurate than machine counts. This is because our machine technology is very imperfect. Remember, the thing we are trying to measure is the will of the voter. At times, a human can discern what the voter intended when a machine, programmed with a very few simple decision making rules, cannot. Over time, as our technology improves, machine counts will become more accurate than hand counts. Right now, we are in transition to new technologies, each of which is susceptible to its own kind of errors. At this point recounts are the only method we have for getting as close as possible to what’s real.
The more people understand this process, the more they are able to advocate their own values and interests and the more we are able to continue improving the system.