A Calvinist will argue that God predestines some to be saved and equally predestines others not to be saved. This is called double predestination. A Lutheran, on the other hand, will argue that God predestines some to be saved and merely fails to predestine the others either way, so that they default, due to their sin nature, to being damned. They are left in their condition, not actively predestined to be damned. This is single predestination.
It may be noted that I have, before today, regarded single predestination as logically absurd. That line of thinking goes like this: God is omnipotent, thus he is able to do whatever he wills. A lack of willing to save is, given what he knows (i.e., given how things are), indistinguishable in its results from a willing to damn. Thus, if God does not will to save some, then those he wills to damn. I am not now changing my position, only raising an objection to such an over-simple argument against single-predestination which will require further investigation as to whether God must intend all that occurs or merely knowingly cause all that occurs (this distinction should become clear soon, if it is not already).
In the philosophy of morals, there is a suggested moral principle, which appears to be at work in most human moral reasoning, called the principle of double-effect. This principle, which may be regarded as an outcome of Kant's second formulation of the categorical imperative (always to treat humans as ends, never merely as means), is that one may cause harm in doing good if the harm is a side-effect of doing good, and not necessary to the doing of that good. This does not yet provide a basis for single predestination.
Let us consider a variation of the classic trolley dilemmas: There is a trolley coming down the track, and if nothing is done, it will run over five men. I am at a switch. If I pull the switch, then the trolley will go on another track which reconnects to the original track before where the five men are (so that if nothing happens on the side-track, the trolley will still run over the five men). Now, let us suppose there is a large weight on the track which will stop the trolley, thus saving the five men if I pull the switch (I should note that this version of the trolley dilemma did not
originate with me, but it also seems to be in a variety of places, so I
am unsure of the source).
The principle of double effect may be considered as the rule that one may knowingly cause harm, but one may not intend harm. This gets us closer to understanding a possible basis for single-predestination. If I do an act, one might ask me what I am doing, and I may say "pulling a switch," and they may ask me what I am doing that for, to which I may respond "saving five people from being run over by a trolley." They may then ask how it will save them, to which I may respond, "it will make the trolley hit that large object, and thus stop before it returns to the track." Now, if there is a man standing in front of the weight, this makes no difference to my intent. However, if the weight is, itself, a very large man, then I am intending harm to a person. The first is allowed, given the principle of double-effect, the second is not.
Now, to return single-predestination, the point of single-predestination is that God intends those who are saved to be saved, but that God does not intend the damnation of the others, despite the fact that he knows that they will be damned. The argument of single-predestination is that there is no action which God does where you could ask what he is doing in any way so as to get the answer "damning some."
Now, the moral problem of an omnipotent God saving some and not others is much more complicated than any trolley dilemma (for one, most would argue that God could have saved all, or none, if he had wanted), and it is not clear that it is right to argue that anything happens in the world which God does not intend, rather there are those who hold, and take comfort from, the belief that God intends all things for his glory and our good. The above was simply to show that, implicit in the disagreement between those who hold single-predestination and those who hold double-predestination, is a disagreement about whether God intends everything or simply knowingly causes everything, while intending only a part.