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Genesis 18:24ff:
And Abraham... said: Will You [God] also cause to perish the righteous one with the wicked one? ...Will You not spare the place for the sake of [say] 50 righteous ones in its midst? ... [Or 45? 40? 30? 20? 10?]
God may even have gone below 10, but Abraham stopped asking.
Why didn't Abraham simply ask, "How many righteous people does there have to be in that place for you not to destroy it?"
We see in Vayeira 18:32
32 And he said, "Please, let the Lord's wrath not be kindled, and I will speak yet this time, perhaps ten will be found there." And He said, "I will not destroy for the sake of the ten."
RASHI
perhaps ten will be found there: For fewer [than ten] he did not ask. He said, “In the Generation of the Flood, there were eight: Noah and his sons, and their wives, but they did not save their generation.” And for nine, together with counting [God] he had already asked, but did not find.
Avraham knew that there had to be ten righteous people because Hashem had already showed at the time of the flood that fewer could not save a society. In the time of Noach, Hashem waited until Mesushelach died before bringing the flood. At that time, Hashem was considered part of the count and Noach, his sons, and their wives totaled eight. Mesushelach was the tenth righteous person who kept the flood from occurring. Avraham realized this and therefore had to stop at ten.
The meforshim do ask why he started at fifty? Rashi explains that Avraham wanted to save all five cities. However, when there were not 50 (10 in each city) or 45 (Hashem being the tenth in each city), then he tried to save as many cities as possible.
Rashi on Vayeirah 18:29
Perhaps forty will be found there: And four cities will be saved, and so thirty will save three of them, or twenty will save two of them, or ten will save one of them. — [from Zohar, vol. 1, omissions, 255b]
Rav Hirsch Vayeirah 18:26 says that the lower numbers might still be considered to show that the society still accepted some righteousness and that they could therefore be allowed to live in the hopes that the next generation might be affected.
God answered: If there are still, in a state like Sodom, fifty righteous men who not only publicly live a moral and just life, but who can even stand up for morality, justice, and humaneness, then not only למענם, not only for the considerationof, for the sake of, these righteous ones, but בעבורם through them, because these righteous ones exist ans are tolerated, the whole city deserves forgiveness.
Their existence and being tolerated would itself be a proof that the degeneration had not yet reached the lowest depth.
Rav Hirsch deals with the continuation of Avraham asking for fewer people and the change in the wording of the answer in verse 28 as follows:
The gradually increasing demand in Abraham's requests and the change in terms used in the replies לא אשחית, לאאשחית, לא אעשה, also seems strange. Perhaps the following suggestions may throw some light. If our assumption of the nature of the incident is correct, then God's reply looks on the saving of the town, if fifty righteous men can be found, from a different point of view from Abraham's supposition. Not out of consideration for them and their feelings but on the ground of their existence, of their being there at all. From the former point of view, of course the cosideration for the righteous would become less and less the fewer their number happened to be, but that could not be the case from the latter point of view. If the number of its members is imposing, it is tolerated out of fear. If it is small enough to be negligible, it is tolerated only because it is overlooked. Only when it consists of a medium number, where it is neither feared nor overlooked, does its existence, its being tolerated, have its full significance. Above this number and below it, its significance lessons.
Perhaps Abraham was seeking clarity concerning this condition and perhaps the change in the expression might correspond to it. לא אשחית, I will not destroy, will not bring כלה, but will perhaps interpose My authority otherwise to effect betterment: אדעה: לא אעשה, I will do nothing at all, there are sufficient moral elements among the masses so that a betterment from within is still not impossible. Hence, with forty five, twenty, and ten, לא אשחית, and only with forty and thirty לא אעשה. Perhaps.
Below ten, not only was the number so negligible as to be ignored, but it was too small for Hashem to be able to use His authority to raise the level of the future generations (as we have seen by Noach).
Rav Hirsch concludes:
Had there been in the purlieus of Sodom and Gomorrah, ten righteous men to be found, God would not have despaired of a better future for all, and would have let them all live for this better future. But where God shows us no reason to despair, we too must courageously preserve an play our part, and unremmitingly and confident of ultimate success stand up for what is right even in it means being in opposition to the whole of our erring contemporaries, and even if this ultimate victory will only dawn long after we are in our grave.
Seems like a standard debating/negotiating tactic. If Abraham asks what amount of righteous people is necessary, he will receive a direct answer. Any further debating/negotiating has to cause a change to the answer.
If he starts with a number that everyone would obviously agree with, and then proceeds to steadily decrease the amount it is much harder to reject the plea. At any point in the discussion the switch from yes to no will seem arbitrary. It may even be possible to get all the way down to 1 by arguing that there is no real difference between 1 and 2, and there is no real difference between 2 and 3, etc. As such, Abrahams’s method may simply have been more conducive to extracting the desired response.
(Whether human debating/negotiating tactics should be used when debating/negotiating with God should perhaps be a separate discussion.)
Leon Kass suggested a novel idea. He felt that Abraham questioned the verdict in Genesis 18 on the grounds of objective justice, and of course, for his nephew Lot. While he was concerned for Lot, he was equally concerned for other good people who may be residing in the city in general. Leon Kass then reveals a novel idea. Abraham had to stop at ten because if he “reduced the argument to (will you save the city for) one (person) it would have been too obvious that he was asking G-d to save Lot.”[1]
Abraham was concerned for all peoples, indeed he taught the truth to whoever he met in his tent. But he couldn't make G-d think that he only cared, selfishly, for Lot alone. Of course, G-d is not oblivious[2], but I think Leon Kass answered this well.
[1] See Peshat Isn’t so Simple by Rabbi Hayyim Angel
[2] Ralbag, as well as Abraham ibn Ezra, felt that G-d only knows the general things but not the particular
