Our Gemara on Amud Beis relates an interesting dialogue between God and Avraham at the time of the destruction of the Temple:

“Rabbi Yitzḥak says: At the time when the First Temple was destroyed, the Holy One, Blessed be He, found Abraham standing in the Temple…”

“Abraham said to God: I have come over matters concerning my children, to discover why God is destroying the Temple and exiling them from Eretz Yisrael. God said to Abraham: The reason is that your children sinned, and therefore they are being exiled from the land. Abraham said to God: Perhaps they sinned unwittingly, and they do not deserve such a terrible punishment. God said to him: “Seeing that she has performed lewdness [hamzimmata],” i.e., her evil actions were intentional. Abraham further said to God: Perhaps only a minority of Jews sinned, and the rest of the people should be spared punishment. God said to him: “With many,” i.e., the majority of the people are culpable.”

Sefer Daf Al Daf brings a question from the Sefer Pnei Pinchas (Vayera 5753): When Avraham was praying on behalf of Sodom he asked if God could relent if there were only 10 righteous people in the city (Bereishis 18:32). If so, why did Avraham stop his request regarding the exile of the Jews when God said, the majority sinned?

The first answer given is that indeed we see that God has a higher standard and having only 10 righteous people would not have been enough to save the Jewish people from exile and captivity. He suggests another answer: Exile is less severe than utter destruction. Therefore, 10 righteous would not be enough to hold back exile, but it might have held back utter destruction.

However, I discovered a Midrash (Bereishis Rabbah 49:13) that says the opposite. It says in regard to the Jewish people, even one righteous person can save the entire city in contradistinction to Sodom.

Therefore, I think we must look for a different answer. The word righteous (tzaddik) in Hebrew can have two meanings. Sometimes it means a person who is an extraordinarily pious and developed person. Other times, it means the person is innocent and free of sin relative to the accusation. 

Consider these two verses and their context :

(Shemos 23:7): “Keep far from a false charge; do not bring death on those who are innocent and in the right (tzaddik), for I will not acquit the wrongdoer.”

From the above context, it is not so much that this person is pious or meritorious, rather he simply is innocent regard to his charges. (See Rashi and especially Ibn Ezra who is explicit on this point.)

However, in Tehilim (92:13) it states:

“The righteous (tzaddik) bloom like a date-palm; they thrive like a cedar in Lebanon.”

From this context, it’s clear that we are talking about a devout, virtuous person. It is hard to imagine that the verse is discussing an ordinary person who merely isn’t too guilty of anything unusually wrong. Why would he merit such success and, he is being compared to the evil doers in the other verses.

He is also notable that the Targum uses two different words to translate tzaddik in these two verses. One is zakey, which has a legal implication that he is innocent of charges. In the latter verse, an Aramic analogue word is used, “tzadikka”.

The latter term probably is closer to the devout, righteous man, and not simply the one who has not committed relative wrong-doing.

A telling verse is in regard to Noach (Bereishis 6:9):

“These are the generations and story of Noah.—Noah was a righteous (tzaddik) man; he was pure “in his times”; Noah walked with God.”

The sages notice the phrase “in his times”, and debate: Does it mean he was only a relatively good person compared to his generation, or he was even more virtuous, and the extra verbiage “in his times“ implies that he would have been even greater if he lived in better surroundings (See Rashi). Notably, the Targum here does not use the word “tzadikka”, but rather the word “zakai”, which seems to follow the connotation as relatively good, as in not committing evil in comparison others around him.

Having made that introduction that the word with the root Z-D-K in Hebrew can mean either a devout pious person, or it can be a person who is relatively innocent compared to potential charges or accusations, we could say that regarding Sodom, Avraham meant the former. Therefore, God required at least 10 to save the city, The Midrash that said even one Jew, who is a tzaddik, also means it in terms of piety and devotion. However, the tzaddik that is being referred to an our Gemara and God’s discussion with Avraham regarding the exile, was the latter connotation, that is people who were relatively innocent of wrongdoing as compared to the sinners, but not particularly meritorious.