(Jewish) Decision Making #1
(טז) לֹא־תֵלֵ֤ךְ רָכִיל֙ בְּעַמֶּ֔יךָ לֹ֥א תַעֲמֹ֖ד עַל־דַּ֣ם רֵעֶ֑ךָ אֲנִ֖י יְהוָֽה׃

(16) Thou shalt not go up and down as a talebearer among thy people; neither shalt thou stand idly by the blood of thy neighbour: I am the Eternal.

שנים שהיו מהלכין בדרך וביד אחד מהן קיתון של מים אם שותין שניהם מתים ואם שותה אחד מהן מגיע לישוב דרש בן פטורא מוטב שישתו שניהם וימותו ואל יראה אחד מהם במיתתו של חבירו עד שבא ר' עקיבא ולימד וחי אחיך עמך חייך קודמים לחיי חבירך
Two people are travelling along the way, and one of them has in his possession a flask of water. If both drink from it, they will both die. However, if only one of them drinks, he will be able to make it out of the desert. Ben Petura expounded, “It is better that both should drink and die that that one should witness the death of his fellow.” Then Rabbi Akiva came and taught, “‘Your brother shall live with you’ (Vayikra 25:36) — your life comes first, before the life of your friend.

(יב) וכן נשים שאמרו להם גוים, תנו אחת מכם ונטמאה, ואם לאו, הרי אנו מטמאים את כלכם, יטמאו את כלן, ואל ימסרו להם נפש אחת מישראל.

(12) Similarly, women who have been told by non-Jews, “Give us one of you that we may defile her; for if not, we will defile you all,” let [the non-Jews] defile them all, and do not hand over to them one soul from Israel.

Yesodei haTorah 5:5 (Maimonides 1135-1204)

If gentiles tell [a group of] women: "Give us one of you to defile. If not, we will defile all of you," they should allow themselves all to be defiled rather than give over a single Jewish soul to [the gentiles].

Similarly, if gentiles told [a group of Jews]: "Give us one of you to kill. If not, we will kill all of you," they should allow themselves all to be killed rather than give over a single soul to [the gentiles].

However, if [the gentiles] single out [a specific individual] and say: "Give us so and so or we will kill all of you," [different rules apply]: If the person is obligated to die like Sheva ben Bichri, they may give him over to them. Initially, however, this instruction is not conveyed to them. If he is not obligated to die, they should allow themselves all to be killed rather than give over a single soul to [the gentiles].

Hazon Ish: Sanhedrin #25

...a thought experiment in Hazon Ish, HM, Sanhedrin #25 s.v. veyesh leayen. It reflects on the predicament of an outside observer who beholds a lethal projectile launched at a large group of people. The observer faces a conundrum: she possesses the capacity to deflect the projectile from its original trajectory, thereby saving the large group of people, but the deflected projectile will instead kill a smaller number of people in the new location where it will land. R. Karelitz, the Hazon Ish, tentatively suggests that it might be permitted to deflect the projectile, because the deflection is fundamentally a noble act of saving many people — with the unfortunate and unintended side-effect of killing a smaller number of people — rather than a vicious act of handing someone over to be put to death (mesira). But he proceeds to raise a counterargument that perhaps the deflection should be proscribed because — absent the observer's intervention — the smaller number of people would have lived, and thus the observer can be said to have, with his own hands, actively sacrificed the smaller number of people, which is unconscionable. Ultimately, the Hazon Ish leaves the conundrum unanswered.

Source: Spira, Shalom C. and Mark A. Wainbergm "HIV Vaccine Triage: Halakhic Considerations." Jewish Law Annual, Volume 20. 2013