During the sinking, something like 1500 passengers and crew were lost, while some 700 were placed in the inadequate number of lifeboats and were eventually saved.
The behavior of those involved was basically orderly and, indeed, heroic. Captain Smith went down with his ship and the final concert of the ship's band as the vessel sank is legendary. There were cowardly acts (apparently one dude donned women's clothing in an attempt to game the "women and children first" ethic) and it would be naive to think there wouldn't have been some violence, but fighting, struggling, and panic seem to have been minimized.
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The Titanic gives us a large scale event among perfect strangers in which many people pretty clearly chose "death before dishonor" and gave up their chance at survival in a real life situation, not a hypothetical exercise.
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Before we get all wispy and sympathetic for the White Star Line and their efforts to rescue passengers, we should stipulate that
- the ship sailed with lifeboat capacity for barely half of the passengers and crew: if the Titanic had sailed full, it would have had capacity for only one third.
- the crew were inadequately trained to conduct an evacuation of the ship. For instance, they didn't know how many to put in the lifeboats, so many boats launched partially full.
- of the 3 classes of passengers, third class passengers were left largely on their own during evacuation: only first and to some extent second class passengers received any organized assistance at abandoning ship. As a consequence, deaths among third class passengers were higher than among first and second. This rate of survival ran right down to the "women and children first" myth - women and children in third class died in far greater percentages than in first or second class.
I'm certain there were some selfless acts of self-sacrifice, and some others of cowardice or selfish attempts to survive in someone else's place in a lifeboat. These were forced upon them however by the White Star Line, who criminally set the ship on course without the minimal means to rescue passengers and crews. Passengers were doomed to their fate by inadequate preparations.