There is a famous hypothetical "problem" that ethicists and philosophers use to test people's ideas and assumptions about morality.  It asks you to imagine that there's a runaway train, and it's charging down the tracks enroute to hit and kill five people standing on the tracks, unaware that the train is coming at them.  You can stop the train and save the five people by pushing someone off a bridge in front of the train, which would slow the train down enough for the other five people to escape and survive.  You'd effectively be murdering one person, but you'd also be saving five others.  Is it the correct thing, is it the moral thing, to not kill and allow the other five people to die, or is the right thing to do to push the one person off the bridge, sacrificing one life to save five?

Most of us recoil at the thought of willfully participating in the death on an innocent person, even if it results in saving the lives of five others.  However, some people's ethics can reconcile the act on the basis of the greater good (better one dies than five) while other people feel that murder under any circumstance is wrong, or that it's immoral to impose one's own decision as to what the best thing to do is onto the innocent bystander on the bridge, who hadn't themself decided to sacrifice their life for the greater good of the other five.  The latter is a free-will argument maintaining that it's better five people die solely due to their own free-will choice to be on those particular tracks at that particular time than it is for one person to die based on a choice made by someone else.

If you argue that it's an act of murder to push the one person off the bridge to save the others, isn't not pushing the one person off the bridge effectively murdering the other five people that you could have otherwise saved?  Or at least manslaughter?  How is participating in the death of one worse than allowing the death of five?

I think there's a problem with the "problem," or at least the way that I've heard it and presented it above.  The problem is that there must be at least two people on the bridge, the person who can be pushed off to stop the train and the person doing the pushing, and the person who can push the other off the bridge is also capable of simply jumping off the bridge themselves, sacrificing their own life to save the other five as well as the one person on the bridge. While suicide may be considered immoral by some, it's a matter of which is worse - suicide or murder? Also, the suicide prevents imposing one's own choice onto someone else's free will. As they say in Game of Thrones, "He who passes the sentence should swing the sword," so if I were asked if I would push the person off the bridge to save the other five or allow the five to die by not pushing, I would answer, "Neither.  I'd jump off the bridge myself and save them all" (the bodhisattva response).

To break all this down mathematically, if you jump off the bridge yourself to save the five people on the tracks and to spare the life of the other person on the bridge, then the ratio of killed to saved is 6 saved (the five on the tacks and the one on the bridge) to 1 killed, or 6:1.  If you push the other off the bridge, the ratio is still 6:1, but you yourself are one of the six and someone else died at your hand, so to my thinking, in this case 6:1 ≠ 6:1, but actually 6:1 > 6:1, where the greater, more moral 6:1 is the one where you jump and spare the other person on the bridge.  If you don't push and you don't jump - you don't do anything - the two of you on the bridge are spared but five other people die and the ratio of saved to killed is 2:5.  Therefore and in summary, the moral equation boils down to 6:1 > 6:1 >  2:5.

But we're not all logicians and we don't experience real life mathematically.  One of the universally regarded highest acts of valor is when a soldier sees a hand grenade tossed into his troop's foxhole, and he reflexively dives on top of it, shielding his fellow soldiers from the blast by using his own body. He doesn't take the time to think through the mathematics or devise moral equations, and he doesn't meditate on the relative morality of one option or the other. If he paused for even a nanosecond they'd all be dead, so he immediately and instinctively goes with his training and reflexes and jumps on top of the grenade.  If the soldier looked around and threw someone else on top of the grenade, he'd be court martialed and reviled as a coward and a traitor (if he wasn't first shot by his own troops on the spot).  Unless, that is, the body thrown on the grenade just so happened to be an enemy combatant, in which case the soldier would be rewarded for his cunning.   

But I can see I'm already getting to another theoretical problem, so I'll just leave you to decide what you would do on that bridge - jump, push, or do nothing?