How would judges rule on this situation using the legal theories?

Analyze the following using the Theories of Law: The Case of the Speluncean Explorers was created by Lon Fuller in his article, “The Case of the Speluncean Explorers,” Harvard Law Review, vol. 62, no. 4 (1949) pp. 616-645. The case tells the story of a group of spelunkers (cave-explorers) in the Commonwealth of Newgarth, trapped in a cave by a landslide. As they approach the point of starvation, they make radio contact with the rescue team. Engineers on the team estimate that the rescue will take another 10 days. The men describe their physical condition to physicians at the rescue camp and ask whether they can survive another 10 days without food. The physicians think this very unlikely. Then the spelunkers ask whether they could survive another 10 days if they killed and ate a member of their party. The physicians reluctantly answer that they would. Finally, the men ask whether they ought to hold a lottery to determine whom to kill and eat. No one at the rescue camp is willing to answer this question. The men turn off their radio, and sometime later hold a lottery, kill the loser, and eat him. When they are rescued, they are prosecuted for murder, which in Newgarth carries a mandatory death penalty.