The practical answer is that most people would indeed put their neck in the noose for those other 10 strangers, because they and they alone can save them. However, if the King were instead to go out onto the marketplace and say "I will hang ten people today unless one person steps up to take their place", no-one would volunteer. This makes little sense from a consequentialist point of view; it's just a fact about human psychology.

One consequence is that if you're ever being attacked on the street while passers by walk on, don't just shout for help: select a particular passer by and ask them for help as specifically as you can.