I'm kind of curious because my immediate thought was the opposite, that peoples that see caring for the sick and elderly as a responsibility for the whole of society rather than the family unit would value socialized medicine higher. Like if you asked me if it should be my duty to take care of my parents I'd say that they pay their taxes and the state should take care of them, but if that's off the table then of course I'd help. I guess that's a pretty glaring issue with the question asked.