Though a free election seems to be the fairest and wisest system for making policy decisions and electing officials, statisticians sometimes fear that a paradox political scientists call "vote cycling" can result in a win for the minority. There's a better way to hold an election.
When I was a little child statistician, my parents would occasionally allow me to make choices about personal things—what to wear, what to eat, which story book to read at bedtime, and so on. I noticed that sometimes the choice was open-ended: "Your choice, Bruce: when would you like to go to bed?" And sometimes the choice was presented as a set of alternatives for me to choose between: "Your choice, Bruce: would you like to go to bed now or in five minutes?"
Of course, the second choice isn't much of a choice, really. When I had to choose between various alternatives, my true opinion wasn't reflected as accurately as when I could choose anything I wanted.
Democracy works like that as well. When it is time to vote for President, or Mayor, or Dogcatcher, we usually must choose between several alternatives. We might not be happy with any of the options, but we vote anyway (at least statisticians do).
Did you ever leave the voting booth, though, and feel that somehow your real feelings weren't represented very well by those choices? Political scientists know that feeling. They have analyzed the sometimes unsatisfying outcomes of votes between alternatives and discovered that ...