Another way to put Arrow’s point is to say that it is a gross error to anthropomorphize a group of people, even when that group makes collective decisions according to democratic norms.
Perhaps the single best way to see why such anthropomorphization is an error is to consider what Arrow identified for each individual decision-maker as being the “irrelevance of independent alternatives.” The language here is confusingly technical, but the idea is not – as revealed by this example that I steal from a lecture given a few years ago by my colleague Alex Tabarrok.
Suppose that you have a hankering for a scoop of ice cream. To satisfy this hankering, you stroll into a diner and ask the waiter what flavors of ice cream are available. The waiter replies, “We have vanilla and chocolate.” You weigh these two options for a moment and then tell the waiter, “Please give me a scoop of vanilla.” But just as the waiter is about to serve the vanilla to you, he says, “Oh, I almost forgot. We also have strawberry ice cream.”
How would you, a rational individual, respond upon learning of this additional alternative? You might respond by saying, “Wonderful! I love strawberry! Give me a scoop of strawberry instead.” If you respond in this way, no one would think you odd.
But suppose that you instead respond by telling the waiter, “Oh, now that I know that strawberry is also an option, please change my order from vanilla to chocolate.” If you respond in this way, everyone would think you to be crazy-odd. Normal – “rational” – individuals don’t react in such a manner. An individual who prefers vanilla to chocolate does not come to prefer chocolate to vanilla upon learning of the availability of strawberry.
Yet in political elections such ‘preference shifting’ is neither unusual nor an indication of irrational or otherwise inexplicable behavior on the part of anyone.
For example, it’s quite possible that Ross Perot’s 1992 candidacy for the U.S. presidency – by taking more popular votes from Pres. George H.W. Bush than from Gov. Bill Clinton – swung the election from Bush to Clinton. If the American people were a creature with a will – if the American people were a giant sentient being – it’s as if this creature walked into a polling place in November 1992 and asked “What presidential options do you have?” Upon being told “Bush and Clinton,” this American People creature replied, “Give me a Bush!” But then upon learning that there is available also a Perot, the creature changed its mind and said, “Oh, well in that case, give me a Clinton!”
No rational being behaves in such a way.