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Politicians and Shopping Carts II

Here’s another way — related to an earlier post — to see just how short politics comes up, compared to the market, at satisfying people’s preferences with precision.

The typical supermarket in the United States today carries 30,000 different types of grocery items – everything from bottled ammonia to fresh zucchini. If each of these items stands just as much chance of being chosen by a shopper as any other item, what are the chances that you and another shopper standing behind you in the checkout line – each of you with 20 different items in your shopping carts – will have in your carts the very same bundle of 20 groceries? The answer is: practically zero. Virtually no chance.

The formula for determining the number of different ways to fill a shopping cart with 20 different items from a total of 30,000 possible choices is 30,000! divided by [(29980!) X 20!] – an impossibly large number. Therefore, the chances of any two shoppers selecting the same collection of 20 items in a supermarket offering 30,000 different types of items is practically zero.

Of course, some supermarket items are more likely than others to be bought by any randomly chosen shopper – for example, milk, eggs, and laundry detergent are each more likely to be selected than is a Halloween card or a honeysuckle-scented candle. On the other hand, one of the dimensions of choice enjoyed by each shopper is choosing how many items to purchase. Some shoppers will choose fewer than 20 items, some will choose more.

Even a shopper choosing a mere 20 items will choose a different bundle than any other shopper choosing 20 items. But in voting booths, we are each obliged to choose among a tiny number of candidates, each embodying a immense number of specific stands on policy issues. The chances that any one of these ‘policy bundles’ – that is, any one candidate – has positions on all of the issues that match the favored positions of even a single voter on all of the issues is too small to contemplate.