Of the 1,990 pages in the healthcare reform bill passed by Congress Saturday night, page 206 is especially touted – and little understood.

That's the page that creates a federal Consumer Operated and Oriented Plan (CO-OP) to establish not-for-profit, member-run health insurance cooperatives.

Supporters say these health cooperatives, or HCs, will reduce costs by giving smaller buyers of insurance (such as small businesses) the ability to act as a large buyer. HCs will level the playing field, giving the "little guy" much more leverage to negotiate lower prices.

They won't. What they will do is put the United States on a track toward nationalized healthcare even faster than the government-run insurance plan called the public option.

The reason HCs won't lower costs has nothing to do with politics or economics but a simple error of logic called the "fallacy of composition." Senators should take a refresher course in logic before they review page 206 and the rest of the legislation in coming weeks.

What, exactly, is a fallacy of composition? The basic idea is that if something is true for the part, it is not necessarily true for the whole. For example, if the Red Sox improve their batting average next year, they'll probably win more games. But if all major-league baseball teams improve their batting average next year, will all teams win more games? Of course not.

Yet proponents of HCs are making a similar mistake in judgment. Their fallacy results because market power is a relative concept. The advantage of being a large buyer comes at the expense of small buyers, so it is a fallacy to expect that any benefit currently derived from large buyers can be enjoyed by everyone if everyone becomes a large buyer.

Suppose, for example, that a pencilmaker sells one pencil per month to 10 separate buyers. Each pencil costs $1 to make and overhead is $10. The pencilmaker needs at least $20 in revenue per month to stay in business, so the average price per pencil must be at least $2.

Now suppose some buyers form a cooperative and use their newfound market power to negotiate a price below $2. To continue generating $20 in revenue, the pencilmaker must now charge the remaining buyers more than $2 because overhead has to be paid by someone.

If the remaining buyers also form a cooperative they may to able to negotiate the pencil price back down to $2, but only if pencil buyers in the first cooperative experience a price increase. Once everyone is large, the advantage of being large disappears.

Similarly, if "Jane" switches from a non-HC plan to a HC plan, she will probably get to pay a lower premium because the HC plan can negotiate lower reimbursement rates. But that also means that she will now be contributing less to her healthcare providers' overhead expenses than before. This forces them to make up the difference by charging non-HC plan patients more.

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