The Central Limit Theorem (CLT) (Hogg and Craig, 1978; Hogg and Klugman, 1984) explains that insurance works because large insurers issue many policies, and the year to year, or portfolio to portfolio, variation in average claim costs approaches population average costs as portfolio sizes increase. Large insurers costs are very predictable, while small insurers tend to earn excessive profits, or incur excessive losses, each year. This exposure to high and low losses is the hallmark of insurer inefficiency. Inefficient insurers, including risk assuming health care providers, are more likely to struggle financially and become insolvent, as has happened for the last forty years (Mayes, 2005).
Despite the greater efficiency of large insurers, most health care (finance) reform recommendations ignore the CLT. Capitation advocates and other health care reformers suggest the opposite effect, that increased competition, among many small insurers will increase health care (finance) system efficiency and consumer benefits. This is demonstrably false. Limited competition among very few, very large, and very efficient insurers would definitely be more efficient and would yield higher policyholder benefits than large numbers of very small, very inefficient insurers (See Section 11).