A pattern of intransitive or cyclic preferences causing a decision maker to be willing to pay repeated amounts of money to have these preferences satisfied without gaining any benefit. The simplest example is a person who evaluates three commodities x, y, and z and prefers x to y, y to z, and z to x. A person may, for example, prefer one lawnmower x to another y because it is larger, and may prefer y to z for the same reason, but may prefer z to x because x would be extremely difficult to take to a repair shop if it were to break down. If the person owns x, then a salesman could offer to replace it with z in return for a fee (there must be some price that a person who prefers z to x is willing to pay for this improvement), then the salesman could offer to replace z with y for a fee, then to replace y with x for a fee, and so on indefinitely or until the money runs out. The concept was introduced by the English philosopher, mathematician, and economist Frank (Plumpton) Ramsey (1903–30) and published posthumously in 1931. Also called a Dutch book, especially when the price of each replacement is reduced until the person is willing to pay for it. See also decision theory, intransitive preferences.