Reference no: EM133132839

A common argument against the transitiyity property of preferences is that people cannot discern between small differences, but, then assuming transitiyity implies that they should be indifferent between two totally different alternatives. {One common example goes as follows: no one can discern the difference between a cup of coffee with 10 miligram {mg} of sugar and another cup with 11 mg. of sugar. Therefore, anyone is indifferent between a cup with 10 mg and another with 11 mg ofsugar, should also be indifferent between a cup with 10 mg and 12 mg of sugar [as she would be indifferent between the two cups with 11 mg and 12 mg of sugar, and the transitiyity implies that 10 mg must be just as good as 12 mg. But, with the same token, one can extend the chain, and say that one should be indifferent between a cup with 10 mg of sugar and a cup with 100 gr (not mg!) of sugar. And, no one is.) Show that with money prizes this argument is not as easily applicable, furthermore argue that, if you were indifferent between lottery L that pays $x with probability p and nothing with probability {1-p) and lottery L' that pays :15): with probability p+d and nothing with probability (1-p-d) where d is arbitrarily small, a conman could soon get all your money (or, yaluable lottery tickets}. The argument you develop to show this result is closely related to what is known as the Dutch Book argument.