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In the theory of fair division, the price of fairness (POF) is the ratio of the largest economic welfare attainable by a division to the economic welfare attained by a ''fair'' division. The POF is a quantitative measure of the loss of welfare that society has to take in order to guarantee fairness. In general, the POF is defined by the following formula: : The exact price varies greatly based on the kind of division, the kind of fairness and the kind of social welfare we are interested in. The most well-studied type of social welfare is ''utilitarian social welfare'', defined as the sum of the (normalized) utilities of all agents. Another type is ''egalitarian social welfare'', defined as the minimum (normalized) utility per agent. == Numeric example == In this example we focus on the ''utilitiarian price of proportionality'', or UPOP. Consider a heterogeneous land-estate that has to be divided among 100 partners, all of whom value it as 100 (or the value is normalized to 100). First, let's look at some extreme cases. * The maximum possible utilitarian welfare is 10000. This welfare is attainable only in the very rare case where each partner wants a different part of the land. * In a proportional division, each partner receives a value of at least 1, so the utilitarian welfare is at least 100. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Price of fairness」の詳細全文を読む スポンサード リンク
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