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A cardinal social welfare function is a function that takes as input numeric representations of individual utilities (also known as cardinal utility), and returns as output a numeric representation of the collective welfare. The underlying assumption is that individuals utilities can be put on a common scale and compared.
An additive agent has a utility function that is an additive set function: for every additive agent i and item j, there is a value ,, such that () =, for every set Z of items. When all agents are additive, welfare maximization can be done by a simple polynomial-time algorithm: give each item j to an agent for whom v i , j {\displaystyle v_{i,j ...
A social indifference curve drawn from an intermediate social welfare function is a curve that slopes downward to the right. The intermediate form of social indifference curve can be interpreted as showing that as inequality increases, a larger improvement in the utility of relatively rich individuals is needed to compensate for the loss in ...
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium , a set of complete markets , with complete information , and in perfect competition , will be Pareto optimal (in the sense that no further exchange would make one person better off without making another worse off).
The Pigou–Dalton principle (PDP) is a principle in welfare economics, particularly in cardinal welfarism. Named after Arthur Cecil Pigou and Hugh Dalton, it is a condition on social welfare functions. It says that, all other things being equal, a social welfare function should prefer allocations that are more equitable. In other words, a ...
Each agent has an additive utility function (this implies that the items are independent goods). The agents may have different rankings on the items, but there is a common scoring function that maps the rankings to monetary values (e.g, for each agent, his best item is worth for him x dollars, his second-best item is worth for him y dollars, etc).
One class of rules aims to maximize a given social welfare function. In particular, the utilitarian rule aims to find a budget-allocation that maximizes the sum of agents' utilities. [7] With cardinal voting, finding a utilitarian budget-allocation requires solving a knapsack problem, which is NP-hard in theory but can be solved easily in practice.
In an auction, there are one or more items and one or more agents with different valuations for the items. The items have to be divided among the agents. It is desired that the social welfare - the sum of values of all agents - be as high as possible. One approach to maximizing the social welfare is designing a truthful mechanism. In such a ...