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Social choice theory studies how individual preferences are aggregated to form a collective choice, such as, for example in voting systems (also known as social choice functions or systems). It is often used interchangeably with Public Choice theory and the fields are not clear cut.
It has been traditionally assumed that as individuals attempt to maximize their individual utilities when arriving at individual choices, in order to arrive at social choices, we can simply add up all of society's utilities to arrive at a socially optimal choice. However this view, which relies heavily on the interpersonal comparison of utility was heavily questioned by positivist thinkers such as Lionel Robbins, who doubted that mental states (including utilities) can ever be compared.
Robbins criticized interpersonal comparisons of utility, and the social choice theory on which it was based, for assuming that we could ever determine the amount of satisfaction other individuals derive from certain situations. For example, the law of diminishing marginal utility states that the more of a good one has, the less utility they receive from an additional unit of the good. Such a principle has been used to defend transfers of wealth from the rich to the poor on the basis that a rich man does not derive as much utility from an extra unit of income as does a poor man. However, Robbins feels this notion is dubious. It is never possible, by testing, introspection, or observation to ever be sure what utility some one gets from their income. A millionare may indeed get just as much, if not more, utility from an extra dollar as a starving peasant. Robbins argues we can never know for sure, and thus interpersonal comparisons of utility and social choice theory, which are based on comparing people's utility gains and losses, are a lost cause.
However, other theorists have argued that Robbins claims too much. John Harsanyi for instance agrees that full comparability of mental states such as utility is never possible. However, he believes that human beings are able to make some interpersonal comparisons of utility. Because human beings share some common backgrounds, cultural experiences, and so on, we should be able to compare utility in some less controversial cases. To borrow an example from Amartya Sen, it should not be difficult to say that Emperor Nero's utility gain from burning Rome did not outweigh the utility loss of the rest of the Romans. Thus, Harsayni and Sen argue we can have partial comparability. Some mental states are easier to compare than others, and we can proceed with ICU and social choice theory based on ICU, as long as we are careful not to claim too much.
However, Sen wants to push beyond partial comparability. Kenneth Arrow's famous impossibility result spelled the second end to social choice theory, by declaring social and individual preference irreconcilable when held to very minimal standards, such as non-dictatorship and Pareto optimality. Partial comparability does away with some of this result. Sen's theory of informational broadening does away with the rest. Sen believes that ICU, even if it were perfect, would still lead to sub-optimal social choices. The reason for this is simple: mental states are malleable. A starving peasant may have a particularly sunny disposition, and may even find a way to get a great deal of utility from a very small amount of income. However, his high utility value should not nullify his claim to compensation or equality in the realm of social choice.
Instead, social choice decisions should be based on variables that are not subject to such malleability like mental states. Sen proposes interpersonal comparisons based on a wider range of real data. Particularly, Sen is worried about access to advantage, which he measures by a persons access to basic needs-satifsfying goods (like food) and freedoms (like a labour market). We can proceed to make social choices based on real variables, and thereby address actual position, and access to advantage. Most importantly, Sen's method of informational broadening allows social choice theory to escape both the objections of Arrow and Robbins, which looked as though they would cripple social choice theory permanently.
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