# The arguments of utility: Preference reversals in expected utility of income models

Lindsay, Luke (2013). The arguments of utility: Preference reversals in expected utility of income models. Journal of Risk and Uncertainty, 46(2):175-189.

## Abstract

There is a debate in the literature about the arguments of utility in expected utility theory. Some implicitly assume utility is defined on final wealth whereas others argue it may be defined on initial wealth and income separately. I argue that making income and wealth separate arguments of utility has important implications that may not be widely recognized. A framework is presented that allows the unified treatment of expected utility models and anomalies. I show that expected utility of income models can predict framing induced preference reversals, a willingness to pay-willingness to accept gap for lotteries, and choice-value preference reversals. The main contribution is a theorem. It is proved that for all utility functions where initial wealth and income enter separately, either there will be preference reversals or preferences can be represented by a utility function defined on final wealth alone

## Abstract

There is a debate in the literature about the arguments of utility in expected utility theory. Some implicitly assume utility is defined on final wealth whereas others argue it may be defined on initial wealth and income separately. I argue that making income and wealth separate arguments of utility has important implications that may not be widely recognized. A framework is presented that allows the unified treatment of expected utility models and anomalies. I show that expected utility of income models can predict framing induced preference reversals, a willingness to pay-willingness to accept gap for lotteries, and choice-value preference reversals. The main contribution is a theorem. It is proved that for all utility functions where initial wealth and income enter separately, either there will be preference reversals or preferences can be represented by a utility function defined on final wealth alone

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