Welfare measurement with income-dependent discrete choice

•The expectation of the compensating variation is standard for measuring welfare with discrete choice.•The expectation of the equivalent variation is equally founded theoretically.•One-dimensional integrals provide both measures. The expectation of the random compensating variation is the welfare change measure that is used in discrete choice models. The expectation of the equivalent variation is equally founded theoretically. When choices are income independent and income enters utilities linearly, the two measures are identical. The case of income-dependent choices remains an area for exploration. The paper provides the equivalent variation counterparts of the formulas that are available for the expectation of the compensating variation.