In this paper we report on the trade-offs that 1,068 Australian university students make between absolute income and the rank of that income in hypothetical income distributions. We find that income rank matters independently of absolute income, with greater weight given to rank by males, migrants, and individuals from wealthy families. Rank-sensitive individuals require as much as a 200 per cent increase in income to be compensated for going from the top to the bottom of the income distribution. In terms of reference groups, we find migrants who reside abroad for longer periods of time, and with more affluent job titles, are more likely to compare themselves to others at the destination. This allows us to derive a dynamic choice model of compensating incomes that allows for endogenous tastes and rates of assimilation. The model predicts the average respondent to need a permanent increase in income of up to $10,000 when moving from a society with a mean income of $14,000 (e.g. Mexico) to a society with a mean income of $46,000 (e.g. the USA).