An agent unable to decide how to trade-off rival goods can turn to a family of welfare functions and choose the option that guarantees the greatest welfare level. The agent will then display a bias in favor of the ‘safe’ options to which all of the welfare functions impute the same level of welfare. When the rival goods are ordinary items of consumption, the safety-biased preferences that result will exhibit complementarities. When the rival goods are commodities delivered at different states of nature, safety-biased preferences will generate the maxmin model of choice under uncertainty. In any setting, the agent’s sets of preferred options will display kinks at the safe options but not at other options. Such agents will therefore tend to consume at just the points where slight changes in consumption have a large effect on agents’ marginal valuations of goods and hence on prices.