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Public opinion polls usually ask people about issues such as health care and immigration using questions that force people to separate issues that may be connected in their minds. But some issues may be connected, or dependent. A person has dependent preferences when her opinion on an issue depends on the expected outcome of other issues. Data from four surveys conducted between 2004 and 2020 include questions to detect dependent preferences and demonstrate that significant percentages of the US public hold opinions on government-provided health care that depend on public policy on immigration. A substantial percentage of Americans want a single-payer health care system only if immigration does not increase. If immigration increases, people are less likely to support a national single-payer health care system. People of color are more likely than whites to express dependent preferences for health care and immigration, controlling for party identification, education, and income.