The ordinary business of life routinely involves choices over unpleasant outcomes. Many commodities can be perceived as having negative affective value or disutility: labor, health conditions and political or societal outcomes such as inequality, poverty, immigration, pollution. We hypothesize and test experimentally that these choices involve widespread violations of one basic property of economic preferences: preferences tend to be non-convex in the domain of bads, or averse to diversification. This hypothesis mirrors the well known reflection effect from prospect theory between the gain and the loss domain. We test this hypothesis in two experiments -- one online with hypothetical scenarios, one lab experiment with actual consumption -- involving binary choices over bundles that are framed as goods or bads in two different treatments. Our results show that dealing with bads reduces the preference for diversification. The curvature of the indifference curve is less pronounced for the representative agent, and a larger fraction of subjects displays non-convex preferences. The bads framing induces optimal choices (and median-voter choices) that are more extreme, thereby providing a possible channel of polarization for political preferences, as well as more elastic demands, with potential implications in markets that involve 'bads' (such as the labor market).