How diverse are the outputs of large language models when diversity is desired? We examine the diversity of responses of various models to questions with multiple possible answers, comparing them with human responses. Our findings suggest that models' outputs are highly concentrated, reflecting a narrow, mainstream 'worldview', in comparison to humans, whose responses exhibit a much longer-tail. We examine three ways to increase models' output diversity: 1) increasing generation randomness via temperature sampling; 2) prompting models to answer from diverse perspectives; 3) aggregating outputs from several models. A combination of these measures significantly increases models' output diversity, reaching that of humans. We discuss implications of these findings for AI policy that wishes to preserve cultural diversity, an essential building block of a democratic social fabric.