Social choice theory, while postulating that voters have preferences over candidates, does not ask them to stipulate where, in their preference rankings, they would draw the line between acceptable and unacceptable candidates. Approval voting (AV) does ask voters to draw such a line, but it ignores rankings above and below this line.
Rankings and approval, though related, are fundamentally different kinds of information. They cannot necessarily be derived from one another. Both kinds of information are important in the determination of social choices. We propose a way of combining them in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that have several desirable properties.
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Brams, S.J., Sanver, M.R. (2009). Voting Systems that Combine Approval and Preference. In: Brams, S.J., Gehrlein, W.V., Roberts, F.S. (eds) The Mathematics of Preference, Choice and Order. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79128-7_12
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