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Top-$k$ voting is an especially natural form of partial vote elicitation in which only length-$k$ prefixes of rankings are elicited. We analyze the ability of top-$k$ vote elicitation to correctly determine true winners with high probability, given probabilistic models of voter preferences and candidate availability. We provide bounds on the minimal value of $k$ required to determine the correct winner under the plurality and Borda voting rules, considering both worst-case preference profiles and profiles drawn from the impartial culture and Mallows probabilistic models. We also derive conditions under which the special case of zero elicitation (i.e., $k=0$) produces the correct winner. We provide empirical results that confirm the value of top-$k$ voting.

The proof of Theorem 10 is incomplete, but the issue is fixed in subsequent work.