  Classical voting rules assume that ballots are complete preference orders
over candidates. However, when the number of candidates is large enough, it is
too costly to ask the voters to rank all candidates. We suggest to fix a rank
k, to ask all voters to specify their best k candidates, and then to consider
"top-k approximations" of rules, which take only into account the top-k
candidates of each ballot. We consider two measures of the quality of the
approximation: the probability of selecting the same winner as the original
rule, and the score ratio. We do a worst-case study (for the latter measure
only), and for both measures, an average-case study and a study from real data
sets.
