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This paper presents a novel theoretical analysis for Borda's algorithm and local search algorithm for rank aggregation, which is a heated topic in the field of search technology nowadays and is also known as a NP-hard problem. In contrast to the previous known approximation ratio of Borda's algorithm, which is 5, we show in this paper that Borda's algorithm is at most 5-8/k approximation for rank aggregation, where k is the number of permutations to be aggregated. Local search algorithm is also widely used in this area but to our best knowledge, there is no approximation ratio analysis for such an algorithm. In other words, this paper proposes the first theoretical analysis for local search rank aggregation algorithm and shows that this algorithm is actually expected-k/2 approximation. At the end of this paper, several simulation results yields that local search algorithm is a good practical way for the approximation of rank aggregation.