The relationship between two algorithms for decisions via sophisticated majority voting with an agenda

Two algorithms have been described in the literature for determining the sophisticated voting decision under amendment procedure. Each depends only on a majority tournament, which represents the majority preferences of the alternatives by the electorate, and a voting order of the alternatives, which represents an agenda. One algorithm is due to Shepsle and Weingast; another was suggested earlier by Miller and treated recently by Reid. Here it is shown that the validity of each of these algorithms can be used to establish the validity of the other.