Although there is disagreement on the normative attributes of vote trading in legislative bodies (is logrolling good or bad?), there is little doubt that it exists as one of the ways by which the political process reduces conflict and takes account of intensities of minority preferences. The existence of coalitions of minorities was posited by Madison (in The Federalist, Paper no. 10) as fact and value. His argument runs along the negative side, i.e., that no tyranny of the majority can exist in the Republic because of the lack of one majority on all issues. He neglected (for good reasons) the obverse side of the coin-minorities can band together to pass legislation as well as to defeat legislation. Americans have made good use of vote trading both to pass and to defeat legislation ever since.
There has been no systematic attempt to relate the possibility of vote trading to different coalition patterns, however, perhaps because the task is tedious and the theoretical significance (after Madison) was unrecognized until recently.1 The advent of the computer has reduced the tedium of the____________________