The Structure of Voters’ Preferences Induced by the Dual Culture Condition

We consider the case of three-candidate elections with large electorates under the assumption of the Dual Culture Condition. It is well known that a perfect relationship does not exist between the probability that Condorcet’s Paradox will be observed and a simple measure of the social homogeneity of voters’ preferences under these conditions. However, we show that this intuitively appealing relationship actually is found to hold on an expected value basis, except for an aberration in one very small region of possible voter situations, and this aberration is completely explainable. It is also found that the expected value of the Condorcet Efficiency of Borda Rule consistently increases as the simple measure of social homogeneity increases, except in the same small region of aberration for voting situations that is noted above.