Finding the Majority-Rule Equilibrium Under Lexicographic Comparison of Candidates

This paper considers the well studied problem of the existence of an undominated point, under the assumption of lexicographic preferences of voters, as espoused by Taylor in [24]. We extend Taylor's model to situations were we allow for (i) voters to have different ranings of the issues in n-dimensional issue space and (ii) a candidate to be disregarded by a voter if his stand on any one or more of the issues involved in the election is perceived to be too extreme by the voter and (iii) combinations of (i) and (ii). We extend the results of Taylor by demonstrating the non-existence of an equilibrium point in these models in general and then showing that under special circumstances, specialized variants of the "median" point(s) represent equilibrium or undominated points in these models too. Thus a model of voting behavior results that is closer approximation of reality in that historically incumbents tend to win. The primary conclusion of the paper is to suggest that incumbents tend to have an advantage when the election process is characterized by a large presence of special interests or as information becomes more expensive to acquire