Measuring consensus and voter influence in ternary preferences

• Proposed a new consensus measure for ternary preferences. • Introduced marginal contributions to consensus inspired by the Banzhaf value. • Developed sampling-based estimations for large voter groups. • Validated methods via extensive simulation studies. • Applied methods to ISTAT and Balkan Barometer data. This paper explores the concept of consensus in the context of ternary preferences, an extension of dichotomous preference approvals, where alternatives are classified into three categories: acceptable, neutral, and unacceptable.We propose a novel distance-based measure to quantify consensus among voters and introduce a method for calculating the marginal contribution of each voter to the overall consensus, drawing parallels to the Banzhaf value in cooperative game theory. To handle large voter groups, we also present an estimation procedure based on sampling techniques to derive the marginal contributions. We performed comprehensive simulation studies to validate the statistical properties and computational efficiency of the proposed approach. Finally, empirical analyses using data from the Italian National Institute of Statistics (ISTAT) and the Balkan Barometer highlight its practical applicability.