Positionality-Weighted Aggregation Methods on Cumulative Voting

The issue in solving social problems is how to respect minority opinions, which are often ignored in general majority rules. To build consensus on pluralistic values and make social choices in consideration of minority opinions, we propose aggregation methods that give weighting to the minority's positionality on cardinal cumulative voting. Based on quadratic and linear voting, we formulated three weighted aggregation methods that differ in the ratio of votes to cumulative points and the weighting of the minority to all members, and calculated the frequency distributions of the aggregation results, assuming that the distributions of votes follow normal distributions. From these calculation results, we found that minority opinions are likely to be reflected as weighting increases proportionally in two of the above three methods. This means that Sen and Gotoh's idea of considering the social position of unfortunate people on ordinal ranking, that welfare economics considers under an axiomatic approach, was shown by weighting the minority's positionality on cardinal voting. In addition, we can know the contents such as the number and positionality of the minority from the analysis of the aggregation results. It will be useful for promoting mutual understanding between the majority and minority by visualizing the contents of the proposed aggregation methods interactively in the consensus-building process. With the further development of information technology, the consensus building on cardinal choices based on big data will be necessary. We would like to use the proposed aggregation methods for making social choices for pluralistic values such as social, environmental, and economic.