Abstract
Respecting minority opinions is vital in solving social problems. However, minority opinions are often ignored in general majority rules. To build consensus on pluralistic values and make social choices that consider 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 assuming that the distributions of votes follow normal distributions, we calculated the frequency distributions of the aggregation results. We found that minority opinions are more likely to be reflected proportionately to the average of the distribution in two of the above three methods. This implies that Sen and Gotoh's idea of considering the social position of unfortunate people on ordinal ranking in the welfare economics, was illustrated by weighting the minority's positionality on cardinal voting. In addition, it is possible to visualize the number and positionality of the minority from the analysis of the aggregation results. These results will be useful to promote mutual understanding between the majority and minority by interactively visualizing the contents of the proposed aggregation methods in the consensus-building process. With the further development of information technology, the consensus building based on big data will be necessary. We recommend the use of our proposed aggregation methods to make social choices for pluralistic values such as social, environmental, and economic.
Highlights
Disparities in wealth, inequalities in income, environmental pollution and cultural collapse amongst others, have become social problems in various countries, regions, and communities
These results obtained indicate that Sen and Gotoh's idea (Sen, 2002; Gotoh, 2015) of giving priority on ordinal ranking to unfortunate people in the position-conscious choice procedure is applied to the positionality of the minority on cardinal cumulative voting
In the dimension related to economic value, Q-NW, originally derived from an economic perspective, will be adopted, and in the dimension related to environmental value, quadratic-square-root weighted (Q-SW) or quadratic-linear weighted (Q-LW) will be adopted to balance economic value while considering the opinion of the minority
Summary
Disparities in wealth, inequalities in income, environmental pollution and cultural collapse amongst others, have become social problems in various countries, regions, and communities. In a survey based on quadratic voting, the aggregated result for a more subdivided and substantially continuous index axis (for example, 20th quantile) has a bell-shaped quasi-normal distribution. This aggregated result is considered to closely approximate the true distribution of respondents’ preferences. We aspire to make social choices that reflect the opinions of the minority, e.g., unfortunate people To achieve this purpose, we propose new aggregation methods that give weight to the minority's positionality by incorporating the position-conscious concept of Sen and Gotoh into cumulative voting.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call