It is widely accepted that indicators such as "vote disparity" and "GDP per capita" are used to represent the state of society and the economy. However, few people question whether these figures are calculated correctly. We spoke with Professor Zhao Liang of Kyoto University, who is working on a project called "Standardization of indicators and the limitations of per capita economic and social criticism aimed at correcting social disparities" through research into mathematical models.
His specialties include graph and network algorithms and machine learning, and he conducts cross-disciplinary research focusing on information.
In recent years, he has been focusing on the design of non-proportional per capita economic and social indicators. He presides over the Future Wisdom Research Group and advocates the theory of information wisdom.
Questions about the "gap in one vote"
After every parliamentary election, there are always newspaper articles about the "disparity in the value of each vote." I became interested in this as it seemed like a major social issue, and one day I looked into how the value of one vote is calculated. This led me to think that there might be a problem with the calculation formula itself.
It is thought that each Diet member costs more than 100 million yen in taxes per year (*1), and I think the public would like the number of Diet members to be as efficient as possible and kept to the minimum necessary. However, if the number is reduced too much, the distance between Diet members and the people will become too great and they will not be able to adequately represent the people. Therefore, it is first necessary to calculate the appropriate number of Diet members. So, how do we determine the appropriate number of Diet members?
The results of the regression analysis show that the number of seats in the Diet is roughly proportional to the population power of 0.39588 (≒ 0.4) (solid line).
(Source: "Chapter 6: The Most Favorable Number of Representatives" by Cho, Tanimoto, and Lu; "Mathematics of Elections, Voting, and Public Choice" edited by Oyama, Kyoritsu Shuppan, 2022)
To find the answer, let's first consider the following question. When asked, "If Japan's population doubled, would you think the number of Diet members should be doubled?", most people would answer, "Do you think we don't need twice as many?" Furthermore, when asked, "If Japan's population halved, would you think the number of Diet members should be halved?", most people would answer, "Do you think we don't need to reduce it that much?" In this way, our sense is that the appropriate number of Diet members is one that does not increase or decrease at the same rate as the population, but rather changes more gradually.
There is evidence to support this feeling. When we look at statistical data from countries around the world (technically, this is called "regression analysis"), we can see that the number of parliamentarians tends to be roughly proportional to the 0.4th power of the population (Figure 1). Moreover, this trend has not changed since the 1970s, when statistics became available. Since every country is free to set the number of parliamentarians, the 0.4th power law can be thought of as an appropriate number of parliamentarians that human society has discovered through trial and error. Therefore, if the population doubles, the number of parliamentarians will roughly double.0.4≒ 1.32 times, if the population were halved, the number of council members would be approximately (0.5)0.4Furthermore, it is estimated that Japan's population in 2070 will be 70% of the current population (i.e., a 30% decrease) (National Institute of Population and Social Security Research, 2023 estimate), so the number of Diet seats at that time will be 0.7 times the current number.0.4This means that a ratio of approximately 0.87 (a 13% reduction) would be better (*2).
Now, if the appropriate number of representatives is proportional to the 0.4th power of the population, you may be wondering how this relates to the disparity in the value of one vote. To show this relationship, let's explain the design of BMI (Body Mass Index). BMI is an international index used to determine obesity levels and ideal weight, and is calculated by dividing weight by the square of height to get a number. But why isn't it calculated to the first or third power? The reason is that changes in weight (of the working population) and changes in the square of height tend to occur at roughly the same rate, so the square is used to align the scale.
On the other hand, the formula for calculating the "disparity in one vote" is to divide the number of seats allocated to the population of Kyoto Prefecture, for example, to get the figure "1 seat per x people" (although the number of voters can also be used, we will use "population" for simplicity). If there is a difference compared to the figures for other prefectures, it becomes an issue as it is "not equal under the law." The formula used here, "number of council members ÷ population," does not take into account the scale relationship between the number of council members and population. Given that the appropriate number of council members changes on a scale of 0.4 to the power of population, in order to determine equality, we must use "number of council members ÷ 0.4 power of population" rather than the formula "number of council members ÷ population." However, because this formula is not per population, we use the equivalent per-population formula, "number of council members2.5÷ population".
However, changing the way things have been done up until now is an extremely high hurdle, so we will continue to consider how we can convince everyone.
(*1) Calculated from the "Details of the General Account Budget Calculated under the Jurisdiction of the Diet" and "Reports on the Use of Political Party Subsidies, etc."
(*2) Zhao Liang, "Diet, Parliament, Vote Gap, Ants, and BMI," Kyoto University Public Relations No. 775, p. 6010, July 2024
I want to create a fair system for society.
I believe that economic indicators such as "GDP per capita (Gross Domestic Product)" and "GNI per capita (Gross National Income)" also suffer from similar design problems. In this project, I would like to propose new indicators to more accurately assess the current state of society. This will lead to effective economic support measures and more accurate analysis of companies, which can be used for investment. I want to create a fairer and more efficient system for society.
My strong motivation to solve the problem of per capita indicators came from questions I had about vaccine prices during the COVID-19 pandemic. In 2022, the unit price of the Pfizer vaccine was $250 in developed countries and $25 in low-income countries (*3). I was curious about how the line was drawn, so I looked into it and found that it was based on a standard set by the World Bank, using GNI per capita (*4). However, the GNI calculation formula also does not take into account changes in scale, which may be problematic. When I calculated it taking changes in scale into account, I confirmed that the rankings (and therefore the unit prices of vaccines) had reversed in some countries.
(*3)https://www.oxfam.org.uk/mc/3znbqg/
(*4)https://www.pfizer.com/news/press-release/press-release-detail/pfizer-supply-global-fund-6-million-paxlovidtm-treatment
Even if it takes 100 years to be recognized
In order to quantitatively observe social phenomena, some kind of indicator is necessary, which is why indicators such as the value of one vote or GDP per capita have been used, but the reality is that these indicators have not been given much thought.
For two thousand years, it was believed that "heavier objects fall faster," but Galileo and others conducted actual experiments to prove otherwise. Like Galileo and others, I am trying to think more deeply about things that are taken for granted.
With regard to disparities in the value of one vote and per capita indicators, many people accept existing methods of measurement without question, so it will be difficult to get them to immediately understand and accept the ideas I propose.
Even so, I have a very strong passion for this project. It's been over a decade since I first wrote something like a memo focusing on the disparity in the value of each vote, but talking to students at the Graduate School of Integrated Studies in Human Survivability and people involved in the project at the SMBC Kyoto University Studio has given me the feeling that "maybe if we take the time, they'll understand," and it's given me confidence. It may take about 100 years for it to be recognized, but I think it's very interesting and important research, so I actually welcome criticism. I want to make this research unique to Kyoto University, with its liberal academic culture.
