nishio In Quadratic Voting, using the appearance of “100 votes per person” or “99 votes per person” is a way of understanding the concept of “splitting one vote”. It is mathematically equivalent to normalizing to one vote per person and stating that “votes can be split”. The interesting point is that a nonlinear function called square root is applied before the tabulation.
nishio and read “Smooth Society” from p.156 to “Linear Voting and Collective Knowledge” and “non-linear voting” after taking into account the non-linearity of Quadratic Voting and its property of distributing votes on multiple topics. and Its Enemies]”, p.156 - “Linear Voting and Collective Intelligence” and “non-linear voting” are interesting to read.
In “Smooth Society and Its Enemies,” p.156 - “Linear Voting and Collective Intelligence,” it is assumed that a linear space of infinite dimension can be represented on a propagating delegate voting system by a linear space of finite dimension as a realistic approximation of it.
- But, well, it’s hard to make the average person understand.
- Cases in which normalization is necessary and cases in which it is not are discussed.
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In the case of tax rates, etc., the value must not exceed 1, so normalization such as dividing by the total number of votes cast would be necessary. Such normalization is not necessarily necessary in cases where the upper limit is likely to be proportional to the number of voters, such as in the case of budget allocation. The more participants, the larger the budget size.
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non-linear voting
In the previous section, we have assumed that the interaction between votes is only linear, but it is theoretically possible to make it nonlinear. For example, if we consider the case in which some non-linear operator is involved in the delegation propagation, we can consider a matrix with the operator as a component. Any networked information model, including neural network models, can be included in this space. Among them, we cannot deny the possibility that there may be operator matrices that are significant as votes.
- And among those nonlinear functions, Quadratic Voting showed that the square root is significant.
- The Smooth Society and Its Enemies, 2013; Quadratic Voting, 2018.
p.152 “Strength per agenda and equality of influence resources across nations.”
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If each person has one vote worldwide, and these votes are freely distributed among the various regions and agendas, then each agenda item can be weighted, with zero votes for items of no interest and votes only for those items that interest them. We call the intensity the strength of a person’s feelings for each agenda item.
- This is something that has a lot in common with Quadratic Voting.
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