What is ⿻ Voting (plural voting)?

A name used in the book Plurality for voting designs that fix the weak points of "one person, one vote, and the most votes win". They try to let a vote reflect how strongly people care, and how people are connected to one another.

Suppose a class picks a trip destination by majority vote. The vote of someone who doesn't mind either way counts exactly as much as the vote of someone who badly wants to go to one place, and the result can feel unsatisfying. ⿻ Voting (plural voting) is a name for ideas that try to capture in a vote what "one person, one vote, majority wins" leaves out.

In short

⿻ Voting (Plural Voting) is the name used in chapter 5-6 of the book ⿻ Plurality. It covers voting designs that fix the weak points of counting one vote per person and letting the larger side win, and that try to reflect in the vote how strongly people want something and how people are connected [1][2].

The best-known examples are Quadratic Voting and liquid democracy.

For example

Taiwan's Presidential Hackathon (from 2019). In Taiwan, the citizens' vote in selecting the winners of the Presidential Hackathon, a contest of citizens' ideas for solving social problems, used Quadratic Voting (QV) (judges' scores also count toward the result). Citizens were given 99 points each (100 at the planning stage) [3][4]. The book ⿻ Plurality describes what QV selects differently in different chapters (the winners in 2-2, the top 20 teams in 7-0; → Quadratic Voting). In a 2023 conversation, Audrey Tang (唐鳳, Taiwan's former Minister of Digital Affairs) said that Taiwan had carried out QV and similar methods, and had recently renamed it (rendered in the Japanese translation as 複数投票制, a plural voting system) [4].

Running the book itself. Plurality says that "Changes to the text in future evolution will be approved collectively by the community using a mixture of the advanced voting procedures described in our ⿻ Voting chapter below and prediction markets" [5]. Participants vote and, at the same time, predict what the decision will lead to, and are rewarded when they are right [6].

The EU and the state of Colorado. According to the book, a rule that weights votes by the square root of a country's population (Penrose's square-root voting) is "approximately used in several elements of governance in the European Union". QV is used "frequently in the Colorado State Legislature to prioritize spending" [7]. However, the concrete example given by the Chinese-language Wikipedia is a single trial by Democratic members of the state House of Representatives in April 2019, and no record of how often it has been used confirms the book's "frequently" [8] (→ Quadratic Voting).

How it works

What is wrong with one person, one vote

The book lists problems with simple plurality voting (the most common rule, where whoever gets the most votes wins) [9]:

Choosing the lesser evil. People are pushed to vote for one of the two leading candidates, even if they would rather support someone else. The book calls this a "lesser of two evils" dynamic.
Equality that ignores differences. Legitimate differences in stake, such as representing different populations, are not taken into account.
Tyranny of the majority. A vote shows only which way the majority leans. It does not show how important an issue is to each person, or how much each person knows about it.

The book also says that other reforms, such as ranking candidates or approval voting (marking as many candidates as you like), each have their own limits [9].

The square-root idea

At the center of the book's thinking is the square root [7]. Votes of people unconnected to one another tend to cancel out on average, so their influence grows only with the square root of the number of votes. So, to give power in proportion to stake, the book says, "its voting weight should grow as the square root of its stake" [7]. Turning this idea into a voting method gives Quadratic Voting; that article walks through the idea with numbers.

Counting connections

The book adds, however, that these clean rules are optimal only when voters are connected to one another in a special way [7] (see the Quadratic Voting article). Real people belong to many overlapping groups. So the book lists several future forms of voting that take connections into account [6]:

Correlation discounting. Votes cast the same way within the same group are counted at a partial discount.
Adaptive representation. Districts are drawn not only by geography but along current social divides, such as urban versus rural, or education.
Predictive voting. People vote and predict the outcome at the same time.
Quadratic liquid democracy. In a system where votes can be delegated to others, the square root keeps power from piling up in one person's hands.
Assisted real-time voting. A digital assistant learns a voter's views and votes on their behalf, subject to the voter's review.

The book stresses that many of these rely heavily on an identity system that records people's connections [7][6].

A proposal for spotting like-minded votes

In his review of the book, Vitalik Buterin, the founder of Ethereum, introduced an idea for measuring from the votes themselves whose opinions are similar [10]. Instead of one vote per person, votes are handed out per pair of people. His example runs as follows. Three people who agree on almost every issue vote in favor of a proposal. Two people who disagree on other issues both vote against it. A simple count gives 3 to 2 in favor. But counted pair by pair, the votes against come out ahead, because the support of the three like-minded people is discounted for their overlap.

A 2023 piece by the economist E. Glen Weyl and co-authors also argues that a design which gives more weight to things backed by diverse groups than by similar groups resists collusion, and that this is exactly the goal of Plurality [11].

What is debated

Voting cannot pose the questions. The book itself admits that "even in its richest form, voting expresses and determines preferences about decisions already posed by other social processes". It adds: "Only in the context of the creative collaborations, deliberations, imaginations, and administrative systems we have sketched can collective decisions be meaningful" [12].
Does compromise erase diversity? The book raises the worry that compromise "throws the baby of diversity out with the bathwater of conflict". Its answer is that systems which discount support from already connected groups avoid reinforcing existing divides and create new coalitions that cut across them, so that a good deal of diversity survives [12].
It does not cross borders easily. Because voting needs trustworthy identity systems, the book judges that "systems of voting are unlikely any time soon to truly reach global legitimacy" [12].
Who decides whether people are unconnected? Buterin points out that organized groups pretending to be unconnected individuals is an old trick. If connections are measured from social media posts, he says, people will behave so as to look unconnected, and will even use bots. In his view, the ideal mechanism is still a matter of research [10].

Where it fits in Plurality

Part 5 of the book arranges seven forms of collaboration among different people by "depth" and "breadth" [13]. ⿻ Voting is the sixth. The book places it this way: the communication voting allows "is far thinner", but it "can often be a much more broadly inclusive process" whose verdicts are "typically thought of as more legitimate" than the outcomes of markets [1][12].

It comes after Augmented Deliberation (technology-supported discussion), and leads on to Social Markets, which the book calls "the thinnest of all the substrates for collaboration" [12]. Applying the square-root idea to allocating money gives Quadratic Funding. Delegating votes is liquid democracy. Using voting and prediction to run the book is the Plural Management Protocol.

In a Japanese context, Weyl said during a 2024 visit to Japan that old and young people should be able to cooperate rather than fight, given systems such as one in which people who have just turned 18, or have just arrived in Japan, gain more voting power over the years, or QV-like systems that take different groups into account [14].

Sources

Plurality, 5-6 "⿻ Voting", opening — https://www.plurality.net/v/chapters/5-6/eng/ ［CC0］
Plurality, chapter summaries (Chapter 5-6) — https://github.com/pluralitybook/plurality/blob/86158859464aee75633acd854c656928121a7fd8/contents/english/8-blurb.md ［CC0］
Discussion of the Presidential Hackathon voting method (2019-02-18, in Chinese) — https://sayit.archive.tw/2019-02-18-%E7%B8%BD%E7%B5%B1%E7%9B%83%E9%BB%91%E5%AE%A2%E6%9D%BE%E7%A5%A8%E9%81%B8%E6%96%B9%E5%BC%8F%E8%A8%8E%E8%AB%96 ［CC0］
DISTANCE.media, Japanese translation of a conversation with Audrey Tang (2024-04-09, in Japanese) — https://distance.media/article/20240409000196/
Plurality, 5-0 "Collaborative Technology and Democracy", opening — https://www.plurality.net/v/chapters/5-0/eng/ ［CC0］
Plurality, 5-6 "Frontiers of voting" — https://www.plurality.net/v/chapters/5-6/eng/ ［CC0］
Plurality, 5-6 "⿻ Voting tomorrow" — https://www.plurality.net/v/chapters/5-6/eng/ ［CC0］
"平方投票法" (Quadratic voting), Chinese-language Wikipedia, section "美國" (United States) — https://zh.wikipedia.org/zh-tw/%E5%B9%B3%E6%96%B9%E6%8A%95%E7%A5%A8%E6%B3%95 ［CC BY-SA 4.0］
Plurality, 5-6 "Voting today" — https://www.plurality.net/v/chapters/5-6/eng/ ［CC0］
Vitalik Buterin, "Plurality philosophy in an incredibly oversized nutshell", section on voting (2024-08-21) — https://vitalik.eth.limo/general/2024/08/21/plurality.html
Miller, Weyl and Erichsen, "Designing Pluralistic Mechanisms for Quadratic Funding" (2023) — https://www.radicalxchange.org/updates/blog/designing-pluralistic-mechanisms-for-quadratic-funding/
Plurality, 5-6 "Limits of ⿻ voting" — https://www.plurality.net/v/chapters/5-6/eng/ ［CC0］
Plurality, 5-0 "The depth-breadth spectrum" — https://www.plurality.net/v/chapters/5-0/eng/ ［CC0］
WIRED.jp, "デジタル・デモクラシーは多元的テクノロジーによって実現する" (Digital democracy is realized through plural technology) (2024, in Japanese) — https://wired.jp/article/glen-weyl-talk-2024/

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