# A Re-Interpretation of the Normative Foundations of Majority Rule

by June Ku2 min read13th Dec 20191 comment

# 11

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This is a working paper on group rationality by Mahendra Prasad, who has previously published, among other things, "Social Choice and the Value Alignment Problem" in Artificial Intelligence Safety and Security, edited by Roman V. Yampolskiy. He's provided me with this summary to share:

## Resolving Majority Rule’s Irrationality

Since the 1950s, majority rule has been interpreted as majority preference. But this has led to problems. For example, suppose there are three voters and three candidates. Suppose:

The first voter prefers: x over y over z

The second voter prefers: y over z over x

The third voter prefers: z over x over y

Notice, a majority (i.e., the first and third voters) prefer x over y. A majority (i.e., the first and second voters) prefer y over x. Thus, by transitivity, since a majority prefers x over y, and y over z, then we should expect a majority prefers x over z.

But that expectation is incorrect. A majority (i.e., the second and third voters) prefer z over x. In other words, the majority prefers x over y over z over x. This is akin to saying 3 > 2 > 1 > 3. Just as such an intransitivity makes the idea of a largest integer in a finite set of integers meaningless, majority preference’s intransitivity makes the notion of a best or winning candidate meaningless.

This paradox, known as Condorcet’s paradox, has been considered so fatal, many serious political philosophers have argued that majority rule and voting are meaningless.

In the linked paper below, Mahendra Prasad argues that by adopting a “consent of the majority” interpretation of majority rule, which we can see in the works of philosophers such as John Locke, Jean Jacques Rousseau, Nicolas de Condorcet, and John Rawls, we can overcome Condorcet’s paradox. Specifically, Prasad takes the standard normative arguments for majority rule on two candidates (i.e., May’s theorem, Condorcet’s jury theorem, the Rae-Taylor theorem, and maximization of the number of self-determined individuals) and generalizes them to multiple candidates using consent of the majority (e.g., approval voting) without falling to Condorcet’s paradox.

The main takeaway from this paper should not be that approval voting is *the* correct way to interpret majority rule; rather it should be that there exists some interpretation of majority rule, which is not majority preference, which fully generalizes the standard normative arguments for majority rule to multiple candidates. Thus, we should not restrict our interpretation of majority rule to just majority preference, but be open to treating majority rule as a non-primitive open to multiple interpretations (e.g., mean rank maximization [Borda count], median rank maximization [Bucklin method], majority preference [Condorcet methods], first preference maximization [plurality voting], etc.) that should be explored and researched. Doing so can improve the rationality and effectiveness of group decision making.

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majority preference’s intransitivity makes the notion of a best or winning candidate meaningless.

No. The social welfare function is *utilitarian*. The best candidate is the one with the greatest sum of utilities among all voters.

http://scorevoting.net/UtilFoundns

When you use this (correct) metric to assess voting methods, you get very interesting results.

http://scorevoting.net/BayRegsFig.html

http://rpubs.com/Jameson-Quinn/vse7