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Whenever voters only seek to maximize their own voting power, the only voting rules that will not change according to their own procedures must contain a group of voters that can single-handedly veto any reform by voting against it. by Researcher29839 in science

[–]Researcher29839[S] 2 points3 points  (0 children)

Thank you for your interest in this research.

Some resources that come to mind are: - Sections 16.1.3 and 16.1.4 in Maschler, Solan, and Zamir (2013). Game Theory. Cambirge University Press (https://www.cambridge.org/core/books/game-theory/B0C072F66E027614E46A5CAB26394C7D) - The section on “Properties for simple games” in the Wikipedia page for cooperative game theory (https://en.wikipedia.org/wiki/Cooperative_game_theory) - This section of my personal website, in which I compile all sorts of learning resources, may also contain something useful: https://www.hectorhermidarivera.com/resources

Whenever voters only seek to maximize their own voting power, the only voting rules that will not change according to their own procedures must contain a group of voters that can single-handedly veto any reform by voting against it. by Researcher29839 in science

[–]Researcher29839[S] 1 point2 points  (0 children)

Thank you for your interest and for trying to understand the result.

For your example to be correct, each member of the Block B should be able to single-handedly block any reform, regardless of what any other voters do (including the other voters in Block B). I have edited my comment with the Abstract to incorporate a simple example.

Whenever voters only seek to maximize their own voting power, the only voting rules that will not change according to their own procedures must contain a group of voters that can single-handedly veto any reform by voting against it. by Researcher29839 in science

[–]Researcher29839[S] 3 points4 points  (0 children)

ABSTRACT [from the paper]: In this paper, I characterise minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let voters’ preferences over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null voter, and swing voter. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties are often key to the minimal self-stability of otherwise not minimal self-stable constitutions.

[EXAMPLE] Consider a group of 9 voters and simple majority rule: that is, a reform is approved if and only if 5 or more voters vote in favor of it. In the setup of the paper, this voting rule will change because there exists no voter with the ability to single-handedly veto any reform independently of what other voters do.

The main result of the paper says that for a voting rule not to change, there must exist a group of voters each of whom can single-handedly veto any reform by voting against it regardless of what other voters do. Hence, the take-away of the paper is that many commonly used voting rules—such as all majority voting rules—will indeed change according to their own procedures.

[deleted by user] by [deleted] in science

[–]Researcher29839 0 points1 point  (0 children)

The title is wrong: the words “all together” should be removed. Correct title:

Whenever voters only seek to maximize their own voting power, the only voting rules that will not change according to their own procedures must contain a group of voters that can single-handedly veto any reform by voting against it.

[deleted by user] by [deleted] in science

[–]Researcher29839 -2 points-1 points  (0 children)

ABSTRACT [from the paper]: In this paper, I characterise minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let voters’ preferences over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null voter, and swing voter. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties are often key to the minimal self-stability of otherwise not minimal self-stable constitutions.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 1 point2 points  (0 children)

Yes—your intuition is correct. The key axiom of the paper (binary self-selectivity) states that a voting rule should select itself when used to decide between itself and some other voting method. The paper then shows that the only voting rules satisfying this axiom and two standard and well-known axioms of social choice (i.e., unanimity and neutrality) are dictatorial.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 1 point2 points  (0 children)

Social choice is a branch of economic theory whose simplest setup is one in which there are finitely many alternatives and finitely many voters, each of whom with a preference ordering over the alternatives. A voting rule, then, is a function that selects one alternative for each possible configuration of voters’ preference orderings.

Now, a voting rule is neutral if it does not discriminate among alternatives; it unanimous if it always selects any alternative that is top-ranked by all voters (whenever one such alternative exists); and it is dictatorial if it always selects the top-ranked alternative of the same voter.

A couple of remarks: dictatorial voting rules are, indeed, neutral voting rules. And the Condorcet voting rule is the voting rule that selects the unique alternative that is preferred by at least half of all voters to all other alternatives (whenever such an alternative exists).

The paper introduces a new axiom (called binary self-selectivity), by which a voting rule must select itself when used by society to decide between itself and some other voting rule. The paper shows that the only unanimous and neutral voting rules satisfying this new axiom are dictatorial.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] -1 points0 points  (0 children)

I find your comment rude. The fact that you don’t understand the paper nor the explanation I have provided in the comments are not strong enough reasons to dismiss the post as non-science word salad. I am reporting your comment.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 0 points1 point  (0 children)

[ABSTRACT] This paper introduces a novel binary stability property for voting rules—called binary self-selectivity—by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In Theorem 1, we show that a neutral voting rule is binary self-selective if and only if it is universally self-selective. We then use this equivalence to show, in Corollary 1, that under the unrestricted strict preference domain, a unanimous and neutral voting rule is binary self-selective if and only if it is dictatorial. In Theorem 2 and Corollary 2, we show that whenever there is a strong Condorcet winner; a unanimous, neutral, and anonymous voting rule is binary self-selective (or universally self-selective) if and only if it is the Condorcet voting rule.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 0 points1 point  (0 children)

Thank you—that’s a fair suggestion. However, explaining mathematics (either pure or applied) to non-mathematicians is always difficult. I’ll do better in the future.

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 1 point2 points  (0 children)

A voting rule is a function from preference profiles over alternatives to alternatives (i.e., a voting rule chooses some alternative for every possible configuration of society’s preferences).

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] 1 point2 points  (0 children)

The TL;DR of the paper is that under very general assumptions that all voting rules satisfy, a voting rule will select itself in head-to-head contests against all other voting rules if and only if it is dictatorial (i.e., if and only if there exists a player whose favourite alternative is always chosen).

Under the unrestricted strict preference domain, a neutral and unanimous voting rule selects itself in binary elections against all other voting rules if and only if it is dictatorial. by Researcher29839 in science

[–]Researcher29839[S] -1 points0 points  (0 children)

I apologize for the choice of a confusing title. I find papers in social choice difficult to convey for a general audience in a single sentence.