Accurately figuring out the cumulative ordering of preferences of an entire society as an aggregation of the orderings of preferences of many individuals would inherently simplify democratic decision processes. However, the social preference ordering is contingent on the specific procedure, or voting rule, used to aggregate the individual preference orderings. This means that different voting rules can lead to different social preference orderings under the input of the same individual preference orderings. This issue effectuates the questions which of the different possible outcomes is the most legitimate, and by extension which voting rule should be used. Arrow sought to answer these questions by demanding that voting rules satisfy a particular set of democratically desirable qualities – these are referred to as axioms or conditions. A voting rule that succeeds in complying with all the conditions could be considered democratically legitimate. The emerging issue is that no voting rule can possibly satisfy all theconditions simultaneously.
The blatant preliminary conclusion of this impossibility theorem is somewhat bleak: our faith in democratic voting procedures might be entirely misguided. The aim of this paper is to ascertain, whether the implications of this impossibility theorem constitute an actual issue for the practical application of preference aggregation – or voting – in a democratic political system.
Having argued that certain evasions of the impossibility can be practically justified in most cases, the paper will conclude that the impossibility is only relevant for a negligible number of scenarios. Thus, inferring that in most cases Arrow’s impossibility theorem, albeit theoretically relevant, does not constitute a profound issue for voting procedures in a democratic political system.
Table of Contents
I. Introduction
II. Arrow’s General Impossibility Theorem
a. Introducing Arrow’s Conditions
b. Evaluating the Condition’s Normativity
III. Arriving at Possibility Results
a. Giving up the Unrestricted Domain Condition
b. Giving up the Independence of Irrelevant Alternatives Condition
IV. Practical Justifications and Implications of the Circumventions
V. Conclusion
Research Objectives and Core Themes
This paper examines whether Arrow's Impossibility Theorem poses a genuine threat to the practical application of voting rules in democratic systems. By analyzing the normative foundations of Arrow's conditions and evaluating common theoretical circumventions, the work aims to determine if the theorem's bleak theoretical implications hold weight in real-world democratic political processes.
- Theoretical analysis of Arrow's five democratic axioms.
- Normative evaluation of the conditions for preference aggregation.
- Examination of domain restrictions, specifically single-peaked preferences.
- Trade-offs between strategy-proofness and preference intensity.
- Practical justification for relaxing standard impossibility conditions.
Excerpt from the Book
II. Arrow’s General Impossibility Theorem
This section will give some insight into Arrow’s impossibility theorem, specifically the conditions and the impossibility he proves. The intention is to construct a foundation for the ensuing discussion, in particular for the conditions’ normative evaluation in part II.b.
Arrow developed his initial conceptions in his doctoral thesis ‘Social Choice and Individual Values’ from 1951, some adaptations have been made since. In simplified terms “[Arrow] asks whether there exists any method of aggregating individual preferences into a social choice that simultaneously conforms to five apparently reasonable conditions, each of which is explicitly normative in nature” (Johnson 2015, p.1). He arrived at the daunting conclusion that there was no voting rule capable of satisfying his conditions simultaneously from which he derived his impossibility theorem. Although, instead of referring to voting rules Arrow employs ‘social welfare functions’. They map all the sets of individual orderings, or profiles, over alternative social states onto a single corresponding social, or collective, ordering over alternative social states. When aggregating preferences, Arrow assumes that there are at least three distinct social alternatives and at least two distinct voters. Ideally, the social ordering maximizes social welfare (Arrow 1963, pp. 22,23). Voting rules appear less abstract than social welfare functions, so for reasons of simplicity, the focus will lie primarily on voting rules from now on. It should also be noted that Arrow (1963, p. 11) designs his theorem around the assumption that “the behavior of an individual in making choices is describable by means of a preference scale without any cardinal significance”. Making use of only ordinal rankings has the purpose of avoiding problems of interpersonal comparability.
Summary of Chapters
I. Introduction: This chapter introduces Arrow's Impossibility Theorem and sets the objective to assess whether the theorem's theoretical conclusions undermine the legitimacy of democratic voting in practice.
II. Arrow’s General Impossibility Theorem: This section details the five axioms of Arrow's theorem and provides a critical normative evaluation of the underlying assumptions required for a democratic voting rule.
III. Arriving at Possibility Results: This chapter explores how relaxing specific conditions, such as the Unrestricted Domain or Independence of Irrelevant Alternatives, can allow for functional voting rules by avoiding the impossibility.
IV. Practical Justifications and Implications of the Circumventions: The author evaluates whether these theoretical mitigations are justifiable in real-world scenarios, concluding that the practical impact of the theorem is limited.
V. Conclusion: The paper summarizes that while Arrow's theorem is theoretically profound, it does not constitute an obstructive issue for the practical legitimacy of democratic elections.
Keywords
Arrow's Impossibility Theorem, Social Choice Theory, Voting Rules, Preference Aggregation, Democratic Legitimacy, Unrestricted Domain, Independence of Irrelevant Alternatives, Condorcet’s Paradox, Single-Peaked Preferences, Borda Count, Strategic Voting, Preference Intensity, Collective Rationality, Normativity, Welfare Economics.
Frequently Asked Questions
What is the primary focus of this paper?
The paper examines the practical relevance of Arrow's Impossibility Theorem within democratic systems, questioning whether its theoretical constraints invalidate actual voting procedures.
What are the central themes discussed in the work?
The core themes include the normative validity of social choice axioms, the trade-off between strategy-proofness and preference expression, and the practical mitigation of theoretical impossibilities.
What is the main research question?
The research asks to what extent Arrow's Impossibility Theorem constitutes a genuine issue for the practical application of voting rules in a democratic system.
Which scientific methodology is utilized?
The author employs a normative and analytical review of existing literature on Social Choice Theory, evaluating the conditions of the theorem against realistic and practical scenarios.
What topics are covered in the main body?
The main body covers the formal introduction of Arrow's conditions, their normative critique, methods of mitigating the impossibility (such as restricting domains), and an evaluation of their practical justifications.
How would you characterize this work through keywords?
The work is characterized by terms like Social Choice Theory, Arrow's Impossibility Theorem, democratic legitimacy, and preference aggregation.
Why does the author suggest that Condorcet's paradox is less of a threat in practice?
The author argues that in sufficiently large electorates, the probability of encountering the cycles inherent in Condorcet's paradox is statistically close to zero.
How does the author view the 'Independence of Irrelevant Alternatives' (IIA) condition?
The author views IIA as perhaps the most arbitrary condition, noting that its enforcement prevents the expression of preference intensity and can be justifiably relaxed to allow for more nuanced voting outcomes.
- Citation du texte
- Johannes König (Auteur), 2018, Arrow's Impossibility Theorem in Practice, Munich, GRIN Verlag, https://www.grin.com/document/448772
