Single Peaked Fuzzy Preferences: Black’s Median Voter Theorem

2015 ◽  
pp. 187-220
Keyword(s):  
Median Voter ◽  
Median Voter Theorem ◽  
Fuzzy Preferences

SINGLE PEAKED FUZZY PREFERENCES IN ONE-DIMENSIONAL MODELS: DOES BLACK'S MEDIAN VOTER THEOREM HOLD?

2010 ◽  
Vol 06 (01) ◽  
pp. 1-16 ◽  
Author(s):  
JOHN N. MORDESON ◽  
LANCE NIELSEN ◽  
TERRY D. CLARK
Keyword(s):  
Median Voter ◽  
Ideal Point ◽  
Binary Relations ◽  
One Dimensional ◽  
Median Voter Theorem ◽  
Political Actors ◽  
Fuzzy Preferences ◽  
Median Position ◽  
Finite Set ◽  
Dimensional Models

Black's Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed on a single-dimensional continuum such that the preferences of all players descend monotonically from their ideal point, then the outcome will be the alternative at the median position. We demonstrate that the Median Voter Theorem holds for fuzzy preferences. Our approach considers the degree to which players prefer options in binary relations.

The median voter theorem and the repeal of the prohibition on abortion in Ireland: an analysis of the passage of the Thirty-Sixth Amendment

2020 ◽  
Author(s):  
Sara E. Guffey
Keyword(s):  
Median Voter ◽  
Driving Forces ◽  
Unborn Child ◽  
Equal Rights ◽  
Median Voter Theorem ◽  
Religious Identification ◽  
Sixth Amendment ◽  
Eighth Amendment ◽  
Irish People ◽  
Elected Representatives

In 2018, the Irish people voted in favour of the passage of the Thirty-Sixth Amendment. This vote abolished the Eighth Amendment, which had previously outlawed abortion by establishing the equal rights of the woman and the unborn child. To uncover potential driving forces behind the vote share in support of the Thirty-Sixth Amendment, this article uses regional data on religious identification, age and a measure of traditional identity. The results of this article show that variation by region in religious identification was significantly correlated with voting behaviour in the 2018 referendum. Furthermore, evidence for the validity of the median voter theorem is developed by analysing data on the reported support of Irish elected representatives for the legislation before the vote. The results of this analysis on the referendum vote suggest a societal shift has taken place in the preferences of Irish citizens, which is complimented by the views of their elected representatives.

Anthony Downs, An Economic Theory of Democracy

2020 ◽  
Author(s):  
Russell Muirhead
Keyword(s):  
Economic Theory ◽  
Political Theory ◽  
Deliberative Democracy ◽  
Democratic Theory ◽  
Median Voter ◽  
Moral Motivation ◽  
Positive Theory ◽  
Median Voter Theorem ◽  
Theory Of Democracy ◽  
Models Of Democracy

Anthony Downs’s Economic Theory of Democracy has been marginalized in normative democratic theory, notwithstanding its prominence in positive political theory. For normative theorists, the “paradox of voting” testifies to the reality of moral motivation in politics, a species of motivation foreign to Downs’s theory and central to the ideals of deliberative democracy that normative theorists developed in the 1980s and 1990s. The deliberative ideal displaced aggregative conceptions of democracy such as Downs’s model. The ensuing segmentation of normative democratic theories that assume moral motives (like deliberative democracy) and positive models of democracy that assume selfish motives (like Downs’s theory) leaves both without the resources to diagnose the persistence of ideological partisanship and polarization that beset modern democracies. Engaging Downs’s theoretical contributions, especially the median voter theorem, would constitute a salutary step toward a democratic theory that integrates normative and positive theory.

scholarly journals Why the current Peak in Populism in the US and Europe? Populism as a Deviation in the Median Voter Theorem

2018 ◽  
Vol 7 (2) ◽  
pp. 154-170 ◽  
Author(s):  
Filipa Figueira
Keyword(s):  
United States ◽  
Public Choice ◽  
Median Voter ◽  
The United States ◽  
Party Competition ◽  
Left Wing ◽  
Median Voter Theorem ◽  
Historical Factors ◽  
The Us ◽  
Political Spectrum

The current surge of populism in Europe and the United States calls for further analysis using public choice tools. In this article, populism is modelled as a deviation from the normal state of the median voter theorem. This study adds to the public choice literature by proposing a model of populism which is suited, not only to left-wing populism, but also to other forms of populism prevalent in Europe and the United States today. It is argued that, due to changes in the assumptions underpinning the median voter theorem, the operation of the model can be modified, and as a result surges of populism occur. Those assumptions concern: the political spectrum; the distribution of ideological preferences; sociological, psychological and historical factors; political party competition; and extreme political preferences. It is shown that the current peak of populism in Europe and the United States can be explained through a simultaneous change in all of these aspects, leading to a “perfect storm” of populism. 

scholarly journals Recognizing Top-Monotonic Preference Profiles in Polynomial Time

2019 ◽  
Vol 66 ◽  
pp. 57-84 ◽  
Author(s):  
Krzysztof Magiera ◽  
Piotr Faliszewski
Keyword(s):  
Polynomial Time ◽  
Median Voter ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Recognition Problem ◽  
Median Voter Theorem ◽  
Weak Preference ◽  
Single Peakedness ◽  
Preference Orders

We provide the first polynomial-time algorithm for recognizing if a profile of (possibly weak) preference orders is top-monotonic. Top-monotonicity is a generalization of the notions of single-peakedness and single-crossingness, defined by Barbera and Moreno. Top-monotonic profiles always have weak Condorcet winners and satisfy a variant of the median voter theorem. Our algorithm proceeds by reducing the recognition problem to the SAT-2CNF problem.

NFL team revenue distribution and revenue sharing: a median voter theorem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Justin Ehrlich ◽  
Shankar Ghimire ◽  
Shane Sanders
Keyword(s):  
Design Methodology ◽  
Median Voter ◽  
National Football League ◽  
Professional Sports ◽  
Revenue Sharing ◽  
Content Type ◽  
Median Voter Theorem ◽  
Sports Leagues ◽  
Average Revenue ◽  
Professional Sports Leagues

PurposeRevenue sharing is ubiquitous among North American professional sports leagues. Under pool revenue sharing, above-average revenue teams of a league effectively transfer revenues to below-average revenue teams. Herein, the authors find and prove that a league will vote into policy a pool revenue sharing arrangement if and only if mean team revenue is greater than presharing median revenue, where this condition is equivalent to the presence of positive nonparametric skewness in a league’s distribution of team revenues. This represents a median voter theorem for league revenue sharing.Design/methodology/approachThe authors consider the case of revenue sharing for the National Football League (NFL), a league that pools and equally shares national revenues among member teams.FindingsThe authors find evidence of positive and significant nonparametric skewness in NFL team revenue distributions for the 2004–2016 seasons. This distribution is observed amid annual majority rule votes of League owners in favor of maintaining the incumbent pool revenue sharing model (as opposed to no team revenue sharing). Distribution of revenues – namely the existence of outlying large market NFL teams – appears to consistently explain the historical popularity of NFL revenue sharing.Originality/valueThe median voter theorem uncovered in the case of NFL applies to all professional sports leagues and can be used predictively as well as descriptively.

Electoral Competition and Redistribution with Rationally Informed Voters

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Valentino Larcinese
Keyword(s):  
Political Parties ◽  
Empirical Research ◽  
Median Voter ◽  
Electoral Competition ◽  
Political Information ◽  
Optimization Process ◽  
Median Voter Theorem ◽  
Negligible Probability ◽  
The Cost ◽  
Decisive Vote

Abstract In spite of the negligible probability that everyone has to cast a decisive vote, political information can be relevant for a number of private decisions. Under quite mild assumptions, the demand for information is increasing in income. Being informed affects responsiveness to electoral platforms and vote-seeking political parties should take this into account in their optimization process. As a consequence, redistribution is generally lower than what the median voter theorem predicts. Moreover, in contrast with what most literature takes for granted, an increase in inequality does not unambiguously increase redistribution. This is consistent with most empirical research in this field. Finally, an increase in the cost of information induces a reduction in redistribution.

FUZZY BLACK'S MEDIAN VOTER THEOREM: EXAMINING THE STRUCTURE OF FUZZY RULES AND STRICT PREFERENCE

2012 ◽  
Vol 08 (02) ◽  
pp. 195-217 ◽  
Author(s):  
MICHAEL B. GIBILISCO ◽  
JOHN N. MORDESON ◽  
TERRY D. CLARK
Keyword(s):  
Median Voter ◽  
Social Preference ◽  
Dimensional Space ◽  
Preference Relation ◽  
Strict Preference ◽  
Median Voter Theorem ◽  
The Social ◽  
Fuzzy Preference Relations ◽  
Simple Rules ◽  
Fuzzy Framework

Under certain aggregation rules, particular subsets of the voting population fully characterize the social preference relation, and the preferences of the remaining voters become irrelevant. In the traditional literature, these types of rules, i.e. voting and simple rules, have received considerable attention because they produce non-empty social maximal sets under single-peaked preference profiles but are particularly poorly behaved in multi-dimensional space. However, the effects of fuzzy preference relations on these types of rules is largely unexplored. This paper extends the analysis of voting and simple rules in the fuzzy framework. In doing so, we contribute to this literature by relaxing previous assumptions about strict preference and by illustrating that Black's Median Voter Theorem does not hold under all conceptualizations of the fuzzy maximal set.

Expected Utility and Political Decision Making

2020 ◽  
Author(s):  
Jona Linde
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Median Voter ◽  
Expected Utility Theory ◽  
Median Voter Theorem ◽  
Political Actors ◽  
Spatial Voting ◽  
Expected Utility Model ◽  
Political Decisions ◽  
Political Decision Making

Expected utility theory is widely used to formally model decisions in situations where outcomes are uncertain. As uncertainty is arguably commonplace in political decisions, being able to take that uncertainty into account is of great importance when building useful models and interpreting empirical results. Expected utility theory has provided possible explanations for a host of phenomena, from the failure of the median voter theorem to the making of vague campaign promises and the delegation of policymaking. A good expected utility model may provide alternative explanations for empirical phenomena and can structure reasoning about the effect of political actors’ goals, circumstances, and beliefs on their behavior. For example, expected utility theory shows that whether the median voter theorem can be expected to hold or not depends on candidates’ goals (office, policy, or vote seeking), and the nature of their uncertainty about voters. In this way expected utility theory can help empirical researchers derive hypotheses and guide them towards the data required to exclude alternative explanations. Expected utility has been especially successful in spatial voting models, but the range of topics to which it can be applied is far broader. Applications to pivotal voting or politicians’ redistribution decisions show this wider value. However, there is also a range of promising topics that have received ample attention from empirical researchers, but that have so far been largely ignored by theorists applying expected utility theory. Although expected utility theory has its limitations, more modern theories that build on the expected utility framework, such as prospect theory, can help overcome these limitations. Notably these extensions rely on the same modeling techniques as expected utility theory and can similarly elucidate the mechanisms that may explain empirical phenomena. This structured way of thinking about behavior under uncertainty is the main benefit provided by both expected utility theory and its extensions.

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