On the empirical relevance of Condorcet’s paradox

Condorcet’s paradox occurs when there is no alternative that beats every other alternative by majority. The paradox may pose real problems to democratic decision making such as decision deadlocks and democratic paralysis. However, its relevance has been discussed again and again since the celebrated works of Arrow (Social choice and individual values, 1963) and Black (The theory of committees and elections, 1958). The discussion varies from one extreme to the other: from very relevant to practically irrelevant. This paper tries to bring more clarity to the discussion by reviewing the literature on the empirical relevance of Condorcet’s paradox. Since a definition of the paradox for even numbers of voters and alternatives, and for weak voter preferences is missing in the literature, we first define the paradox clearly and simply. Then, three topics are investigated, namely domain conditions, culture and the likelihood of the paradox, and the empirical detection of the paradox. Domain conditions express regularities in voter-preference profiles that prevent the paradox. Frequent observations of these domain conditions would make Condorcet’s paradox empirically less important. Cultures define probability distributions over the set of voter preferences. Observation of cultures might be a first step to indicate the relevance of the paradox. The empirical detection of the paradox speaks for itself; we will try to identify the number of observations of the paradox so far. The overall conclusion is that the empirical relevance of Condorcet’s paradox is still unsettled.     

Prime Ministers, Presidentialism and Westminster Smokescreens

This article asks, 'how do practitioners understand the relationship between the prime minister, ministers and the rest of Westminster and Whitehall?' We focus on three topics. First, we review tales of a Blair presidency. Second, we explore the governance paradox in which people tell tales of a Blair presidency as they recount stories of British governance that portray it as fragmented with several decision-makers. Finally, we argue that this paradox reveals the distorting influence the Westminster model still exerts on many accounts of British politics. It acts as a smokescreen for the changes in executive politics.     

Paradigms and Paradox: The Politics of Economic Ideas in Two Moments of Crisis

This article argues that there is a paradox at the heart of Hall's “Policy Paradigms” framework stemming from the desire to see both state and society as generative of social learning while employing two different logics to explain how such learning takes place: what I term the “Bayesian” and “constructivist” versions of the policy paradigms causal story. This creates a paradox as both logics cannot be simultaneously true. However, it is a generative paradox insofar as the power of the policy paradigms framework emerges, in part, from this attempt to straddle these distinct positions, producing an argument that is greater than the sum of its parts. In the second part of the article, I discuss the recent global financial crisis, an area where we should see third‐order change, but we do no not. That we do not strengthens the case for the constructivist causal story.     

The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.     

Empirical evidence of paradoxes of voting in Dutch elections

In this paper we analyze four national elections held in 1982, 1986, 1989 and 1994 in the Netherlands on the occurrence of the Condorcet paradox. In addition, we investigate these elections on the occurrence of three so-called majority-plurality paradoxes. The first paradox states that a party having a majority over another party may receive less seats. The second states that a Condorcet winner may not receive the largest number of seats and even may not receive a seat at all. The third says that the majority relation may be the reverse of the ranking of parties in terms of numbers of seats.     

To vote or not to vote: The paradox of nonvoting

One paradox of voting states that, in a general election, in which many citizens vote, the probability that a single voter can affect the outcome is so small that in general citizens have no rational reason for voting. However, if all citizens accept this reasoning, then none will vote, and so each vote has a large probability of affecting the outcome. Hence all should vote after all. The adoption of mixed strategies resolves this paradox: if each citizen adopts a certain (small) probability of voting, then the actual number of citizens voting will be just enough to make it worth those citizens' while to vote. A Nash equilibrium point thus occurs. Here we compute Nash equilibria for the simple case of majority voting; for the more complicated case of composite voting (for example, as in a presidential election), we draw certain qualitative inferences.     

Frequency of paradox in a common n-winner voting scheme

This paper investigates the extent to which a commonly used electoral scheme — voting for n candidates when there are n vacancies to fill — is likely to lead, in practice, to paradoxical results. Two types of paradox are investigated. One occurs when an increase in the number of vacancies causes a candidate to drop from the list of winners. The second occurs when the Condorcet candidate fails to win. Using a Monte Carlo study, we show that the likelihood of paradox can be substantial and depends critically on the degree of homogeneity of voters' preferences and on the number of voters.     

中国古代监察制度的启示与悖论——以《中国廉政史鉴》典章制度卷为视角

通过对《中国廉政史鉴》典章制度卷的梳理,我们可以看到中国古代监察制度表现出来的几个特点:监察权是治权之权,监察官是治官之官;监察与权力相伴而生;监察权是耳目之寄;国家要培养监察官的锐气;监察官有特殊的任职要求;监察必须保持充分独立。同时,我们也发现,中国古代监察制度依靠权力集中来制约权力,注定就是一个悖论,只要分权和民主还未得到启蒙,这个悖论就难以克服。了解这些,对于进一步完善当前的监察制度具有一定的启发意义。     

Paradoxes of Constitutional Democracy

Drawing on the work of Frank Michelman and Jürgen Habermas, I outline two interconnected paradoxes of constitutional democracy. The paradox of the founding prevents a purely democratic constitution from being founded, because the procedures needed to secure its legitimacy cannot be spontaneously self-generated. It displays an infinite regression of procedures presupposing procedures. The paradox of dynamic indeterminacy heads off any attempt to resolve this problem through constitutional amendment. It shows that we cannot evaluate the legitimacy of a dynamically evolving constitution based on projections of its future development. To do so, we would need a stronger basis for making probabilistic judgments about the constitution's future path. After exploring the problems of using constitutional patriotism as such a basis, I outline an alternative built on the ideas of dynamic constitutionalism and reflexive citizenship. It shows how a dynamically evolving constitution can promote its own legitimacy from within, simultaneously resolving both paradoxes.     

The civilian's visual security paradox: how open source intelligence practices create insecurity for civilians in warzones

ABSTRACT

Images taken by civilians and shared online have become an important source of conflict intelligence. This article explores issues around how states and non-state actors appropriate civilians’ images to produce intelligence about conflict, critically scrutinizing a practice often called open source or social media intelligence. It argues that image appropriation for open-source intelligence production creates a new kind of visual security paradox in which civilians can be endangered by their everyday visual practices because their digital images can be appropriated by outside actors as conflict intelligence. The transformation of everyday images into conflict evidence relies on what Barthes termed the photographic paradox, the paradox that while a photograph is clearly not the reality it depicts, the photograph is casually interpreted as a copy of that reality. When images are appropriated as conflict intelligence this photographic paradox translates into a security paradox. A visual security argument can be made without the intention or knowledge of the image producer, who then comes to perform the role on an intelligence agent. Yet civilians in warzones can hardly refrain from producing any images when they need to call attention to their plight, and to stay in contact with friends and relatives. The paradox, then, is that such vital visual signs of life can rapidly become sources of danger for the civilian. This civilian visual security paradox, it is argued, demands that intelligence actors respect the protected status of civilians in their online collection practices. So far, however, there is little sign of such respect.     

Voting,Collective Action,and Liberalisation in Latin America: The Rise and Fall of the Hillinger Paradox

Chile's economic and political evolution after the 1982–83 financial crisis has been offered as a model for the rest of Latin America. This paper interprets the 1973 military coup, and national recovery during the 1980s and 1990s, in terms of the presence and absence, respectively, of the Hillinger (1971) paradox. The paradox arises when democratic voting on platforms consisting of several issues leads to majority support for a platform, itself consisting of issues, none of which is supported by the majority. In the early 1970s, a particular expression of the Hillinger paradox led Chile to the verge of a bloody civil war, and to a prolonged military dictatorship. In the mid 1980s, an important policy question, that of differentiated industrial protection versus free trade, was solved by a stable compromise in favour of the latter. This avoided the Hillinger paradox and eventually made electoral politics possible again.     

The elimination paradox: apportionment in the Democratic Party

To award delegates in their presidential primary elections, the US Democratic Party uses Hamilton’s method of apportionment after eliminating any candidates (and their votes) that receive less than 15% of the total votes cast. We illustrate how a remaining candidate may have his or her delegate total decline as a result of other candidates being eliminated; this leads to a new elimination paradox. We relate that paradox to the new states, no show, and population paradoxes and show that divisor methods are not susceptible to the elimination paradox. We conclude with instances in which the elimination paradox may occur in other contexts, including parliamentary systems.

     

The inevitability of the “paradox of redistribution” in the allocation of voting weights

In voting bodies, when voting weights are reallocated, it may be observed that the voting power of some members, as measured by the Shapley-Shubik and Banzhaf power indices, increases while their voting weight decreases. By a simple constructive proof, this paper shows that such a “paradox of redistribution” can always occur in any voting body if the number of voters, n, is sufficiently large. Simulation results show that the paradox is quite frequent (up to 30 percent) and increases with n (at least for small n). Examples are given where the Banzhaf and Shapley-Shubik indices are not consistent in demonstrating the paradox.     

Geometry of run-off elections

We present a geometric representation of the method of run-off voting. With this representation we can observe the non-monotonicity of the method and its susceptibility to the no-show paradox. The geometry allows us easily to identify a novel compromise rule between run-off voting and plurality voting that is monotonic.     

Immigration and Citizenship in Germany: Contemporary Dilemmas

The paper starts from a paradox of contemporary German politics: after the unification of the two Germanies the ethnocultural grounding of German citizenship has lost its historical meaning; at the same time violent conflicts and heated debate over the rights to full membership for immigrants in the German state have developed. After a theoretical discussion of the notions of nation state, citizenship, and immigration, the development of the contemporary paradox of citizenship is sketched historically using two pairs of distinctions: nationhood v. statehood and political v. social (state-mediated) inclusion. The paradox of 'ethnicized' conflicts over Germans v. foreigners is interpreted as a discrepancy between membership in the state on the one hand and membership in the welfare state system on the other—a discrepancy which currently is 'overdetermined' by the socio-economic consequences of unification.     

Efficient Rent-Seeking in Experiment

In a series of experiments we show that people learn to playthe efficient outcome in an open-ended rent-seeking game. Thisresult persists despite quite different experimentenvironments and designs, like different propensities ofcompetition, group sizes etc., and is interpretable as aresolution of the so-called Tullock paradox which states thatreal-world rent-seeking expenditures are much lower than whatthe standard rent-seeking model predicts.     

Democracy in an Age of Tragedy: Democracy,Tragedy and Paradox

Abstract

Democracy and tragedy captured a delicate poise in ancient Athens. While many today perceive democracy as a finite, unquestionable and almost procedural form of governance that glorifies equality and liberty for their own sake, the Athenians saw it as so much more. Beyond the burgeoning equality and liberty, which were but fronts for a deeper goal, finitude, unimpeachability and procedural norms were constantly contradicted by boundlessness, subversion and disarray. In such a world, where certainty and immortality were luxuries beyond the reach of humankind, tragedy gave comfort and inspired greatness. The purpose of this article is to draw explicit links between democracy, tragedy and paradox. Given that tragedy's political ascendancy coincided with the birth of democracy in ancient Athens, we may assume that democracy was somehow, if not implicitly, tragic. But what was it that made democracy and tragedy speak so intimately to each other and to the Athenians who created them? The answer, at least the one which this article entertains, is paradox.     

Developing Practice‐Oriented Theory on Collaboration: A Paradox Lens

Collaboration is present throughout public administration as a means to address social issues that sit in the interorganizational domain. Yet research carried out over the last three decades has concluded that collaborations are complex, slow to produce outputs, and by no means guaranteed to deliver synergies and advantage. This article explores whether a “paradox lens” can aid the development of practice‐oriented theory to help those who govern, lead, and manage collaborations in practice. It draws on a long‐standing research program on collaboration and a synthesis of relevant literature on paradox and collaboration. The article develops five propositions on the application of a paradox lens that explicitly recognizes the context of collaboration as inherently paradoxical; acknowledges the limitations of mainstream theory in capturing adequately the complex nature of and tensions embedded in collaborative contexts; and uses the principles of paradox to develop practice‐oriented theory on governing, leading, and managing collaborations.     

Economic choice, political decision, and the problem of limits

Assesses the arguments for the use of market, or political, processes for making collective choices. The border between “what is mine” and “what is ours” is contested, but it is unguarded. Where should it lie? How would we know when it should be adjusted? I uncover an old paradox: A society can never use political means to guard against incursions across the border for political ends. Some other mechanism, such as constitutional or other extra-statutory rules, are required.     

Time to vote?

Despite the centrality of voting costs to the paradox of voting, little effort has been made to measure these costs accurately, outside of a few spatially limited case studies. In this paper, we apply Geographic Information Systems (GIS) tools to validated national election survey data from New Zealand. We calculate distance and travel time by road from the place of residence to the nearest polling place and combine our time estimate with imputed wages for all sample members. Using this new measure of the opportunity cost of voting to predict turnout at the individual level, we find that small increases in the opportunity costs of time can have large effects in reducing voter turnout.