Johnston Index Research Articles

On generating functions to compute some power measures for weighted majority games

AbstractIn this paper we introduce new procedures, based on generating functions, for calculating some power measures for weighted majority games. In particular, we present methods for computing the Johnston index and the Colomer–Martínez measure. Besides, we introduce a new power measure that combines the principles underlying the Johnston index and Colomer–Martínez measure as well as a procedure for computing it using generating functions. Finally, we introduce the new R package and describe its capabilities to compute some power measures by means of generating functions. We illustrate its performance with a real example.

Low-Frequency Seismic Noise Properties in the Japanese Islands.

The records of seismic noise in Japan for the period of 1997–2020, which includes the Tohoku seismic catastrophe on 11 March 2011, are considered. The following properties of noise are analyzed: The wavelet-based Donoho–Johnston index, the singularity spectrum support width, and the entropy of the wavelet coefficients. The question of whether precursors of strong earthquakes can be formulated on their basis is investigated. Attention is paid to the time interval after the Tohoku mega-earthquake to the trends in the mean properties of low-frequency seismic noise, which reflect the constant simplification of the statistical structure of seismic vibrations. Estimates of two-dimensional probability densities of extreme values are presented, which highlight the places in which extreme values of seismic noise properties are most often realized. The estimates of the probability densities of extreme values coincide with each other and have a maximum in the region: , . The main conclusions of the conducted studies are that the preparation of a strong earthquake is accompanied by a simplification of the structure of seismic noise. It is shown that bursts of coherence between the time series of the day length and the noise properties within annual time window precede bursts of released seismic energy. The value of the lag in the release of seismic energy relative to bursts of coherence is about 1.5 years, which can be used to declare a time interval of high seismic hazard after reaching the peak of coherence.

Computing power indices for weighted voting games via dynamic programming

We study the efficient computation of power indices for weighted voting games using the paradigm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley-Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of smallest size, as well as a very first method for computing Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.

Deegan-Packel & Johnston spatial power indices and characterizations

In this paper, we propose two spatial power indices in political games, taking into account ideological preferences of players. To do this, we develop an explanatory spatial model linked to the asymmetry Deegan-Pakel index introduced by Rapoport & Golan [Rapoport, A., Golan, E., 1985. Assessment of political power in the israeli knesset. American Political Science Review 79 (3), 673-692], which is the original Deegan-Packel index readjusted for measuring power according to the spatial preferences of players in real political games. In addition to extending such a readjustment for the original Johnston index | transforming it concomitantly into the Johnston spatial power index | this paper presents both the general versions of these two spatial indices, and their axiomatic characterizations through new axioms such as the vetoer property and others mainly inspired from Lorenzo-Freire et al. [Lorenzo-Freire, S., Alonso-Meijide, J. M., Casas-M´endez, B., Fiestras-Janeiro, M. G., 2007. Characterizations of the deegan-packel and johnston power indices.

Modified indices of political power: a case study of a few parliaments

According to yes–no voting systems, players (e.g., parties in a parliament) have some influence on making some decisions. In formal voting situations, taking into account that a majority vote is needed for making a decision, the question of political power of parties can be considered. There are some well-known indices of political power e.g., the Shapley–Shubik index, the Banzhaf index, the Johnston index, the Deegan–Packel index. In order to take into account different political nature of the parties, as the main factor for forming a winning coalition i.e., a parliamentary majority, we give a modification of the power indices. For the purpose of comparison of these indices of political power from the empirical point of view, we consider the indices of power in some cases, i.e., in relation to a few parliaments.

The inverse problem for power distributions in committees

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.

The cost of getting local monotonicity

Committees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight.In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004).In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good.As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan–Packel, Deegan–Packel, and Johnston indices.

The Inverse Problem for Power Distributions in Committees

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.

The minimum sum representation as an index of voting power

We propose a new power index based on the minimum sum representation (MSR) of a weighted voting game. The MSR offers a redesign of a voting game, such that voting power as measured by the MSR index becomes proportional to voting weight. The MSR index is a coherent measure of power that is ordinally equivalent to the Banzhaf, Shapley–Shubik and Johnston indices. We provide a characterization for a bicameral meet as a weighted game or a complete game, and show that the MSR index is immune to the bicameral meet paradox. We discuss the computation of the MSR index using a linear integer program and the inverse MSR problem of designing a weighted voting game with a given distribution of power.

Egalitarian property for power indices

In this study, we introduce and examine the Egalitarian property for some power indices on the class of simple games. This property means that after intersecting a game with a symmetric or anonymous game the difference between the values of two comparable players does not increase. We prove that the Shapley–Shubik index, the absolute Banzhaf index, and the Johnston score satisfy this property. We also give counterexamples for Holler, Deegan–Packel, normalized Banzhaf and Johnston indices. We prove that the Egalitarian property is a stronger condition for efficient power indices than the Lorentz domination.

Computing power indices: Multilinear extensions and new characterizations

Abstract Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n-person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.

Miners' Lung: A History of Dust Disease in British Coal Mining (review)

Reviewed by: Miners' Lung: A History of Dust Disease in British Coal Mining P. W. J. Bartrip Arthur McIvor and Ronald Johnston. Miners' Lung: A History of Dust Disease in British Coal Mining. Studies in Labour History. Aldershot, U.K.: Ashgate, 2007. xviii + 355 pp. Ill. $99.95 (ISBN-10: 0-7546-3673-9, ISBN-13: 978-0-7546-3673-1). The history of occupational health has flourished in recent years. McIvor and Johnston have themselves made notable contributions to this burgeoning literature, particularly with their book, Lethal Work. A History of the Asbestos Tragedy [End Page 483] in Scotland (2000), but also with a string of articles. Scotland looms large in the present study but, unlike several of their previous collaborations, Miners' Lung also considers England and Wales. Since coal workers' pneumoconiosis (CWP) was particularly prevalent in the huge South Wales coalfield, the Welsh connection is prominent. McIvor and Johnston describe work-induced respiratory disease among coal miners as "the largest occupational health disaster in British history" (p. 2). It could hardly be otherwise given the size of the workforce, which peaked at substantially over a million laborers, a large proportion of whom worked in extremely confined areas and dusty conditions deep underground. The neglect of labor and medical historians is, therefore, surprising. Contrast this position with the plethora of studies on asbestos-related disease. Even the multivolume History of the British Coal Industry (1984–93) provides scant coverage. So the appearance of Miners' Lung is a long-overdue addition to the historiography. In many ways, the book does for Britain what Alan Derickson's Black Lung: Anatomy of a Public Health Disaster (1998) did for the U.S. Unlike Derickson, however, McIvor and Johnston have used oral evidence: mainly interviews with miners born between 1909 and 1953. This personal testimony provides a valuable insight into the experience of living with chronic pulmonary disease. Recognition that the inhalation of coal dust could impair health came slowly. Coal dust was long thought to protect against tuberculosis, and a British expert continued to insist in the 1930s that coal dust was benign. Although CWP became a compensable disease in 1943, the precise nature of the coal-dust hazard remained in doubt; as Archie Cochrane, a leading expert, wrote in 1951, "the factors which may make coal dust dangerous are not yet known" (p. 112). Only in the 1990s, when British coal mining had virtually ceased, were bronchitis and emphysema accepted as diseases of coal miners. Scholars have often blamed high rates of occupational disease on exploitative industrialists. Governments, organized labor, and the medical profession, with their eyes on other issues, have also been criticized. As for the workers, they are usually portrayed as helpless victims. McIvor and Johnston do not fully subscribe to such interpretations. They criticize the prenationalization private coal owners but are much more generous (unwontedly so, perhaps, given their numerous caveats) in their appraisal of the National Coal Board. Medical science, which created a "long tradition of high-quality research into miners' lung disease" (p. 124), is largely exonerated from blame. The policies and practices of the labor unions and Trades Union Congress are viewed far more sympathetically than is often the case. Miners are seen as victims but also as architects of their own ill health through refusing to wear respirators, "cutting corners," working excessive hours, and engaging in dry hewing. They accepted a high degree of risk partly because such an attitude suited the hard-man culture of which they were a prominent part. It is pleasant to encounter a volume with that rarest of paraphernalia in modern academic publishing: footnotes. Unfortunately, praise cannot be heaped on McIvor and Johnston's index and bibliography, both of which are far from satisfactory. [End Page 484] Numerous individuals mentioned in the text, some of them significant figures, do not appear in the index. Similarly, many publications cited in the notes are absent from the bibliography. This complaint apart, Miners' Lung is a thorough, balanced, and readable study; it will be a standard reference for years to come. P. W. J. Bartrip University of Northampton Copyright © 2008 The Johns Hopkins University Press

A method for evaluating the behavior of power indices in weighted plurality games

In this paper, a systematic method to facilitate the comparison of a priori measures of power in an n-player r-candidate (n, r) weighted plurality game is proposed. This method, which exploits the notion of a structure of embedded winning coalitions (SEWC), enables the listing of all power profiles relevant to an (n, r) game under a given index and permits the computation of the probability of occurrence of each of these profiles. The vulnerability of an index to different paradoxes of power can also be systematically studied. For the purpose of illustration, we apply this method to the analysis of four well-known 2-candidate power indices namely the Shapley-Shubik index, the Banzhaf index, the Johnston index and the Deegan-Packel index. In each case, the set of power profiles and the likelihood of occurrence of each of these profiles are enumerated. The superadditivity property of these indices is also studied.

State power in a multilateral context: Voting strength in the Asian development bank

This article assesses how weighted voting in the Asian Development Bank (ADB) impacts members’ abilities to influence the formation of winning coalitions in its Board of Directors. Voting weights do not adequately measure an actor's ability to affect outcomes because they do not account for either the possible number of coalitions that may form or the number of votes needed to pass a resolution. In short, weighted voting systems cannot be straightforwardly analyzed with reference to voting weights but instead require the determination of . relative voting power. Using the Johnston index of voting power, values are presented for all members at four time points starting in 1980. Results indicate that the United States and Japan, as expected, hold the largest percentages of voting power. Also as expected, most borrowing members do not hold voting power in the Board of Directors. Unexpectedly, there is a pattern of dictators in the syndicates that comprise the Board of Directors whereby some members are able to ensure their election to the Board. Hence, non‐dictatorial members of these syndicates have no formal influence on the Board of Directors. These countries include relatively large donors such as the United Kingdom, the Nordic countries, and New Zealand. This raises the question, posed in the conclusion, of why a member would provide substantial monetary support for an organization where it holds little or no voting power. The answer I offer is simply that formal institutional rules do not always result in the intended political outcomes.

The Bicameral Postulates and Indices of a Priori Voting Power

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power).

Postulates and paradoxes of relative voting power ? A critical re-appraisal

This paper re-evaluates the problem of measuring thea priori relative voting power of a voter in an assembly. We propose several new intuitively compelling postualtes that any reasonable index of voting power ought to satisfy. At the same time we argue that most of the paradoxes of voting power discussed in the literature are paradoxical only in a weak sense, if at all. This leaves three crippling paradoxes — the well-known paradox ofweighted voting, and two new ones presented here: thebloc anddonation paradoxes. We evaluate the four main relative power indices discussed in the literature with respect to these three severe paradoxes. The Shapley-Shubik index is seen to be immune to all three paradoxes, while the Deegan-Packel index is vulnerable to all three. The Banzhaf and the Johnston indices are demonstrably immune to the paradox of weighted voting. However, they are shown to suffer from both the bloc and the donation paradoxes. We argue that this seriously undermines these indices in a hitherto unsuspected way. Several other theoretical issues relating to voting power are discussed.

The Problems of Measuring Power in Europe

This paper compares alternative methods of measuring power in European institutions. On the one hand there is the index used by Johnston in recent articles in this Journal; on the other there is an index more typically used by political scientists. Problems of interpreting and applying each index are discussed. The conclusion is that the Shapley–Shubik power index, used by political scientists, is easier to interpret in terms of the dynamics of bargaining. The Johnston index (which is certainly easier to calculate) might function as an ad hoc empirical measure, but needs therefore to be tested.