Voting power measurement: a story of misreinvention

In this account of the history of voting-power measurement, we confine ourselves to the concept of a priori voting power. We show how the concept was re-invented several times and how the circumstances in which it was reinvented led to conceptual confusion as to the true meaning of what is being measured. In particular, power-as-influence was conflated with value in the sense of transferable utility cooperative game theory (power as share in constant total payoff). Influence was treated, improperly, as though it were transferable utility, and hence an additive and distributive quantity. We provide examples of the resulting misunderstanding and mis-directed criticism

An equivalent formulation for the Shapley value

The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1.An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.Peer ReviewedPostprint (published version

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections

Am empirical comparison of the performance of classical power indices

Power indices are general measures of the relative voting power of individual members of a voting body. They are useful in helping understand and design voting bodies particularly those which employ weighted voting, in which different members having different numbers of votes. It is well known that in such bodies a member's voting power, in the sense of their capacity to affect the outcomes of votes called, rarely corresponds to the actual number of votes allocated to him. Many voting bodies for which this is an important consideration exist: examples include international organisations (notably the World Bank, the IMF, the European Union), the US presidential Electoral College and corporations in which votes are proportionate to stockholdings. Two classical power indices dominate the literature: the Shapley-Shubik index and the Banzhaf index (also known by other names). Both are based on the idea that a member's power depends on the relative number of times they can change a coalition from losing to winning by joining it and adding their vote. They may be defined in probabilistic terms as the probability of being able to swing the result of a vote, where all possible outcomes are taken as equiprobable. The indices differ however in the way they count voting coalitions. In probabilistic terms they use different coalition models and therefore differ in precisely what is meant by equiprobable outcomes. The indices have been used in a number of empirical applications but their relative performance has remained an open question for many years, a factor, which has hindered the wider acceptance of the approach. Where both the indices have been used for the same case, they have often given different results, sometimes substantially so, and theoretical studies of their properties have not been conclusive. There is therefore a need for comparative testing of their relative performance in practical contexts. Very little work of this type has been done however for a number of reasons: lack of independent indicators of power in actual voting bodies with which to compare them, difficulties in obtaining consistent data on a voting body over time with sufficient variation in the disposition of votes among members of actual legislatures and the lack of independent criteria against which the results of the indices may be judged. It has also been hampered to some extent by lack of easily available algorithms for computing the indices in large games. This paper assesses the indices against a set of reasonable criteria in terms of shareholder voting power and the control of the corporation in a large cross section of British companies. Each company is a separate voting body and there is much variation in the distribution of voting shares among them. Moreover reasonable criteria exist against which to judge the indices. New algorithms for the Shapley-Shubik and Banzhaf indices are applied to detailed data on beneficial ownership of 444 large UK companies without majority control. Because some of the data is missing, both finite and oceanic games of shareholder voting are studied to overcome this problem. The results, judged against these criteria, are unfavorable to the Shapley-Shubik index and suggest that the Banzhaf index much better reflects the variations in the power of shareholders between companies as the weights of shareholder blocks vary

Conduction in ulnar nerve bundles that innervate the proximal and distal muscles: a clinical trial

<p>Abstract</p> <p>Background</p> <p>This study aims to investigate and compare the conduction parameters of nerve bundles in the ulnar nerve that innervates the forearm muscles and hand muscles; routine electromyography study merely evaluates the nerve segment of distal (hand) muscles.</p> <p>Methods</p> <p>An electrophysiological evaluation, consisting of velocities, amplitudes, and durations of ulnar nerve bundles to 2 forearm muscles and the hypothenar muscles was performed on the same humeral segment.</p> <p>Results</p> <p>The velocities and durations of the compound muscle action potential (CMAP) of the ulnar nerve bundle to the proximal muscles were greater than to distal muscles, but the amplitudes were smaller.</p> <p>Conclusions</p> <p>Bundles in the ulnar nerve of proximal muscles have larger neuronal bodies and thicker nerve fibers than those in the same nerve in distal muscles, and their conduction velocities are higher. The CMAPs of proximal muscles also have smaller amplitudes and greater durations. These findings can be attributed to the desynchronization that is caused by a wider range of distribution in nerve fiber diameters.</p> <p>Conduction parameters of nerve fibers with different diameters in the same peripheral nerve can be estimated.</p

Clinical utility of tibial motor and sensory nerve conduction studies with motor recording from the flexor hallucis brevis: a methodological and reliability study

<p>Abstract</p> <p>Background</p> <p>Standard tibial motor nerve conduction measures are established with recording from the abductor hallucis. This technique is often technically challenging and clinicians have difficulty interpreting the information particularly in the short segment needed to assess focal tibial nerve entrapment at the medial ankle as occurs in posterior tarsal tunnel syndrome. The flexor hallucis brevis (FHB) has been described as an alternative site for recording tibial nerve function in those with posterior tarsal tunnel syndrome. Normative data has not been established for this technique. This pilot study describes the technique in detail. In addition we provide reference values for medial and lateral plantar orthodromic sensory measures and assessed intrarater reliability for all measures.</p> <p>Methods</p> <p>Eighty healthy female participants took part, and 39 returned for serial testing at 4 time points. Mean values ± SD were recorded for nerve conduction measures, and coefficient of variation as well as intraclass correlation coefficients (ICC) were calculated.</p> <p>Results</p> <p>Motor latency, amplitude and velocity values for the FHB were 4.1 ± 0.9 msec, 8.0 ± 3.0 mV and 45.6 ± 3.4 m/s, respectively. Sensory latencies, amplitudes, and velocities, respectively, were 2.8 ± 0.3 msec, 26.7 ± 10.1 μV, and 41.4 ± 3.5 m/s for the medial plantar nerve and 3.2 ± 0.5 msec, 13.3 ± 4.7 μV, and 44.3 ± 4.0 msec for the lateral plantar nerve. All values demonstrated significant ICC values (<it>P </it>≤ 0.007).</p> <p>Conclusion</p> <p>Motor recording from the FHB provides technically clear waveforms that allow for an improved ability to assess tibial nerve function in the short segments used to assess tarsal tunnel syndrome. The reported means will begin to establish normal values for this technique.</p

Towards a consolidation of worldwide journal rankings - A classification using random forests and aggregate rating via data envelopment analysis

AbstractThe question of how to assess research outputs published in journals is now a global concern for academics. Numerous journal ratings and rankings exist, some featuring perceptual and peer-review-based journal ranks, some focusing on objective information related to citations, some using a combination of the two. This research consolidates existing journal rankings into an up-to-date and comprehensive list. Existing approaches to determining journal rankings are significantly advanced with the application of a new classification approach, ‘random forests’, and data envelopment analysis. As a result, a fresh look at a publication׳s place in the global research community is offered. While our approach is applicable to all management and business journals, we specifically exemplify the relative position of ‘operations research, management science, production and operations management’ journals within the broader management field, as well as within their own subject domain