The Prediction Value

Koster, Maurice; Kurz, Sascha; Lindner, Ines; Napel, Stefan

doi:10.2139/ssrn.2361444

Cited by 2 publications

(3 citation statements)

References 19 publications

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“…Carrying methods and insights from non-binary strategic voting over into this domain looks promising. The domain of conventional power index research has also been left by Koster et al's (2014) investigation of the predictive value of knowing an individual voter's decision or voting inclination. Taking the latter as input into a model of an opinion formation process could merge traditional power analysis with the analysis of social dynamics and networks.…”

Section: Discussionmentioning

confidence: 99%

Mostly Sunny: A Forecast of Tomorrow's Power Index Research

et al. 2014

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Section: Discussionmentioning

confidence: 99%

Mostly Sunny: A Forecast of Tomorrow's Power Index Research

et al. 2014

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“…The above concept of 'conditional influence' was identified in [19], where it was shown to be the correct adaptation of absolute influence in proofs of sharp-threshold theorems for certain families of dependent measures arising in stochastic geometry and statistical physics. It has featured recently in work [32] on so-called prediction values within probabilistic games. Remark 2.3 (Success probability).…”

Section: Definitions Of Absolute and Conditional Influencesmentioning

confidence: 99%

“…Uniform bias was discussed in [46], and polarised bias in [19]. Conditional influence is essentially the prediction value of [32].…”

Section: Examples Of Influencesmentioning

confidence: 99%

On influence and compromise in two-tier voting systems

Grimmett

2019

Mathematical Social Sciences

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We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota.Square-root weights originate in the Penrose square-root system, which assumes that votes are cast independently and uniformly at random, and is based around the concept of equality of influence of the voters across the Union. There are (at least) two distinct definitions of influence in current use in probability theory, namely, absolute and conditional influence. These are in agreement when the underlying random variables are independent, but not generally. We review their possible implications for two-tier voting systems, especially in the context of the so-called collective bias model. We show that the two square-root laws invoked by Penrose are unified through the use of conditional influence.In an elaboration of the square-root system, S lomczyński andŻyczkowski have proposed an exact value for the quota q = q * to be achieved in a successful vote of a two-tier system, and they have presented numerical and theoretical evidence in its support. We indicate some numerical and mathematical issues arising in the use of a Gaussian (or normal) approximation in this context, and we propose that other values of q may be as good if not better than q * . We discuss certain aspects of the relationship between theoreticians and politicians in the design of a two-tier voting system, and we reach the conclusion that the choice of quota in the square-root system is an issue for politicians informed by theory.

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The Prediction Value

Cited by 2 publications

References 19 publications

Mostly Sunny: A Forecast of Tomorrow's Power Index Research

Mostly Sunny: A Forecast of Tomorrow's Power Index Research

On influence and compromise in two-tier voting systems

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