TL;DR
This paper investigates how well voting power can be approximated by voting weights, providing precise error bounds for certain power indices and demonstrating limitations of such approximations.
Contribution
It offers new quantitative bounds on the approximation of voting power by weights and establishes impossibility results for certain cases.
Findings
Approximation bounds with explicit error margins for power indices.
Impossibility results showing limitations of weight-based power approximation.
Insights into when power is nearly proportional to weights.
Abstract
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights, which is very beneficial for both theoretical considerations and practical computations with many members. We present quantitative approximation results with precise error bounds for several power indices as well as impossibility results for such approximations between power and weights.
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