Power measures in large weighted voting games : asymptotic properties and numerical methods This thesis deals with the asymptotic properties of weighted voting games (WVGs) when there are many &lsquo;small&rsquo; voters. It comprises three main parts. Part I is concerned with Penroses̉ Limit Theorem (PLT). This research goes back to a presumption of L.S. Penrose concerning an asymptotic property of some sequences of WVGs with an increasing number of voters: under certain conditions the ratio between the voting power of any two voters (according to various measures of voting powers) approaches the ratio of their weights. So far there has been no rigorous proof of PLT for any non trivial class of cases and counterexamples to Penroses̉ claim can be constructed. Part I introduces the concept of q chains of weighted voting games and considers the question whether for a given q chain and a given power index the PLT holds true ...