Wider share ownership?: investors in English and Welsh Bank shares in the nineteenth century

The joint-stock banks that established after the liberalizing legislation of 1826 were periodically criticized during the nineteenth century for their low-quality and rapidly deteriorating shareholder constituencies. The quality of a bank's shareholding constituency was of paramount importance because of unlimited shareholder liability. Using archival records, this article examines the quality of bank shareholder constituencies over the nineteenth century. The main finding is that shareholder constituencies did not deteriorate in quality until the introduction of limited liability. The non-deterioration of constituencies is attributed to bank deeds which locked in the aggregate quality of shareholder constituencies by empowering directors to vet all share transfers.

Extending Zipf’s law to n-grams for large corpora

Experiments show that for a large corpus, Zipf’s law does not hold for all rank of words: the frequencies fall below those predicted by Zipf’s law for ranks greater than about 5,000 word types in the English language and about 30,000 word types in the inflected languages Irish and Latin. It also does not hold for syllables or words in the syllable-based languages, Chinese or Vietnamese. However, when single words are combined together with word n-grams in one list and put in rank order, the frequency of tokens in the combined list extends Zipf’s law with a slope close to -1 on a log-log plot in all five languages. Further experiments have demonstrated the validity of this extension of Zipf’s law to n-grams of letters, phonemes or binary bits in English. It is shown theoretically that probability theory
alone can predict this behavior in randomly created n-grams of binary bits.