But, equal security established, the right of every adult rational being, male or female, to free labour, entire use of its products, and voluntary exchanges, being established; a new question presents itself. Is there no mode of human labour consistent with security – whose paramount importance even to production has been demonstrated [in the Inquiry]- but that of individual competition? May not a mode of labour be found, consistent with security, and still more productive of happiness, than labour by individual competition? […] Nay more, may there not be found a mode of labour consistent with security, which will not only obviate the evils of individual competition, but which will afford its peculiar benefits – abundant production and development of all the faculties – to a greater, an incalculably greater extent, than the best arrangements of individual competition could afford?
No mode of labour can produce preponderant good, which does not respect the natural laws of distribution, “free labour, entire use of its products and voluntary exchanges”, or the principle of equal security regarding wealth.
Such a mode of labour has been proposed. It has been called the system of labour by mutual co-operation; and its object and effect are to produce perfect voluntary equality of enjoyment of all the fruits of united labour.
From chapter V of An inquiry into the principles of the distribution of wealth most conducive to human happiness; applied to the newly proposed system of voluntary equality of wealth (1824) by William Thompson (available on archive.org). This book (along with the Appeal) is regarded as his greatest work.
This crucial chapter is the point where Thompson accepts that his construction of an economic system based on classical liberalism does not fulfil the utilitarian goal of achieving the greatest happiness. The chapter also outlines the various laws which create and perpetuate inequalities (including inheritance.)
“For Thompson, the science of happiness is concerned with the functions of society and social institutions broadly understood, and how these affect individual happiness.” (Mark Kaswan in Happiness, Democracy and the Cooperative Movement: The Radical Utilitarianism of William Thompson).