In making the case to pass beyond the contemporary geopolitical order based on sovereign nation states to some form of overarching supranational World Authority with enforcement powers, we can draw inspiration from the political philosophy of Hobbes Leviathan. Therein, Hobbes argued that people in an anarchic state of nature which in the absence of restraints would descend into a war of all against all and people would be led rationally to surrender all of their natural rights to a sovereign authority with real enforcement powers with a view to instituting a peaceful, law abiding and civilised community. We argue that the Hobbesian argument can be applied to the war of all against all that in effect characterises the geopolitical order today based as it is on absolute sovereignty of nation states and despite the efforts of international law. Hobbes never really defined the geographical extent of his supreme sovereign charged with keeping the peace: but in the context of the cotemporary world with its heightened interdependence and manifold shared policy challenges, we argue that today the Hobbesian Leviathan needs to be conceived as a World Authority. Following Kant, we argue moreover that the world sovereign does not need to be a full-blown centralised world state but rather some kind of supranational authority with enforcement powers over precisely defined supranational competences. These competences would most basically include binding and enforceable dispute settlement powers but could also include a variety of policy competences designed to deal with suitable regulation of certain aspects of the globalised world economy and the shared policy challenges which it throws up, for example, in respect of environmental sustainability and of international financial stability.