The Lisbon Treaty from 2009 introduced the possibility for individual member states to withdraw from the European Union (EU) on the basis of a unilateral decision. In June 2016 the United Kingdom decided to leave the EU invoking article 50 of the treaty. But is withdrawal democratically legitimate? In fact, the all-affected principle suggests that it is undemocratic for subunits to leave larger political units when it adversely affects other citizens without including them in the decision. However, it is unclear what the currency of this affectedness is and, hence, why withdrawal would be undemocratic. We argue that it is the effect of withdrawal on the status of citizens as free and equal that is decisive and that explains why unilateral withdrawal of subunits from larger units is democratically illegitimate. Moreover, on the ‘all-affected status principle’ that we develop, even multilaterally agreed withdrawal is undemocratic because the latter diminishes the future ability of citizens to make decisions together regarding issues that affect their status as free and equal. On this basis, we conclude that it is undemocratic for a member state such as the United Kingdom to withdraw from the EU.

How should the geographic boundaries of democratic participation be set? This has been a notoriously difficult theoretical question, beset by paradoxes around determining democratic participants democratically. It also is seen as increasingly important in practical terms, amid deepening interdependence between states, immigration tensions, and suprastate regional integration. Numerous recent accounts have called for extending participation beyond the state. The case is generally made on intrinsic grounds: democracy demands it. Respect for individual autonomy is said to be violated when outsiders are deeply affected by decision processes, or subject to coercion from them, without being able to participate in them. Yet, familiar problems around restrictions on the autonomy of persistent democratic minorities remain in such accounts, and they could be magnified with expanded boundaries. An alternative approach is offered here, grounded in a rights-based instrumental justification for democracy. It sees participation as foundationally – though not solely – valuable as a means of promoting and protecting fundamental rights. It recommends extending participation boundaries to reinforce protections within regional and ultimately global institutions. Democratic participation would remain crucial at all levels, not principally as an expression of autonomy but to provide checks on power and promote accountability to individuals in multilevel polities.

Let A be a domain of the boundary of a (weakly) pseudoconvex domain Ω of ℂn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain E of ℂn, depending only on Ω and A, and a complex variety W⊂E such that bW=M in E. Moreover, a generalization to analytic sets of depth at least 4 is given.

It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique. We revisit this model. A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation. The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive. The boundary problem where all observations in one particular development year or on particular underwriting year is zero is also analysed.

A global optimal control algorithm was developed with the aim of finding a control which satisfies some special requirements in the sense of obtaining singular position free movement of the redundant robot mechanism. The solution of the developed global optimal control algorithm is a boundary value problem. The additional constraints in the boundary value problem were constructed with the use of an optimization process. The usefulness of the developed global optimal control algorithm is demonstrated by the example of the 3 DOFs planar redundant robot mechanism of SCARA type.