What are the elements that link the public institutions that make up the Welfare State with the democratic rights awarded to the the status of citizen?
You've got two basic choices. Either, democracy is a precursor to the welfare state, or the welfare state is a precondition for democracy. Presumably, the reality is some combination of the two.
Historically, an extending franchise put pressure on government to develop basic welfare arrangements. Later, those arrangements promoted increased levels of political participation. But they become self-reinforcing up until the demise of the economic regime that spawned them.
The relationship between the welfare state and democracy, stop giving elements in order to explain the complexities of the present; contrary to a Martian tradition that closely foresaw the uselessness of the State or its disappearance, this, the State, today plays an enormously significant and substantial role; the nationalist or populist stakes make it look like this, and as society shrinks or expands on the tenor of the tensions between the groups -circles, as Simmel called them-, as well as the problems of asymmetries and socio-economic disparities, the precariousness in the opportunities and a certain pessimism in the future, these elements, without a doubt, pass bill of collection at the time of diagnosing the state of democracy, its problems and vicissitudes.
in the welfare state people are protected against particular risks through social security measures. These social security systems emerged in the Industrial Revolution and -at least to some extend- democratic institutions and processes were important to achieve this (in addition to to Unions, and the State, which also had an interest to strengthen social security. I think that democracy helped to strengthen the welfare state.
If you want to put it more dramatically and/or picturesque: Wolfgang Streeck (2015, p. 53) once described the relationship between liberal capitalism and social democracy as a forced ‘shotgun marriage’. The source of this quote and the article Streeck refers to provide lots of answers to your initial question.
Streeck, W. (2015). Comment on Wolfgang Merkel, “Is capitalism compatible with democracy?”. Zeitschrift für vergleichende Politikwissenschaft, 9(1-2), 49-60. http://doi.org/10.1007/s12286-015-0232-2
If we consider democracy a process much more complex and wide than the garantee of regular and universal elections - which representants legitimacy of all people's rule - than we may say welfare state is the realization of full democracy, with equality of rights and public policies.
According to systems theory, we can say that Welfare State is a form of political organization that is marked for its patterns of inclusion of population to functional systems. That means, for example, that the population, as the People, now closes operationally the Political System, giving legitimation to its procedures.
Democracy, thus, is a form of alternation of power (power as a circular means of communication between government / opposition).
Without the inclusion of people, made possible by the welfare state, there would be a structural deficit that would either make political activity (more specifically legifferent) assume an ideological character, or alibi (where problem-solving political activity is always puts on a horizon that is not reached, or experienced by most citizens).
In other words, it could be said that without sufficient inclusion of large portions of the population in the functional systems (politics, law, economy ...), there is no realization of a democratic rule of law, or even just a "rape democracy".
Interesting readings would be from the works of Marcelo Neves, on the theme "symbolic constitutionalization"
Human beings have two fundamental moral aims and ends....
Ultimate provision and absolute protection.
If we gain those things we imagine we have all we need. and everything else is extra.
Democratic government is an after-effect of production and trade. So democracy is invariably a government over a wealthy nation.
Consequently, the government tries to satisfy both our basic human urges by building up its military and providing assorted welfare programs.
In poorer countries democracies do not develop. So governments remain small and weak and whatever wealth is available is monopolized by the ruling family and backed by the military which is usually used to keep the rulers in power.
In poor countries government us usually little more than police forces and the military.
As the nations grows richer and develops into a democracy, wealth makes the welfare state possible.
Government becomes industrial regulators, school providers, healthcare providers and everything else along with an ever-growing military.
Domocracies don't necessarily need a welfare state. You would imagine they do. But what about neoliberalism which man states adopted, which rolled back the state, and gave big tax cuts to Business.
The rational was that the rich woul create jobs and spread wealth around