Public reason liberalism is an important approach to social and political philosophy that has two main tenets. We could summarize these tenets as

  1. Laws and institutions must be justified from the point of view of the people who are expected to obey them — and those people have diverse beliefs.
  2. “Liberal” laws and institutions are the ones most likely to be justified to all those diverse people. Indeed, liberal institutions may even be unique in having such justification in modern, deeply diverse societies.

I will explain each of these tenets in turn.

Justification and Diversity

The basic context for the notion of public justification is the recognition that even well-informed people of good will have very different religious, moral, and philosophic views. In light of this diversity of views, public reason theorists hold that certain shared institutions, such as coercive political institutions or systems of social-moral rules, must be justified to each person.
If we are to respect each other, have a fair system of cooperation between free and equal people, or realize other fundamental values, then our institutions must be justified to the diverse members of society. When there is adequate justification for each person, we say that the institution is publicly justified or supported by public reason.

Shared vs. Convergent Reasons

Now, there are different ways in which such public justification may be achieved. Some theorists emphasize (or exclusively permit) the use of “shared” reasons. This means finding some core values that each member has and then discerning what institutions may be justified by appeal to those alone.
Other theorists emphasize the use of “convergent reasons,” in which different people’s diverse beliefs and values lead to a common point. How does that differ from the “shared” approach?
Let’s use an everyday example: for a Friday night meal with friends, using shared reasons may lead us to get a pizza (because everyone likes pizza). Convergent reasons may lead us to go to a restaurant where I like the sandwiches and you like the soups. In that case, we may not like any of the same foods, but our interests “converge” in going to the same restaurant that lets us get the different foods we do like.
Through either of these forms of reasoning, we can share a meal we can all agree on, rather than some of us having to just live with the choice imposed by others.
That’s the big idea of the public reason in “public reason liberalism.” But what does the liberalism part mean?

Liberalism

By “liberalism,” here, I mean institutions incorporating individual liberties such as those regarding religion, association, speech, bodily integrity, and personal property, as well as political institutions characterized by democratic procedures, the rule of law, limited powers, and systems of checks and balances.
Liberal institutions entrench individual liberties, giving them a very high, if not absolute, priority when in conflict with other concerns. So, for instance, freedom of speech is restricted only in rare and special circumstances.

Liberal institutions entrench individual liberties.”]
Consider the institutions of freedom of religion and the separation of church and state. No institution that politically imposed one particular religion on a group of diverse people could be publicly justified. But freedom of religion could be supported by all persons as something at least acceptable, even if not optimal, from their own perspective. This freedom provides for each person a valuable system of peaceful coexistence in which she can at least pursue her values to a significant degree and promote those values to others.
Moreover, different perspectives may provide convergent reasons for this set of liberal institutions. Atheists may want the separation of church and state so that the state does not promote (what they take to be) false views. Members of various religions may support the separation in order to insulate churches and mosques and so on from the corrupting influence of politics.
In general, public reason liberals argue, the liberal system of personal liberties and limited government ensures for each person a sphere of action in which they can pursue their own values and conceptions of the good life.
Of course, theorists within public reason liberalism argue about exactly which institutional features are necessary or would be publicly justified. And there is particular disagreement among theorists with regard to systems of private property rights, economic planning and regulation, and the provision of health and educational services.
Despite these disputes, public reason liberals share an embrace of the core liberal institutions, and remain focused on the search for institutions that can be justified to all in light of our deep and enduring diversity.