So, let's see some definitional choices. You have several options: you could define each word separately (which we'll do first), or define the phrase (which we'll attempt at the end).
Dictionary.com (Random House):
government by the people; a form of government in which the supreme power is vested in the people and exercised directly by them or by their elected agents under a free electoral system.Merriam-Webster: 1: of, relating to, or favoring democracy. Democracy, of course, meaning:
1 a: government by the people ; especially : rule of the majority b: a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free electionsBlack's Law Dictionary (8th edition) defines democracy thusly: Government by the people, either directly or through representatives.
Notice a pattern? All of these are focused on democracy as a form of government, which is fine--and defensible. When combined with "society," the phrase would mean a people or culture sharing a representative or directly-elected government. This is the definition that probably squares best with a "social contract" case based on Rousseau's conception (in particular) or Locke's version (with slight modification or allowances).
However, "democratic" also has a different connotation. Dictionary.com:
2. pertaining to or characterized by the principle of political or social equality for allMerriam-Webster's:
3: relating to, appealing to, or available to the broad masses of the people <democratic art>4: favoring social equality : not snobbishThese definitions work best with a value of equality or equal treatment under the law.
Next, "society." This shouldn't be too problematic. I like Merriam Webster's here:
3 a: an enduring and cooperating social group whose members have developed organized patterns of relationships through interaction with one another b: a community, nation, or broad grouping of people having common traditions, institutions, and collective activities and interestsEither one would probably work for the purposes of your case.
Can we define the phrase as a phrase? Perhaps. A definition that comes quite close is found in an analytical passage from Cuban Communism, by Horowitz and Suchlicki, p. 430:
A truly democratic society is defined not only by its party structure, constitution, delegation of authority, or electoral representation, but by its capacity to tolerate and incorporate dissent.If felon disenfranchisement becomes a way of squelching dissent, we have a germane definition.
If I can find better examples, I'll update this entry.
Last, for a more substantial analysis of the normative attractions and problems of democracy, see the Stanford Encylopedia's entry on the subject. Particularly useful is the section discussing the values justifying democracy--a few of which could be used as core values in your constructive.