In Mixed Company, players select topics for debate, vote on each other's choices then debate the topic that gets the most votes. Players have 'trophy' cards to award each other at the end of a debate; for example, 'Best personal example' and 'Most enjoyable conversation'. To that extent, players are grading each other's contributions, but the main thrust of Mixed Company is to encourage discussion and debate.
There are optional 'action' and 'challenge' cards that can be introduced to shake things up a bit. With 'action' cards, players can pose a question to the speaker, ask for an example or for more details, or demand that the speaker cite a source. The 'challenge' cards make things more difficult for the speaker by, for example, imposing limitations on the words a speaker can use or preventing them from using their hands. A 'counter point' card requires the speaker to take a contrary view of their own argument.
The topics in Mixed Company are divided into 'all ages' and those rated 'Age 16+'. The latter doesn't mean the cards are NSFW ('not safe for work'; ie: rude or offensive) just that they include some topics that would be of less relevance to younger participants, mostly relating to work or relationships. That said, there were certainly topics in both sets of cards that some of us felt would better belong in the other.
In the UK, most primary schools make use of 'Circle Time' where children are seated in a circle and discuss a topic suggested by the teacher or by the children themselves. These are used to discourage bullying or issues arising from unkind behaviour as well as to reinforce children's listening skills and turn taking. Mixed Company is not so much a game in the conventional sense as a tool to be used in 'Circle Time' or its equivalent. There will certainly be families who will find it helpful to reinforce the four 'Conversation Guide' principles that are printed on each player's card and which underpin the game.
Mixed Company is due to come to Kickstarter tomorrow. You should be able to access the campaign by clicking here.