I doubt that we give enough thought to what we mean by the common good, because a good may be common, or shared, in a number of different ways:
Type 1. It may be like the good of conversation for those participating in it: Unless they are competing for approval, if the conversation is better for some, it is better for all.
Type 2. It may be like the good of a bridge: This is a “public” good as economists use the term, so that if one has the benefit, all have it, unless access is artificially restricted.
Type 3. It may be like the good of national security: This is another public good in the economic sense, except in this case it is hard to see how access even could be restricted. If invaders are kept out of the country for me, they are also kept out of the country for you.
Type 4. It may be like the good of virtue: You get one kind of benefit from having it, but I get another kind of benefit from the fact that you have it -- and if you have greater virtue than I do, you didn’t get it by taking it from me.
There are some things that are often called common goods, that aren’t. For example, the so-called aggregate pleasure of which utilitarians speak is not a common good in any reasonable sense. In the first place, pleasure can’t be aggregated. But even if it could, some things that give one person pleasure may give other persons pain.
And then there some things that are often called common goods, but may or may not be. For example, it’s not hard to see why the country’s prosperity is called a common good, because we do all share material needs. But it is really a common good only if I can get more than I have without making you poorer; otherwise it isn’t. Whether this is possible depends on our social arrangements.