That's one approach, favoured by the Ayn Rand types. The other perspective is that society is greater than the sum of it's parts, more of a Marxian take on things. I favor the latter view.
We are not voting for a mayor of you or me, but a mayor of the city. In some instances, decisions will be made that run against my best interest but that are better for the city overall. And in the end, a healthy city is good for me too. Fact is, I can't think of a single policy that benefits me directly, but there may be millions of rules that impinge on me, from taxes to one-way streets. But somehow I end up better off in the end with a functioning, liveable city than I could in the libertarian fantasyland envisioned by the right.