You could throw darts at a list of large companies and weight them with some really dumb rules and get an index that's pretty close to "the market"; that's basically what the Dow is.
The difference between even the S&P 500 and a total market index (i.e. all the smaller stocks that exist) is pretty insignificant to returns (and recently bad for them), and I believe the total market funds have become more popular than the traditional S&P 500 ones anyway.