Why must the outcome "be representative of the total population"? If group X is Y% of the national population, must group X also be exactly Y% of the student body at universities? It is inevitable that, in anything, some groups will be overrepresented and other groups underrepresented, partly just by random chance, partly due to all kinds of complex cultural and historical reasons. To the extent under-representation is due to bad historical reasons (past oppression/persecution/discrimination/etc), then yes I think something should be done about it. But why not do that at the individual level, of the individual who is socially disadvantaged due to that history of oppression?
I have no problem with the idea that people from disadvantaged backgrounds get some special consideration. But compare two individuals: (a) a person from an under-represented racial/ethnic minority who comes from a privileged background (e.g. parents who are university professors, politicians, corporate executives, doctors, lawyers, etc) (b) a person from the ethnic/racial majority (or a minority which is not considered to be "under-represented") who grew up in extreme poverty, suffering from child abuse and neglect, parental drug addiction and criminality, homelessness, etc. How is a system fair if (a) gets given a preference but there isn't one for (b)? That's why I think affirmative action should be based on individualised assessment of social disadvantage, not group membership.