It’s been a while since Maria Sobolewska suggested to me, that perhaps the association between public attitudes and political representation may be different under different electoral systems (PR versus majoritarian). The intuition here is that institutions always work in a particular context. To some extent, my work acknowledged this by leaving out unfree countries because the expected dynamics are different — but there indeed is more to it.
I have shown that there is a strong association between positive attitudes to minorities and the inclusion of minorities in political offices.
If we look at the interaction between attitudes and electoral system, we find that this association is much stronger under majoritarian/MMM systems. Although I’m not sure that we should read much into the blue line here (PR/MMP systems) because the ethnic representation score does not vary that much.

At the same time, looking at gender representation, we find a strong association between attitudes in the population and gender representation scores.

Maybe someone wants to dig deeper here? Possibly a consideration of why PR systems may be good for minorities could complement this.
Ruedin, Didier. 2009. “Ethnic Group Representation in a Cross-National Comparison.” The Journal of Legislative Studies 15(4):335–54. doi: 10.1080/13572330903302448.
Ruedin, Didier. 2012. “The Representation of Women in National Parliaments: A Cross-National Comparison.” European Sociological Review 28(1):96–109. doi: 10.1093/esr/jcq050.
Ruedin, Didier. 2013. Why Aren’t They There? The Political Representation of Women, Ethnic Groups and Issue Positions in Legislatures. Colchester: ECPR Press.
Ruedin, Didier. 2020. “Ethnic and Regional Minorities.” Pp. 211–28 in Handbook of Political Representation in Liberal Democracies, edited by R. Rohrschneider and J. J. Thomassen. Oxford: Oxford University Press.