Evidence that countries with proportional electoral systems have lower levels of income inequality has been compiled by Fair Vote Canada on their Evidence webpage at this link. The below is an excerpt/quote from that webpage:
Income Inequality
Lijphart (2012: 282) found that countries with proportional systems had considerably lower levels of income inequality.
Likewise, Birchfield and Crepaz (1998:192) found that “consensual political institutions [which use PR] tend to reduce income inequalities whereas majoritarian institutions have the opposite effect.” The results of the regression work they present were highly significant, with PR accounting for 51% of the variance in income inequality across countries. Birchfield and Crepaz explain this result in terms of the higher degree of political power of people in PR systems. In their words (1998:191):
“The more widespread the access to political institutions, and the more representative the political system, the more citizens will take part in the political process to change it in their favour which will manifest itself, among other things, in lower income inequality. Such consensual political institutions make the government more responsive to the demands of a wider range of citizens.”
Vincenzo Verardi, in a study of 28 democracies (2005), also found that when proportionality increases, inequality decreases. Iversen and Soskice (2006) found that PR is associated with greater efforts to promote income redistribution.
Bernauer, Giger and Rosset (2015) looking at 24 Parliamentary democracies, found that the political preferences of low income citizens are better represented in a more proportional system, and the political preferences of the rich are better represented in a winner-take-all system.
Footnotes:
Lijphart, Arend (2012). Patterns of Democracy. Government Forms and Performance in 36 Countries. New Haven, CT: Yale Press.
Birchfield, Vicki and Crepaz, Markus (1998). “The Impact of Constitutional Structures and Collective and Competitive Veto Points on Income Inequality in Industrialized Democracies.” European Journal of Political Research 34: 175-200.
Verardi, Vincenzo (January 2005). ”Electoral Systems and Income Inequality.” Economics Letters, 86-1: 7-12.
Iversen, T., & Soskice, D. (2006). “Electoral Systems and the Politics of Coalitions: Why Some Democracies Redistribute More Than Others". American Political Science Review 100-2: 165–81.
Bernauer, Giger and Rosset (2015). “Mind the gap: Do proportional electoral systems foster a more equal representation of men and women, poor and rich?” International Political Science Review. 36-1: 78-98.