Political participation theory seems to lack consensus among academics:
La Ferrara, E. (2002). Inequality and group participation: theory and evidence from rural Tanzania. Journal of Public Economics, 85(2), 235-273.
Teorell, J. (2006). Political participation and three theories of democracy: A research inventory and agenda. European Journal of Political Research, 45(5), 787-810.
Brady, H. E., Verba, S., & Schlozman, K. L. (1995). Beyond SES: A resource model of political participation. American Political Science Review, 89(02), 271-294.
Fund voting is an answer, see Democracy with sequential choice and fund voting by Björn S. Stefansson. More about the idea of fund voting in On Arrow´s possibility theorem by the same author.
I would suggest finding a general theoretical model on intention to vote, motivation or participation models and build off of one to include minority concerns, obstacles etc. Try emailing: Todd Rodgers author of the book below and see what he has to offer:
Gerber, A. S., & Rogers, T. (2009). Descriptive Social Norms and Motivation to Vote: Everybody's Voting and so Should You. The Journal of Politics, 71(1), 178-191.
You may consider looking at the theory of planned behaviour, which is a predictive model that can be modified to include minority intentions to vote. The USA voting patterns during the 2008 election demonstrated that when minority interests are front-and-center that they will involve themselves.