A reasonable argument can be made that various provisions of the Michigan Constitution violate concepts of popular sovereignty, political equality, political liberty, justice, and/or democracy, depending on how those terms are defined.
Bear in mind that these are all points on which reasonable minds can (and do) differ. Here are some possible arguments.
The term "popular sovereignty" describes the idea that the power of government derives from the consent of the people to be governed. The Michigan Constitution states this principle outright in article 1, section 1: "All political power is inherent in the people. Government is instituted for their equal benefit, security and protection."
However, the Michigan Constitution treats the idea that political power derives from the people as somewhat academic. Political power may derive from the people as a whole, but it is exercised by three separate, co-equal branches of state government: the executive (headed by the governor), the legislative, and the judicial branches.
The people do not exercise these powers directly; they do so by electing certain individuals, who generally appoint their own subordinates. For instance, instead of voting on each bill or executive order individually, Michigan residents vote for a governor, for state legislators, and for state and local court judges. While this is consistent with how a republic runs, it is inconsistent with a pure democracy, where the citizens would vote on every move the government made.
Questions about whether or how Michigan's laws violated concepts of political equality came to a head in the 2018 election. In 2018, Michigan's voters voted to amend the state Constitution to change the way the state creates voter districts (used to determine which population groups vote for state legislators and what geographic area those legislators represent).
The new rules are in article 4, section 6. Because the redistricting commission created by the new rules doesn't begin its work until late 2020, it's currently too soon to tell what effect these new rules will have on concepts of political equality. They were enacted, however, to address the fact that gerrymandering causes a decrease in political equality by changing the balance by which certain votes affect the outcome within a district.
The goal of the new rules is to move the state closer to a "one person, one vote" form of political equality, although critics claim that this will be impossible in practice. If so, article 4, section 6 will remain an example of a provision that doesn't actually guarantee political equality, despite its attempts to do so.
"Political liberty" and "justice" are perhaps the most difficult terms in this list to define. However, I would argue that a case can be made that article 1, section 26 of the Michigan Constitution affronts both. Passed in 2006 by popular vote, article 1, section 26 prohibits public schools and colleges in Michigan from using an affirmative action–based enrollment policy.
The goal of these schools' affirmative action policies was to correct longstanding imbalances in access to higher education among different racial groups. By doing so, the schools sought to create a student body that more closely resembles the actual population of the state.
The US Supreme Court ruled in 2003 that while the University of Michigan's undergraduate affirmative action policy was unconstitutional, the University of Michigan Law School's policy was not (see Grutter v. Bollinger and Gratz v. Bollinger). In other words, at least one public school had an affirmative action policy that was known to be federally constitutional—yet voters decided to prohibit the use of that policy anyway.
One could argue that this provision restricts notions of political liberty by perpetuating old patterns of imbalance in access to higher education, effectively cutting minority groups off from the political and social conversations that take place in the state's public universities. One could also argue that it restricts notions of justice by making it harder for certain citizens to access public education.