Following the recent US Supreme Court decision that gerrymandering for political purposes is not prohibited by the US Constitution, I realized that it can be hard to understand what rules related to elections and voting rights are actually constitutionally guaranteed. Are any, or are the rights US voters have instead conferred by federal, state, and local laws?
I'm not just interested in a readout of constitutional wording but a summary of what such text actually means in practice.
Regarding constitutional guarantees and rules related to elections and voting rights:
The relevant text of the United States Constitution, article 1, section 4 reads:
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing Senators.
The 14th amendment section 2 is also relevant
...when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.
So very simply, state legislatures have the power to oversee elections, but the US Congress has the power to step in when they see fit. Also everyone has the right to vote except for criminals. It says males, but, of course, it was later extended to women as well with the 19th amendment.
Regarding the recent court decision about gerrymandering on these constitutional protections:
In the case you're referencing, the opinions of the justices are publicly available and quite readable. One relevant section from Robert's majority opinion:
Appellants suggest that, through the Elections Clause, the Framers set aside electoral issues such as the one before us as questions that only Congress can resolve. See Baker, 369 U. S., at 217. We do not agree. In two areas— one-person, one-vote and racial gerrymandering—our cases have held that there is a role for the courts with respect to at least some issues that could arise from a State’s drawing of congressional districts. See Wesberry v. Sanders, 376 U. S. 1 (1964); Shaw v. Reno, 509 U. S. 630 (1993) (Shaw I ).
But the history is not irrelevant. The Framers were aware of electoral districting problems and considered what to do about them. They settled on a characteristic approach, assigning the issue to the state legislatures, expressly checked and balanced by the Federal Congress. As Alexander Hamilton explained, “it will . . . not be denied that a discretionary power over elections ought to exist somewhere. It will, I presume, be as readily conceded that there were only three ways in which this power could have been reasonably modified and disposed: that it must either have been lodged wholly in the national legislature, or wholly in the State legislatures, or primarily in the latter, and ultimately in the former.” The Federalist No. 59, p. 362 (C. Rossiter ed. 1961). At no point was there a suggestion that the federal courts had a role to play. Nor was there any indication that the Framers had ever heard of courts doing such a thing.
Here he argues that while the courts can step in clearly enumerated rights like one person one vote or racial discrimination, the courts weren't designated power to intervene in partisan political disputes over districting.
In Kagan's dissent, she argues that the 1st and 14th amendments provide protection against partisan gerrymandering, in a somewhat more abstract way.
Partisan gerrymandering operates through vote dilution—the devaluation of one citizen’s vote as compared to others. A mapmaker draws district lines to “pack” and “crack” voters likely to support the disfavored party. See generally Gill v. Whitford, 585 U. S. , __– (2018) (slip op., at 14–16). He packs supermajorities of those voters into a relatively few districts, in numbers far greater than needed for their preferred candidates to prevail. Then he cracks the rest across many more districts, spreading them so thin that their candidates will not be able to win. Whether the person is packed or cracked, his vote carries less weight—has less consequence—than it would under a neutrally drawn (non-partisan) map. See id., at __ (KAGAN, J., concurring) (slip op., at 4). In short, the mapmaker has made some votes count for less, because they are likely to go for the other party.
That practice implicates the Fourteenth Amendment’s Equal Protection Clause. The Fourteenth Amendment, we long ago recognized, “guarantees the opportunity for equal participation by all voters in the election” of legislators. Reynolds v. Sims, 377 U. S. 533, 566 (1964). And that opportunity “can be denied by a debasement or dilution of the weight of a citizen’s vote just as effectively as by wholly prohibiting the free exercise of the franchise.” Id., at 555. Based on that principle, this Court in its one-personone-vote decisions prohibited creating districts with significantly different populations. A State could not, we explained, thus “dilut[e] the weight of votes because of place of residence.” Id., at 566. The constitutional injury in a partisan gerrymandering case is much the same, except that the dilution is based on party affiliation. In such a case, too, the districters have set out to reduce the weight of certain citizens’ votes, and thereby deprive them of their capacity to “full[y] and effective[ly] participat[e] in the political process[].” Id., at 565. As Justice Kennedy (in a controlling opinion) once hypothesized: If districters declared that they were drawing a map “so as most to burden [the votes of] Party X’s” supporters, it would violate the Equal Protection Clause. Vieth, 541 U. S., at 312. For (in the language of the one-person-one-vote decisions) it would infringe those voters’ rights to “equal [electoral] participation.” Reynolds, 377 U. S., at 566; see Gray v. Sanders, 372 U. S. 368, 379–380 (1963) (“The concept of ‘we the people’ under the Constitution visualizes no preferred class of voters but equality among those who meet the basic qualifications”).
And partisan gerrymandering implicates the First Amendment too. That Amendment gives its greatest protection to political beliefs, speech, and association. Yet partisan gerrymanders subject certain voters to “disfavored treatment”—again, counting their votes for less— precisely because of “their voting history [and] their expression of political views.” Vieth, 541 U. S., at 314 (opinion of Kennedy, J.). And added to that strictly personal harm is an associational one. Representative democracy is “unimaginable without the ability of citizens to band together in [support of] candidates who espouse their political views.” California Democratic Party v. Jones, 530 U. S. 567, 574 (2000). By diluting the votes of certain citizens, the State frustrates their efforts to translate those affiliations into political effectiveness. See Gill, 585 U. S., at ___ (KAGAN, J., concurring) (slip op., at 9) (“Members of the disfavored party[,] deprived of their natural political strength[,] may face difficulties fundraising, registering voters, [and] eventually accomplishing their policy objectives”). In both those ways, partisan gerrymanders of the kind we confront here undermine the protections of “democracy embodied in the First Amendment.” Elrod v. Burns, 427 U. S. 347, 357 (1976) (internal quotation marks omitted).
Given this relates directly to the Supreme Court ruling, turning to the majority opinion, which covered this, sheds some light on what rights they explicitly upheld. It's also worth noting that these are directly related to Congressional redistricting:
In two areas—one-person, one-vote and racial gerrymandering—this Court has held that there is a role for the courts with respect to at least some issues that could arise from a State’s drawing of congressional districts.
So your answer is, federally and in relation to Congressional districts, two points:
They go on to clarify:
The claim of population inequality among districts in Baker v. Carr, for example, could be decided under basic equal protection principles. 369 U. S., at 226.
This seems to support adding a third:
Racial discrimination in districting also raises constitutional issues that can be addressed by the federal courts. See Gomillion v. Lightfoot, 364 U. S. 339, 340.
They do contend that partisan gerrymandering is, at least in some cases, explicitly allowed:
Partisan gerrymandering claims have proved far more difficult to adjudicate, in part because “a jurisdiction may engage in constitutional political gerrymandering.” Hunt v. Cromartie, 526 U. S. 541, 551.
Specifically:
Partisan gerrymandering claims rest on an instinct that groups with a certain level of political support should enjoy a commensurate level of political power and influence. Such claims invariably sound in a desire for proportional representation, but the Constitution does not require proportional representation, and federal courts are neither equipped nor authorized to apportion political power as a matter of fairness.
They also directly address one-person, one-vote and racial gerrymandering as it relates to political gerrymandering:
The fact that the Court can adjudicate one-person, one-vote claims does not mean that partisan gerrymandering claims are justiciable. This Court’s one-person, one-vote cases recognize that each person is entitled to an equal say in the election of representatives. It hardly follows from that principle that a person is entitled to have his political party achieve representation commensurate to its share of statewide support. Vote dilution in the one-person, one-vote cases refers to the idea that each vote must carry equal weight. That requirement does not extend to political parties; it does not mean that each party must be influential in proportion to the number of its supporters. The racial gerrymandering cases are also inapposite: They call for the elimination of a racial classification, but a partisan gerrymandering claim cannot ask for the elimination of partisanship.
I've added a link to justiciability, as it directly relates to the majority ruling. It's a complicated issue but boils down to whether the courts have authority to intervene.
It's worth noting the dissenting opinion offers a scathing rebuke:
The partisan gerrymanders in these cases deprived citizens of the most fundamental of their constitutional rights: the rights to participate equally in the political process, to join with others to advance political beliefs, and to choose their political representatives. In so doing, the partisan gerrymanders here debased and dishonored our democracy, turning upside-down the core American idea that all governmental power derives from the people. These gerrymanders enabled politicians to entrench themselves in office as against voters’ preferences. They promoted partisanship above respect for the popular will. They encouraged a politics of polarization and dysfunction. If left unchecked, gerrymanders like the ones here may irreparably damage our system of government.
