Gerrymandering is the art of drawing single-seat districts so that one party's voting strength is used more efficiently than a rival's. Typically, a majority party arranges several 55-45 districts for itself for each lonely 90-10 ghetto granted to "the enemy".
To achieve such segregation, tortured district boundaries often end up looking like animals with legs (e.g. salamander). A 19th century politico named Gerry became (in)famous for some of the earliest such districts in America. Gerry + salamander => gerrymander.
When it can be enacted, such exploitation can convert one election's simple majority in the electorate into the next election's supermajority in the legislature, perhaps able to modify its state's Constitution to its own advantage. Thus, gerrymandering can most undemocratically enable a simple majority to arrogate to itself new powers that only a supermajority (or virtual consensus) of the people should properly be allowed to grant.
Failing that, if a once-majority faction's popularity slips, gerrymandering can prop up a 40% electoral minority into a narrow legislative majority that might continue the cycle in the next redistricting. Therefore, gerrymandering can most undemocratically entrench an unpopular minority faction long after its should have been swept from power.
In short, gerrymandering, along with other electoral exploits, cuts at the heart of democracy (enlightened representative government by universal consent of the governed).
Fortunately, both the calculations and process of gerrymandering are prone to systemic weaknesses that can inhibit their abuse:
If state constitutions were modified to exploit gerrymandering's weaknesses along the opportunities I've revealed, then it (and two-party tyranny) would vanish like a bad dream.
Requiring legislative supermajorities to redistrict would reduce the chance for any one faction to control all decision points. Unfortunately, State legislatures often have so much difficulty agreeing on new district lines that requiring a supermajority might be impractical.
Even better than making control difficult is to remove it altogether. Just breaking the feedback loop between redistricting and the politicians elected therefrom reduces tyranny somewhat. Going further and deliberately balancing a commission can in practice come close to proportional representation (at least between the presumed two majority parties). Sometimes, miracle of miracles, a commission even produces some competitive districts.
Referendum is the ultimate in decision point removal. However, the electorate at large can't afford to devote full-time attention and energy to analyzing the pros and cons of very many complex decisions, so referendum should be invoked only sparingly, like when a conflict of interest exists between our representatives' personal ambitions and their public duties. I think that redistricting is one of those decisions, so a referendum would be in order. It could work something like this:
Have a separate referendum for each set of districts (US House, state senate, other state chamber). For each set, allow the governor and each legislator (co)sponsor one and only one legitimate (population balanced) redistricting plan. Require each such plan to be referred to the state's voters at large. Optionally, allow voters to add their own (population balanced) plans via initiative petition.
For each plan, show a map of the district borders and list how many voters voted for each gubernatorial candidate in each proposed district in the last general election. Have voters vote up or down on each plan. For each set of districts, adopt the one plan garnering the greatest number of favorable votes.
I expect only a handful of plans for each set of districts, each having many cosponsors. The winner in each referendum will probably be a plan that neither favors nor shafts any particular faction. Voters may even favor plans that offer competitive districts, which are more likely to be drawn by outsiders and qualified by petition.
Tighten each district's ratio between perimeter and area, and map makers would have less maneuvering room to skew representation. Unfortunately, that won't stop them from trying.
Until it is tried on a large scale, I can't prove that AV completely neutralizes gerrymandering. However, I have many reasons to expect AV to hit multiple points described above:
Combined, these go a long way toward cracking the two-party "system" and therefore liberating voters from tyrants:
Parties would still exist and endorse candidates. I would never propose anything as oppressive of free association and free speech as what commonly passes for "nonpartisan" in many Counties and municipalities. However, I would leave political parties to their own devices for admitting members, endorsing candidates, and communicating those endorsements to voters.
The effect of this separation is indirect yet profound: Once political parties are divorced from the formal electoral process, then the government can no longer justify regulating them and their free speech. Abolishing such abhorrent restrictions removes an entire arsenal of weapons by which America's two major parties entrench themselves in power (both singly and in combination).
Further, If ballots are blind to party affiliation, then access thereto shouldn't depend on it. Therefore, separation of party and state should also abolish outrageous ballot access rules whereby powers that be violate equal protection of the law to grant special privileges to themselves and heap unfair expense upon outside challengers.
The founding fathers may have structured the government with internal checks and balances, but they left legislators entirely too much unfettered latitude to corrupt the electoral process, thereby undermining their elegant structure. If We the People truly want a more perfect union, then we need to finish the structure by defining a few checks and balances connecting the government to its electoral foundation.