There is a simple, game theoretically optimal solution to gerrymandering: an iterative process of I cut, you choose.
https://www.cmu.edu/news/stories/archives/2017/november/i-cu...
https://www.cmu.edu/news/stories/archives/2017/november/i-cu...
As one example, people want to both have majority-minority districts and avoid situations in which "specific populations of voters" (to quote the article) are concentrated into a district. These goals are often opposed to each other, especially when the minorities involved skew toward one of the two parties under consideration.
So it's quite possible for a redistricting plan using the "I cut, you choose" process to end up falling afoul of Section 2 of the Voting Rights Act by diluting the voting strength of a minority...
I wonder if the game can be fairly expanded to X number of parties?
As a mathematical exercise, trying to extend the game to more than 2 parties is interesting, for sure. Real-world relevance is unclear, unfortunately.
Point being, optimizing districting to maintain a 2-party system may not be desirable, even if that's the system we've fallen into. We could change voting systems to introduce more viable parties (which has it's own problems - look at unstable governments in Europe based on oddball alliances).
That's not a problem, that's a feature. It ensures the parties need to learn to cooperate and compromise to get things through when voters are not in firm agreement. As a result you get continuity: It's rare to get the kind of drastic shifts that you get in the US when the balance shifts between the Republicans and Democrats, because it is rare for a single party to get an absolute majority, and so alliances shift with voting patterns, and the negotiated compromises tends to have to reflect a wider range of interests or not get passed.
A lot of places this leads to a tradition of broad compromises to ensure lasting reforms that won't just get undone by the next government.
So while the specific governments may not sit as tightly, I'd argue it tends to lead to a lot more stability in government direction.
Also, there's another bad consequence: In two party system when you lose the elections you really loose: other party takes the whole prize, and for you there's really nothing to do for the next four years. In multi party system even if you finish the elections on 2nd or 3rd place you may still end up joining the ruling coalition of parties, just maybe with somewhat weaker position.
Basically European system shifts focus of political parties from making deals with their voters to making deals with other parties.
The US two-parties-that-are-obviously-fractious-coalitions plus separation of powers system provides far more of those for any elected leader (because it's not a parliamentary system and lacks real mechanisms for party discipline, even a party with control of both political branches and the judiciary isn't analogous to a parliamentary-system ruling party with an outright, non-coalition majority, and isn't held accountable the way those can be.
Keeping separation of powers and adopting a more proportional system for the House of Reps, even straight party list (which would require Constitutional change), or state level party list or STV with or without some level of districting (which may or may not require Constitutional change) would not meaningfully add to the excuses for failure to deliver on promises.
In fact, systems with greater proportionality in legislative elections produce higher satisfaction with government, which should be unsurprising: electing a government that's views actually align with those of the population results in government policy more aligned with public preferences. Which, after all, is the whole premise of representative democracy.
Well yes, but since you have more than three parties (I don't know what country you're from, or how many viable parties you have), voters can be less forgiving.
I heard somewhere[0] that a market needs at least four somewhat viable players, in the sense that one is a monopoly (bad), but two and three players can still control the market in an undesirable manner.
It probably also depends very much on the particulars of the government, how much power the opposition parties still have versus the coalition, if there's multiple Houses and how they interact, etc.
Either way, I do believe that having multiple viable parties (and preferably at least four?) is a good thing compared to having only two real contenders. But this is mainly because I'm looking at the UK and US for examples of two-party systems. From both I understand that a very large portion of the voting population are rationally aware that their votes will almost certainly not make any difference whatsoever. If anyone knows about other countries with two-party systems that actually make many voters feel well (or at least fairly) represented, I'm curious to hear about them.
[0] I don't have a citation sorry. It was on the news, in the context of the number of mobile network operators in the Netherlands being down to three, due to a merger. And afaik all of them are now multinationals. But not only do I not have a citation, neither can I really say whether the same holds for political parties in a democracy. So take this for what you like :)
Those systems aren't really unstable, they just formalize things that go on behind the scenes in the US system where the major parties are actually internally diverse coalition with competitive factions.
vs hammering through legislation with zero bipartisanship.
Which is actually a problem in parliamentary systems that end up with majorities.
These coalition governments are a feature, not a bug.
https://www.quantamagazine.org/new-algorithm-solves-cake-cut...
And it's not clear if one of the cake cutters could sacrifice their own slice to benefit one of the others (in return for a bribe).
(Suppose four players, P1 to P4. They each get to place two settlements, and there's an advantage to getting first pick. You place settlements in this order: P1, P2, P3, P4, P4, P3, P2, P1)
Now, there is a cake (map) to cut, and 4 parties. P1 draws one line, then P2, then P3. Then, each party picks one of the 4 slices, starting with P4.
Cake? Maybe. Equal-population single-winner firdt-past-the-post political districts, no. But that's okay, because single-winner districts don't practically support more than two competitive parties, especially when you have separately elected statewide and national executives rather than a parliamentary system.
Of course, get rid of single-winner FPTP districts, and you not only can support more parties, you make gerrymandering mostly pointless, even if you do still have districting.