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FYI, you can play a nice implementation of this game online for free at BoardGameArena.com:

https://boardgamearena.com/gamepanel?game=mapmaker

(Note: as with most games on BGA there's no AI/solo mode -- you'd be playing against other players).

Looks like fun. Wonder how many HN readers will end up playing together today off this link!
This is why we can’t have nice things. How on earth do we make politicians do something that goes against their electoral interests?
Somehow some countries like New Zealand managed to move away from these issues so it is possible.
It sure is way easier with a < 5 MM population and an overall small country. I don't think it's a good example of what's possible or not.
Now remember kids.

There's only two political parties, so vote for the one that's going to win. It feels good to be on the winning team after all.

If you'd like to be a politician, daddy wasn't part of the political elite. You're gonna have to become a communist, or corrupt billionaire before people want to vote for you.

Lying, propaganda and fear mongering is allowed provided you only do it for votes. And to curry favours for donations.

You must harshly judge everyone else on their past -- especially when they were s teen-ager saying stupid stuff on Twitter. Don't worry as a politician, you're immune.

No matter what your opponent says, even if it's a fantastic idea. Shoot it down for the greater good.

Black people and minorities are a tool for pandering to or vilifying depending on the colour of your tie. They can't think for themselves after all.

War is a fantastic way to save the economy by confusing everyone.

And that kids is how you become president of USA/Canada/France or prime minister of UK/Australia/New Zealand.

---

Please make them game instructions.

The are several algorithms which could fairly and objectively divide up a region, like by minimizing the surface area of a number of equal population squares. So technically it's easy to solve.

The problem the courts have identified is that there are multiple ways to do it and each will benefit one side over another. So the court has no way to say which is correct and force a place to use a single algorithm.

But this is something the legislature could easily do - any algorithm is better than what we have now, it just needs to be fixed once and put into the constitution so it's hard to change.

The problem of picking one thing is that obviously if the thing getting picked isn't in your favour you generally have a legitimate case in calling bias.

...unless there's a random element to it, so that at the time of picking a method the pickers have no way of knowing what party it will swing in favour of. Then there's no way to claim they made a biased choice, as long as the expectation of the randomness is zero.

> So technically it's easy to solve.

The problem is not the assignment of the dividing lines. The problem is getting millions of people to agree to a new and different system: the tyranny of the installed base. Writing and releasing the patch is trivial. "Solving" also means deployment.

An even bigger issue is that most algorithmic districting would violate the Voting Rights Act, strangely! There are many, many requirements to designing what seems like a "good" set of district boundaries, but several of them are contradictory!

An excellent source to see such a algorithm in action is https://projects.fivethirtyeight.com/redistricting-maps/#Com...

The way to solve Gerrymandering is not geometry, but by removing the incentive.

It's easy to remove the incentive: Just add some statewide delegates that are elected based on the "wasted" votes. That way you get both local representation and overall proportionality.

I never see this discussed in the US context, even though it's done like that all over the world. Apparently people will rather come up with obscure algorithms based on problematic census data.

Is that doable? My understanding is it would require a constitutional change in contrast to a simple law which is even more unlikely considering the current political climate. Then again, why bother with the district thing for non-local politics if you are at it in changing the constitution of a country.
I believe that would require a change to the constitution, which is currently politically impossible, as it would require Republican support, and it is Republicans that created the current extreme gerrymanders and benefit from them.

The only way I could see something like what you suggest happening would be for the Democrats to gerrymander the blue states to even things out, and then a better solution could be agreeable to both sides.

> I believe that would require a change to the constitution, which is currently politically impossible

I guess you are right, but isn't that the same deal with the filibuster? Anvf that hasn't stopped people from talking about it.

THe filibuster in the senate can be changed or removed with a simple majority, i.e. 9 less than the number of votes needed to break a filibuster.
The filibuster isn't written into the Constitution: it's actually just Congress setting its rules of order. Changing the Constitution is a big and difficult process.
Only the state constitutions as far as I know. Every state decides on its own how to conduct elections.
No, at-large reps used to be a thing until a lawsuit made its way to the Supreme Court, who said it was illegal. I believe that the death knell of the idea might have been the reapportionment bill in 1929.
Personally I find one representative per 700,000+ constituents a little unrepresentative. I don’t call my representative “local” if they are representing more then a few thousand. I wonder why we bother with single party electorates at this point, and not just move to all proportional voting.
The https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore... more or less states that there's no solution to the representative problem.

I live in a country using another method, and in each election a lot of people begs for a change in the aggregation system. Some even say that the U.S. system is the best solution, while you are defending basically our election system.

That's not was Arrows theorem says at all. It just says that all (deterministic) voting systems can sometimes incentivise tactical voting.

"Tiered" voting, where we add up local majorities, is known as the tribe system in mathematical social choice theory and can be proven to be the worst possible in terms of making the individual vote matter.

I thought the standard interpretation of Arrow's theorem was that if no voting system satisfies the hypotheses, then there is no such thing as an objective electoral mandate, and therefore almost any set of rules that's generally acceptable to the constituents is equally valid. Am I misunderstanding something? I'm not an expert on this at all.
It's crucial especially in practice for something in the real world like US gerrymandering, to remain aware that Arrow is talking about the hypothetical worst case. This isn't "No system can work" it's "No system will always work".

If out of 5000 voters, 4985 voters prefer Alice to anybody else, 10 prefer Bob and only 5 prefer Charlie; Arrow does not mean Bob and Charlie can tell their voters "See, nobody knows who really won". Alice won. Overwhelmingly the voters prefer Alice. Arrow has nothing interesting to tell us about this scenario.

But if only 2400 prefer Alice, 1800 prefer Bob and 800 prefer Charlie, it gets trickier and Arrow starts to appear on the horizon. After all, what if every one of those Charlie supporters hates Alice and would rather have voted for Bob than see Alice win? We can try to improve our system to try to ensure we get this case right, but Arrow proves that we can't ever do a good enough job for every such case.

Especially in the case of US election it's worth remembering that if you only have two candidates, Arrow doesn't actually apply at all. A straight-forward majority works fine if all you wanted to do was decide whether the Red or Blue team wins.

I think you're talking about Gibbard–Satterthwaite theorem

Arrow's Theorem doesn't care about "tactical voting", it's about the Impossibility of what appear to be intuitively reasonable fairness constraints on the outcome. Specifically you cannot have: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives

Gibbard–Satterthwaite says if there are at least three candidates, then either one of them can't win, or some of the electorate should offer an insincere preference (ie tactical voting) to best achieve their goal.

They're closely related, if you have proved Arrow then you can get to Gibbard–Satterthwaite from there, but they are not the same exact thing.

Say you get rid of "independence of irrelevant alternatives", then I may influence the result by tactically ordering my candidates.
I am from a country which has 1 representative per around 5000 residents in the national assembly. There are around 10-13 representatives per constituency with additional seats handed to parties that are underrepresented given the national popular vote.

Even though this is around 140 times more representative then the USA, and the party distribution is a lot more reflective of the popular vote then in the USA (or the UK for that matter), people are still complaining that it is not good enough. There is a huge popular support for uniting the constituencies into just a single national constituency. E.g. people don’t see the point in having the local representatives on the national assembly. And I agree with it.

That said, if the people in the USA disagree with this (or think it is not applicable in the USA) and demand a local representative. The 700,000 residents per representative is kind of ridiculous. It is so low that it begs some questions about what we consider a true democracy. Even China (a country most people don’t consider democratic) has around 500,000 residents per representative in their national assembly (40% more representative then the USA).

Why not instead have an independent entity draw districts?
That just moves the problem around. It might sort-of work for a time but all the incentives are still there so the parties will find a way.
Nobody ever believes the entity is really independent. We have an independent entity in the UK and people still aren't happy.
It's also a terrible system that basically makes it impossible for a country-wide third party to ever gain significant representation.

See, e.g., Scottish National Party having 35 seats with 3% of the vote vs. Lib Dems having 12 seats with 7%.

But it allows areas with a national identity, like Scottish or Welsh seats, to be represented.
If 50% of the seats is enough to control the legislator, you could argue that the Scottish and Welsh nationals don’t have true representation either.
That has nothing to do with how districts are drawn.
Specifically whoever is likely to lose seats is always unhappy, and so the reforms (and they are reforms, the UK in particular knows what happens when you don't have boundary reform for an extended period, that's where "rotten boroughs" came from) are frequently delayed or tweaked slightly by Parliament even though that's contrary to the purpose of an independent commission.

I live near to the Island, and so this comes up here very often. The Island currently has one Member [of parliament], but its population is far too large for only one district, yet too small to just become two districts. So the obvious reform, considering the practical links between the Island and its relatively rural coastal neighbours, is to redistrict so as to create two districts which each contain half the island plus a chunk of rural Hampshire.

However, a considerable number of people would prefer to be grossly under-represented (all the people on the entire Island get just one Member) rather than risk either or both of their two Members being less interested in the Island because they also represent some coast dwellers on the mainland.

Sure, but removing the incentive entirely is usually a much better solution.
ICRCs can easily run awry of constitutional issues; more to the point: being an elected official is a job: gerrymandering improves incumbency rates. Why would you write yourself out of a job?
> It's easy to remove the incentive: Just add some statewide delegates that are elected based on the "wasted" votes.

Can you make this more generic so that people who don't understand the US political system could follow your proposal?

He is proposing MMP (https://en.m.wikipedia.org/wiki/Mixed-member_proportional_re...) or something like it. Where some seats are awarded based on who gets the most votes in the election district while the rest of the seats are awarded in a way which compensates and achieves a total seat distribution which matches popular vote.
I was actually thinking about Party-list proportional representation (https://en.wikipedia.org/wiki/Party-list_proportional_repres...), but mostly because I hadn't heard about MMP. I'm still not quite sure what the difference is.
The difference is that with mixed you vote for a person and a list of people ( party), not only for a party.
In party list systems you also often vote for a candidate: "Voters may vote for the party, as in [...]; or for candidates whose vote total will pool to the party/parties.
MMP by definition guarantees a direct representative for each district.

You can think of it as FPTP (per district) and a party-list election at the same time. The FPTP winner in each district gets a guaranteed seat, but the remaining seats are filled (based on the party lists) such that the final proportions in parlament match the party-list election.

In theory, you get the best of both worlds: a direct representative for everyone and parlament according to popular vote.

There are quite a few voting systems that removes/minimizes incentive of gerrymandering. My favourite is https://en.wikipedia.org/wiki/Random_ballot .
Sortition really only works with increased term durations; without constitutional changes, you’d need something like a random incumbency mechanism.
Random ballot is different from sortition.
This is happening in the UK, we are having voter ID requirements, limits on postal voting and redrawing of constituency boundaries. It’s really an elective dictatorship at this point. Might as well just join the Tory party and stop pretending there is an alternative outside of them at this point.
I blame labour as well. Remember when they joined forces in a ridiculously aggressive campaign against voting system reform?
Sure. I remember that vote, it was considered a joke by the media at the time, I think given the mess we’re in I’d say a move to all votes counting would be much better even if this has its own issues.