How would anti-gerrymandering work?

I don’t know much about advanced mathematics, but it seems to me that drawing districts based on 1) the state population divided by the number of each state’s representatives, and 2) the shapes that are closest to a square (four equal lines), or 3) in the case of odd shapes caused by wacky geographical boundaries, the fewest number of straight lines need to contain that population size, would be objectively achievable.

I’m thinking that you might have some "leftover "areas when you’re done drawing the straight lines which might be added to the surrounding districts (which would then need to be reduced elsewhere to keep each district in line with principle number 1).) But has anyone come up with a fair, objective way to draw district lines that is subject to mathematics rather than politics, or are we doomed to have this question fought out along largely political lines?

There’s no simple mathematical formula because the process has multiple conflicting goals - minimize size to avoid weird shapes (the classic “Salamander”); keep like communities in the same district, contiguity, don’t split them up; keep voters per district equal. it’s always going to be a trade-off, and any model is going to reflect the designers’ bias.

Canada seems to do it without the gerrymandering claims. Our basic rules are here:

Redistribution of the Federal Electoral Districts – Elections Canada

Each province forms an independent non-partisan commission after each census, there are public hearings, and it’s a done deal. The map for Ontario has squarish ridings with allowances for population centres and geography:

Map of Ontario | Elections Canada Online

There was some interesting research done on this fairly recently - not in a mathematical formula for drawing the boundaries, but arranging a process that involve both parties in which cheating can’t actually pay off.

I feel the scheme as proposed is probably too long-winded for prime time, but the general principle of giving both sides decision-making capacity of their own (rather than just objecting to the bad decisions the other side made) is a very good one.

The problem is not that nobody has come up with a system. Rather, people have come up with many systems… And in any given case, one of those systems is going to be more favorable to the party in power than the others. So they can just choose that system.

There are also a number of proposals for alternative voting systems that are less vulnerable to gerrymandering - IE drawing the borders differently doesn’t have to translate to a concrete advantage in representation.

I understand most of these and some of them seem closely related if not the same: “minimize size,” “contiguity,” and “don’t split them up” seem pretty much on a par with each other if I’m understanding them correctly.

The one I don’t understand is “keep like communities in the same district.” Can you explain what this means, and why it is a legitimate goal for voting districts?

It mainly means not “cracking” communities to destroy their voting power. Imagine a hypothetical blue county with ten thousand Democrats living in it. A gerrymander-minded redistricting plan might split that county into five pieces and toss two thousand Democrats into each of five surrounding counties that are solidly Republican. You have effectively robbed ten thousand people of representation, even if you’re keeping all the districts the same size.

Representatives are also able do their jobs better if they represent somewhat homogeneous communities. A representative from a community with a massive elderly population is going to have different goals than one representing a spring break destination. Districts with weird and conflicting populations are much more difficult to represent with fidelity. So even in a situation where you’re splitting up, say, a very large and reliably blue city, you’re going to want to try to keep communities whole so that they can be properly represented.

But not too whole. Making any electorate drastically dominated by one group potentially robs that group of influence as well. This is a problem when there is a closely matched pair of parties. Filling an electorate to the brim with one party makes it sure they win that one, but depletes their chances in the remaining electorates.
The ideal is very hard to manage. You want the final result to match the aggregate popular vote, but still reflect local opinions.

I was sitting in on a boundaries commission hearing once. The Commission had produced a draft map, and was calling for public comments on it.

The reeve of one rural municipality appeared and stated that they didn’t like that the R.M. had been divided between two different ridings. His concern wasn’t so much the impact that division had on voting patterns, but rather on the effect it would have on their ability to lobby the local member on issues that were important to the R.M. Instead of having to lobby one member, representing a group of 10,000 voters, they would have to lobby two members, representing a group of 5,000 voters to each one. So more lobbying would be needed, and with less voting weight in either member’s riding.

The Chair of the Commission seemed a bit skeptical, and clearly thought that this was a partisan argument dressed up as a representation argument. He said, “So, you’d rather be all in one riding, than split?” “That’s right,” said the reeve. “Which riding do you want to be in?” the Chair asked, obviously thinking that this question would pin them down on a partisan motive. “Don’t really care,” said the reeve, “either one, so long as we’re all in one riding.” The Chair was a bit surprised.

The final map proposed by the Commission had a little jog in the boundary between the two ridings, to make sure that R.M. was located entirely in one riding.

Minor quibble: the boundaries commissions aren’t formed by the provinces, but rather the federal government forms one boundary commission for each province.

Read up on the Iowa system:

Dr. Moon Duchin of the Tufts Math Department formed the Metric Geometry and Gerrymandering Group (MGGG) to study the mathematics of drawing district lines. There’s a lot of fascinating research at the MGGG site, but Dr. Duchin’s work on random walks through the space of district maps is probably the coolest.

I think that in the case of the US one start point is to look at the history of changes, that would offer a huge clue to the extent of gerrymandering in a particular area.

The point made by @NorthernPiper seems to be the most important, how the boundaries affect representation by lobby as you go upwards through the representative heirarchy.

We had significant boundary changes in the UK with the creation of certain port counties in 1972, in particular Humberside. This took areas from previous historic counties and was almost universally despised even before the Law came into effect. The idea had been to create one area of common interest around a large port estuary which might appear logical given that there are many ports of varying sizes and loading stages both north and south on the estuary.

Those changes were driven by administration practicality rather than by gerrymandering so the motive was very different.

In practice, the estuary is so large that the logistics of it really didn’t work out well, it was divided into the northern half and southern half by the river, and at that time the only link was by a pretty modest ferry.

The thing that really did for it though was the pretty roughshod manner that overrode the public sentiment in a sort of ‘we the policy makers know what is good for you’. It was percieved as arrogant imposition and rightly so because it turned out not to be a great idea anyway, and the issue of common interests for the maritime activities could easily handled in other ways.

Humberside was largely unpicked in 1996, and actually increased representation at Westminster Parliament because the return to the original boundaries meant that more Members of Parliament then were able to band together in House debates.

All I am saying is that it can work both ways but public sentiment is also important - areas often develop along corridors of access so its not surprising that you might get unusually shaped districts if you go by common logical interests.

I think that there really should be some sort of US electoral commission, but your division of powers makes it difficult to do this on a fully national scale, perhaps there should be a system of appeals process where concerns can be taken up to an equivalent of a Supreme Boundaries Commision similar to how the courts system operates.

Just to amplify casdave’s (and some other) comments above, in relation to the UK:

Shapes on the map don’t really come into it, except to the extent that one of the criteria involved is to keep parliamentary constituency boundaries contiguous to local government boundaries. But in the most recent set of changes, that is one that had to be sacrificed in some cases (within big cities mostly, if memory serves) in favour of the other criteria, particularly one limiting the range of variation of the size of the likely electorates. I see that the policy has been changed again, abandoning the last set of plans to reduce the total number of MPs, which may make it easier for the Boundary Commission in the next review (due 2023).

As important as trying to equalise the numbers of voters in each constituency is the idea of communities, as mentioned above: where do people work, shop, work, entertainment, which area(s) do they identify with, and other such subjective considerations. This is where arguments can get heated, and it can be quite amusing to see how the parties can stretch ideas about “natural communities” as a figleaf for what’s obviously a matter of their own party interests, or how people can get up in arms about who they’re being lumped in with - here’s a summary of one such brouhaha. Nor can it be denied that changes can work to one party’s favour or another (but so does leaving them alone in times of demographic change) - but having an independent non-partisan Boundary Commission working through a process of public consultation does limit any one party’s ability to fiddle with the system (same with the administration of elections, but that’s another matter).

Meant to add: the Commissioners work with the “building blocks” of the wards for electing councillors to the local authority area. So my London Borough has two MPs, and 20 wards.

Just throwing in that proportional representation is an obvious alternative to an electoral system based on single-member districts, and therefore immune to the problems of drawing the district (aka constituency, aka riding) boundaries. It has its own drawbacks (such as giving more power to party bigwigs in setting up the party lists ahead of the election, and reducing the embeddedness of candidates within their local communities), so you may or may not prefer it over the single-member-district system. But it is not prone to gerrymandering.

Single Transferable Vote in multi-member constituencies (as in Ireland) gets round the “party list” problem by voters ranking individual candidates of any or all parties. The trouble with it is, though, that counting and redistributing the lower preferences on the surplus votes of those candidates achieving the quota for election and of those eliminated at each round - it all takes time, even in relatively small constituencies. I see that in the most recent Irish election, some seats went to 14 counts to arrive at the final results.

Dr.* Duchin (mentioned above) created a measure of badly gerrymandered districts. It doesn’t tell you how to draw up the districts but does give a measure of how bad they are. A non-partisan committee can draw lines that try to minimize badness.

*I hope the Wall St. Journal doesn’t object to calling her Dr.

You’ve hit on a major point here. This is one of those things that falls to the state level rather than the Federal level. Each state is able to make their own mapping; each state sets its own rules within some federal guidelines. For example, before the Feds lowered the voting age for national elections down to 18, you had a number of states who allowed 18-year-olds to vote in state and local elections. Each poling place would have to have two separate ballots based on age.

Illinois is broken up into counties; counties are broken into townships; townships into precincts. Can’t tell you who (or how) draws the lines for precincts, but one thing I’ve long thought is that the district lines should be determined along the lines of “start with the largest available body; if it needs to be divided to keep things equal, go down to the next largest body; keep going until done, trying to keep things as compact as possible”. We’ve got a district in Chicago that looks like a set of headphones; if that ain’t gerrymandering, I don’t know what is.

Saw an article in the Chicago Tribune a little while back, where they took this kind of approach. It didn’t change the representative count by party; what it did do was force multiple incumbents into one district. Yeah, the gerrymandering can be used to improve party count; it is often used to preserve the jobs of the incumbents.