A well known curse of many representative democracies is gerrymandering. People in power draw the districts to assure they will stay in power. There are some particularly ridiculous cases in the USA.
I was recently pointed to a paper on a simple, linear system which tries to divide up a state into districts using the shortest straight line that properly divides the population. I have been doing some thinking of my own in this area so I thought I would share it. The short-line algorithm has the important attribute that it's fixed and fairly deterministic. It chooses one solution, regardless of politics. It can't be gamed. That is good, but it has flaws. Its district boundaries pay no attention to any geopolitical features except state borders. Lakes, rivers, mountains, highways, cities are all irrelevant to it. That's not a bad feature in my book, though it does mean, as they recognize, that sometimes people may have a slightly unusual trek to their polling station. The main problem with it is that people can overstate the problems with it. Attempts to stop gerrymandering will face strong opposition from the powerful figures who created it in the first place. By definition, they have political power and will work to protect it. As such, to make this happen, there must be no vaguely credible arguments against the system which can be used by the gerrymanderers. That's a tall order, because it's amazing what classes as vaguely credible.
My own thoughts have been based on a principle I will call "non-concavity." That means we seek to not have concave (inward curving) borders on our districts. Here's a rough rule:
For any district, no line between any two points within the district may leave the district, except at a county border.
This requires a district be entirely convex, except another district can intrude into it along a county border. The short-line algorithm discussed above meets this condition, in fact it meets it with state borders as the only concavities allowed. I suggest a county border as a proxy for many of the other borders we would like to use, including city borders, rivers, mountains, lakes or interstate highways. There may be a better set of borders to allow concavity on -- "rivers and freeways" makes some sense. Mountain ridges seem important but it's harder, but not impossible to write a nice definition.
Some gerrymandering is still possible here. My proposal allows complex snakes of counties, so they may be too small. And indeed, whatever gerrymandering can be done will be done so this deserves more thought. However, most representative systems are intended to provide some amount of representation based on true geographic and social commonalities, so using groups of counties may still have merit.
There is one other tweak I would add to the rule that is a bit hard to write out but is probably needed. We want to allow concavities caused by a single piece of property, so that we can draw the borders along property lines. As such we would say that no line between points in the district may cross a single deeded property which does not itself belong to, or border on the district. Or alternately, "no line between two properties within the district that do not form part of the district border may pass out of the district." This allows rough, crinkly edges along property lines -- which may get visibly crinkly in rural areas -- but should not allow a great deal of manipulation.
All of these methods (and indeed today's crazy lines) require a detailed, property by property census and fancy computerization. But we have that today.
There are other systems, some of which have been used, for example in Connecticut. What matters of course is not simply what the best system is, but what can be sold to the voters against the imaginary objections of the powerful. (That's why I don't like my property line exception very much, as it makes it harder to explain, compared to my basic rule which is very simple to write, and any fool can test against it with a map and a ruler.)