Gerrymandering distorts the will of the people, but the basic math of geographic representation makes it difficult to get rid of, unless we get rid of representation for geographic districts.
So the conclusion seems to be that smaller districts more responsive but increasing the number of districts would require increasing the number of representatives, which can be harder in larger countries. What would happen if we were to assign seats based on the total percentile average for each district (for example if there were 6 districts with 100 people each and the blues won three of them with 60 votes and lost the other three with 40 votes which would give them 50 seats in an 100 seat senate?)
You might want to take a look at STV (Single Transferable Vote), which is a way of getting closer to proportional representation without having a party list system. It's a form of Ranked Choice Voting that elects multiple winners in a single election.
The more representatives per district, the closer to proportional representation you can get, but you can still have geographical districts, which is a good thing because there are regional concerns and interests in politics. So there is a tradeoff between locality of representation and granularity of proportional representation. Multiple representatives per district, elected with a proportional system such as STV, makes gerrymandering very difficult if not impossible.
Approval voting is problematic because it violates one-person-one-vote, it violates later-no-harm, and may also be subject to manipulation by organized groups.
The dilemma here looks like one that is based on some unstated assumptions on what kind of voting systems are allowed. With a bit of creativity the dilemma can be broken. For example:
1) The *number* of seats (N) each party gets is based on the popular vote.
2) Each party then gets the N districts where they did best.
So in the Katechon example, 60% of the people vote blue, so blue gets 6 out of the 10 seats. 40% votes violet so violet gets 4 seats. Then we rank all the districts in order from most blue-leaning to most violet-leaning, and the blues win the 6 most blue leaning districts, while the violets win the 4 most violet leaning districts.
So there we have full representation of ideas and still a good representation of land. With a pure two party system this works very straight forward, in a multi party system deciding which party gets which district becomes more tricky, but any solution still achieves fine grained representation of both ideas and land.
There are also many variants of hybrid systems that achieve fine grained representation of ideas and districts without blowing up the size of the parliament. Wikipedia describes them under "mixed electoral systems", so I won't quote them here.
Such systems don't solve the impossibility theorem but they do get rid of the incentive for gerrymandering, as a party can't increase their total share of seats by changing the districts.
There's also the assumption that the elected representatives are equal. But what if they're not?
What if their voting power would be proportional to the amount of votes they get? Sure, put all your blues in one district. You now get a super-representative who laughs at the violet representatives. Don't like that? Then draw your districts more proportionally.
(Also in case there's an opinion shift, that eats at the representative's voting power).
I think the idea most "normal" people have of how districts should be drawn is very different to any suggestions here. When I explained MPs to my 6 year old daughter, what I said is: every town in the UK picks someone to send to parliament.
It's actually hilariously more complicated than that, but isn't that in fact the implicit model that the public have? Boundaries are drawn around existing communities, like towns. They include all types of people and voters in whatever proportions that that town happens to have.
I get that this approach is under-specified (what is a community anyway?), and can be very arbitrary (but sometimes not - towns are often quite clearly demarcated!), but that's kind of the point....
We agree that trying to draw districts to allocate votes is impossible to make fair, so don't we need an outside view like this that allocates not based on the fairness of votes but on existing real-world community borders? That it's clearly impossible to formalize might be a point in its favour, make this sort of thing too legible and it just becomes an optimization game for interested parties.
I'd be interested to see more thinking on how we could make this implicit model the public imagines more rigorous and explicit.
You COULD make districts bigger (i.e., instead of 10 districts with a single representative each, have 3 districts with 4 each). Having multi-seat districts creates "mini-PR" systems (well, sort of, and under certain systems -- some systems make it worse), that limit how unfairly votes can be expressed within a district. So you still get regional representations, but your regions are larger, and more of your voters get their vote to matter.
You can easily get rid of gerrymandering simply by proscribing an algorithmic process for districting.
For example: Allow local areas to define precincts (one for each voting place). Then conduct a census. Then define the districts to be the most compact aggregations of precincts that have a population variation of less than 2%. Choose the definition of compactness in advance.
There are obvious optional adjustments for anything you could care about. Precisely define the formula for determining goodness before the census, and use small precincts, and gerrymandering becomes impossible.
This doesn't guarantee any sort of fairness (which as you point out can't really be guaranteed). But it does provide independence from political manipulation.
I think you're too dismissive of the idea of making legislative bodies much, much bigger. What exactly is it about a several-thousand-person house of representatives that couldn't work? There are many people out there who think this is the simplest way to make a significant improvement to the problem of unequal representation; I don't have a specific favored place to link to, but a quick search will turn up many articles supporting the idea from major publications.
So the conclusion seems to be that smaller districts more responsive but increasing the number of districts would require increasing the number of representatives, which can be harder in larger countries. What would happen if we were to assign seats based on the total percentile average for each district (for example if there were 6 districts with 100 people each and the blues won three of them with 60 votes and lost the other three with 40 votes which would give them 50 seats in an 100 seat senate?)
You might want to take a look at STV (Single Transferable Vote), which is a way of getting closer to proportional representation without having a party list system. It's a form of Ranked Choice Voting that elects multiple winners in a single election.
The more representatives per district, the closer to proportional representation you can get, but you can still have geographical districts, which is a good thing because there are regional concerns and interests in politics. So there is a tradeoff between locality of representation and granularity of proportional representation. Multiple representatives per district, elected with a proportional system such as STV, makes gerrymandering very difficult if not impossible.
Approval voting is problematic because it violates one-person-one-vote, it violates later-no-harm, and may also be subject to manipulation by organized groups.
The dilemma here looks like one that is based on some unstated assumptions on what kind of voting systems are allowed. With a bit of creativity the dilemma can be broken. For example:
1) The *number* of seats (N) each party gets is based on the popular vote.
2) Each party then gets the N districts where they did best.
So in the Katechon example, 60% of the people vote blue, so blue gets 6 out of the 10 seats. 40% votes violet so violet gets 4 seats. Then we rank all the districts in order from most blue-leaning to most violet-leaning, and the blues win the 6 most blue leaning districts, while the violets win the 4 most violet leaning districts.
So there we have full representation of ideas and still a good representation of land. With a pure two party system this works very straight forward, in a multi party system deciding which party gets which district becomes more tricky, but any solution still achieves fine grained representation of both ideas and land.
There are also many variants of hybrid systems that achieve fine grained representation of ideas and districts without blowing up the size of the parliament. Wikipedia describes them under "mixed electoral systems", so I won't quote them here.
Such systems don't solve the impossibility theorem but they do get rid of the incentive for gerrymandering, as a party can't increase their total share of seats by changing the districts.
There's also the assumption that the elected representatives are equal. But what if they're not?
What if their voting power would be proportional to the amount of votes they get? Sure, put all your blues in one district. You now get a super-representative who laughs at the violet representatives. Don't like that? Then draw your districts more proportionally.
(Also in case there's an opinion shift, that eats at the representative's voting power).
GREAT discussion - going to stick with me.
I think the idea most "normal" people have of how districts should be drawn is very different to any suggestions here. When I explained MPs to my 6 year old daughter, what I said is: every town in the UK picks someone to send to parliament.
It's actually hilariously more complicated than that, but isn't that in fact the implicit model that the public have? Boundaries are drawn around existing communities, like towns. They include all types of people and voters in whatever proportions that that town happens to have.
I get that this approach is under-specified (what is a community anyway?), and can be very arbitrary (but sometimes not - towns are often quite clearly demarcated!), but that's kind of the point....
We agree that trying to draw districts to allocate votes is impossible to make fair, so don't we need an outside view like this that allocates not based on the fairness of votes but on existing real-world community borders? That it's clearly impossible to formalize might be a point in its favour, make this sort of thing too legible and it just becomes an optimization game for interested parties.
I'd be interested to see more thinking on how we could make this implicit model the public imagines more rigorous and explicit.
You COULD make districts bigger (i.e., instead of 10 districts with a single representative each, have 3 districts with 4 each). Having multi-seat districts creates "mini-PR" systems (well, sort of, and under certain systems -- some systems make it worse), that limit how unfairly votes can be expressed within a district. So you still get regional representations, but your regions are larger, and more of your voters get their vote to matter.
You can easily get rid of gerrymandering simply by proscribing an algorithmic process for districting.
For example: Allow local areas to define precincts (one for each voting place). Then conduct a census. Then define the districts to be the most compact aggregations of precincts that have a population variation of less than 2%. Choose the definition of compactness in advance.
There are obvious optional adjustments for anything you could care about. Precisely define the formula for determining goodness before the census, and use small precincts, and gerrymandering becomes impossible.
This doesn't guarantee any sort of fairness (which as you point out can't really be guaranteed). But it does provide independence from political manipulation.
I think you're too dismissive of the idea of making legislative bodies much, much bigger. What exactly is it about a several-thousand-person house of representatives that couldn't work? There are many people out there who think this is the simplest way to make a significant improvement to the problem of unequal representation; I don't have a specific favored place to link to, but a quick search will turn up many articles supporting the idea from major publications.
Definitely look into Score Voting where each candidate gets a score much like in the Olympics. Highest average wins. Much. better. results.
The answer to your question is New Zealand...