The "slices" are done so that each slice have roughly the same amount of people.
So if one party has sliced things so that all the slices are nicely cracked and packed, the "picking" just doesn't matter. The slicing is the picking.
However, a variation of your idea is to have each party take turns drawing districts. But that doesn't really work, because you'd quickly learn that the winning strategy is to draw districts to maximize the other party's voters. Because you want to force the other party to draw districts favorable to you.
As the sibling to your comment noted that cake slicing only works like that if there’s a homogeneous preference for slices between parties but that’s not the case with districts.
What I don’t get here though is what is the other party picking in this scenario. Is this saying in lue of voting just give both parties equal amount of districts to represent? Then what’s the point of cake slicing?
On the one hand -- I love this spirit, of trying to adapt the "I cut you choose" technique to something that might work for gerrymandering. We need as many ideas as we can get!
On the other -- unfortunately I don't see how it would actually help, because the first party which defines the half-districts is generally going to "win".
If party 1 is the Republican party which wants to maximize rural votes, they just split up every city like a pie, with each slice extending far into the countryside, halfway to the next city. Then it doesn't matter which slices party 2 (Democrats) combine, because they're always stuck with rural votes outweighing city votes.
While if party 1 is the Democratic party which wants to concentrate city votes, they do the opposite and surround the city with two halves of a ring that is half-urban half-rural, so the city can't be diluted. Party 2 (Republicans) can combine rural areas only with the ring, while the inside remains totally protected.
So one strategy is skinny pointed daggers to invade the cities, the other is about skinny ring shields to protect the cities. By controlling the initial shapes, you control nearly everything.
(Of course with real geography it becomes more complex, but the general principle of districts shaped as skinny daggers or shields is still going to be the primary strategy here -- you're not going to win all the districts, but it'll get you the extra 10% or 15% you need.)
I was thinking that there would be an overlay of squares, each identical, like graph paper. As long as the squares contain a relatively small population as compared to the rest of the state, then the two parties are forced to make real choices. And that's the real goal - for both partoes to make real choiced, and not to simply game the system via gerrymandering.
It's kind of a half-assed idea at this point. But I was thinking that, by forcing identically drawn boundaries, then it would force both parties to choose.
Now that I think about it more, it probably wouldn't work. Both parties would just grab squares that guaranteed their victory. It would end up ultra-gerrymandered.
Could you use a cake slicing algorithm? I.e. you get one party to choose a fraction, and the other party chooses whether it's theirs or not, until the number of fractions is gone? Does this scale to n parties of different shares and allegiances splitting a 2d plane?
Or maybe just generate the borders with a heat map after elections with PR?
My older brother's "solution" to being told he must cut the cake and let me choose which half to take was: a sloped cut similar to the one in this picture [1] but which slightly exaggerated the uppermost surface area of the smaller volume.
An analogous tactic against this "I-cut-you-freeze" task might be to provide especially appealing district boundary for your opponent to freeze, while harbouring some knowledge about that district that that your opponent is unaware of (eg suppose that you know the trajectory of demographic changes much better than your opponent)
By explicitly not selecting for voting behavior for any party during the drawing of the districts, but basing the borders of the districts purely on a geographic or statistical property such as area and/or population. As soon as you start taking voting behavior into account you will be favoring either one or the other party.
Suppose you're defining as Party B, and you draw 8 majority-B districts (2:3) and 2 majority-A districts. Then, when Party A is combining, they would pair each of the majority-A districts with a majority-B district with a smaller margin, resulting in 2 A districts and 3 B districts. This is an improvement compared to if B drew 5 districts unilaterally, where it could draw 4 majority-B districts.
Right. Say a state has nine districts. Say the state favors one party 55% - 44%. How should the districts be drawn?
Should each district be as competitive as the state, so each district roughly works out to be 55% - 44%, knowing that by definition the state's districts would be 9-0 for one party?
Should you instead have five districts clearly for one party, and four districts clearly for the other, knowing that by definition each district would have a huge incumbency advantage?
A lot of people would say they want the districts to be both representative of the state's population, and competitive, without realizing those two principles are in tension.
How would this work in reality? One party committee proposes 5 voting district maps that lean toward their desired outcome. The other party chooses the least damaging one. Not sure this helps much.
Or how about 5 random maps that evenly divide the state? Voters vote on the maps and most voted map wins.
If you do this with perfect knowledge and both sides playing optimally, I believe that just ends up being the popular vote, so the democrats win. Whoever has the popular vote simply has more people to shuffle around.
I suppose what you mean instead is that each side gets one round, and the new goal is for the democrats to create a distribution which the republicans cannot win by moving people around.
I believe that ends up being identical to the knapsack problem since you now simply have the democrats wishing to maximize their margin in each state based on its number of EVs; in fact, I think that's an even more straighforward knapsack problem than the one in the article since we don't have to take the complement.
Perhaps you meant something else entirely different, in which case I don't think you described it clearly enough.
The same principle applies how voting district borders are fought over in some countries.
You try to make the borders so for your party that you will lose by a big margin in one district while winning with a small margin in many other districts.
I wonder if similar math could lead to a way of setting up voting districts, as a fair alternative to gerrymandering. Of course you wouldn't want to cut people into pieces, so it would have to be an approximation of some sort.
The only thing I can think of is to start with the districts we have and then produce an algorithm that uses a random number generator to redraw lines. The algorithm can fuzz the current boundaries making a district larger or smaller or it can choose to split a district or combine two districts. Just keep randomizing the districting for each election starting with the output of the last time it was randomly fuzzed.
Sometimes the randomness will work in favor of one party, sometimes against it. In the long term, it adds in some non-partisan non-determinism, which is probably good for justice long-term.
The problem with this is that it defeats the purpose of having per-district representation in the first place, which is supposed to be about shared geographic interests. If your randomly cut districts end up including parts with vastly different interests, one of them ends up denying representation to the other. You can say that it averages out across the country, but again, the whole point of such districts is to have representation that is unique to their needs. If we're okay with averaging things out, we might as well just ditch the districts, and count party votes on the national level.
The thing about pack and crack is that if you try to do something most people think is fair (“preserving the integrity of communities of common interest”), you find that in areas with a urban core and suburban peripheries you end up naturally with pack-and-crack favoring Republicans because Democrats are often hyperconcetrated in the urban areas with Republicans holding a relatively narrow majority in the suburbs.
Of course, if you adopt something like STV in small (say ~5 seat) multimember districts, the opportunity for altering representation by how you draw district lines goes way down, and you still retain individual candidate accountability to the general electorate (unlike in party-list proportional schemes).
The problem isn't “how do you draw lines fairly in single-member, FPTP districts”. The problem is single-member, FPTP districts.
Or you could enlarge them and guarantee 3-5 winners, where each party can have only a single winner. That makes it almost impossible for any party to monopolize the districts (which right now they are by definition, because they are winner-takes-all elections):
It shouldn't be hard to divy up states (granted you might have to cut a state into more than two parts in some cases) in a way that results in no net gain for either party. It's a simple math problem.
The "slices" are done so that each slice have roughly the same amount of people.
So if one party has sliced things so that all the slices are nicely cracked and packed, the "picking" just doesn't matter. The slicing is the picking.
However, a variation of your idea is to have each party take turns drawing districts. But that doesn't really work, because you'd quickly learn that the winning strategy is to draw districts to maximize the other party's voters. Because you want to force the other party to draw districts favorable to you.
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