We can’t even get something as ultimately trivial as college football rankings entirely done by algorithmic, or even objective methods. What makes you think something much higher-stakes like congressional districts would accomplish that?
Actually not. An exeact distribution would get an exact result: a random distribution on average gets an average distribution an average amount of the time. The rest of the time, it gives you a random result close to the exact distribution.
So a state with 54% Democrat would give you 100% Democrat 54% of the time, or would have a 54% chance of giving you 100% Democrat, or would give you 54% of the districts Democrate, or something like that. It would be EXTERMELY UNLIKELY to give you all districts exactly 54% Democrat. Even if you only had two districts, it would not “ensure” that both districst would be 54% democrat, and the more districts you have, the more variation you would see.
Fair enough. It is true that a system of single-member seats tends to introduce distortions. But I think we should draw two conclusions from that:
First, the one you draw; a discrepancy between vote proportion and seat proportion doesn’t necessarily mean that gerrymandering has occurred. (But it may mean that the system is “unfair”; for a reasonable and defensible definition of “fair” you can argue that such systems are inherently unfair.)
Secondly, sticking for a moment with the specific problem of gerrymandering, such systems create a substantial incentive to engage in gerrymandering. And, since we have devised a system which will reward gerrymandering if it occurs, we need to balance that with a mechanism which prevents or punishes gerrymandering. If we have no such mechanism, we should assume that the system is more likely gerrymandered than not. Therefore, while the discrepancy between seats and votes is not necessarily the result of gerrymandering, it is more likely than not that it is partly the result of gerrymandering.
I’m 99% sure that you are just wrong about your math here, because of how probability works with large sample sizes. If you have a million people, 55% of them are democrats, and you randomly divide them into 10 subsets of 100K, the average number of those districts that are majority democrat is much higher than the 5.5 you seem to think it should be. I’d guess it’s >9.9, although I admit that I don’t actually know how to do the math myself.
That said, a case like Pennsylvania, in which a majority of democratic votes turns into a majority of republican legislators, is far more likely to be due to gerrymandering than a case like California, in which a majority of democratic votes turns into a larger majority of democratic legislators
My numbers are “illustrative only” :~), but I remember that you get much wider distributions than at first seem intutitive.
Not sure what you’re saying here… are you claiming that it’s more likely than I think for a random subset of voters to have a different party majority than the entire state?
If so, well, you might be right, there are nonintuitive results in math sometimes. Hopefully someone who is more up to date on stats than I am will set us straight.
I tend to side with Max on this one. My intuition would be that the numbers at this scale would average out.
Is there a mathematician in the house? For the sake of argument, let’s assume there are three million voters; 1,650,000 (55%) are Democrats and 1,350,000 (45%) are Republicans. The voters are randomly divided up into ten groups of 300,000 apiece. What are the odds that none of the groups will have a Republican majority? One of the groups? Two/three/four/five/six/seven/eight of the groups? (My math skills are sufficient to determine you can’t have more than eight groups with a Republican majority.)
I think you think zip codes are larger than they are. Or you want a lot more members of Congress if you want some to represent a partial zip code (which I kind of doubt). There would be dozens and dozens of residential zip codes even in a densely-populated district, so they’d just have the same fight over where to assign which ones.
It seems to me like you could get some wonky results.
Let’s say that we have a district where there a six seats up for election and there are three parties competing. The results are as follows:
Clinton (Democrat) 205,000
Trump (Republican) 198,000
Sanders (Socialist) 97,000
O’Malley (Democrat) 95,000
Cruz (Republican) 93,000
Webb (Democrat) 88,000
Kasich (Republican) 85,000
Chafee (Democrat) 70,000
Rubio (Republican) 69,000
Now when you divide the votes up by party, you get:
Democrats 458,000 (45.8%) - 3 seats
Republicans 445,000 (44.5%) - 3 seats
Socialists 97,000 (9.7%) - 0 seats
So the six people elected are Clinton, Trump, O’Malley, Cruz, Webb, and Kasich. Sanders, who came in third place and was ahead of four of the people who got elected, didn’t get a seat.
It’s 100% minus epsilon, where epsilon is a very, very small number (the online binomial distribution calculators I found wouldn’t even allow trial counts as high as you stipulated).
300k out of 3M is a very high-quality sampling, assuming it’s truly random. It would only be insufficient if the overall bias was extremely small, like 50.00001% Democrats.
That’s not a wonky result- there are six seats, and Sanders only got the support of one voter in eleven. Surely, for the Socialists to have a “moral claim” to a seat in a six-seat constituency, they should have the support of one-sixth of the voters, or something close to that?
In real life, in such a system, the Socialists would presumably run more than one candidate. There might be people who lean Socialist, but aren’t attracted by Sanders, and you have to give them the possibility of voting for you.
Smith would get about 4 Congressmen and Johnson 3 Congressmen, so you’d need a tiebreaker. Despite that there are few Asians or Hispanics with these surnames, these districts would not be GOP locks — according to Wikipedia 34% of Johnsons in the U.S. are Black.
Hispanics would get several lock Representatives — one each for Rodriguez, Garcia, Martinez, Hernandez, Lopez, Gonzalez, Perez, Sanchez, Ramirez. That is a form of “gerrymandering”.
The Vietnamese would get their own Congressman because of Nguyen. Although there are less than 350,000 Nguyens (and not all Nguyens would vote the ethnic ticket), the way elections work they’d be Nicely assured of having their say, despite that their “district” would be diluted by Newton, Niblett, or even … wait for it … Nicely.
Chinese would have to make do with a single Congressman for Lee. (38% of Lees are Asian.) Of course it would be luck of the draw whether most of the Lees end up in a single district or get split between two.
Blacks would get some lock seats. Jackson is 53% Black and would get a Congressman. (Actually, we need to know the partitioning details. If Jackson gets split in two, one group would be diluted with Jackowski etc., the other with Jacobs.) Williams would get 2 or 3 Congressmen and are about half Black.
No — I think there’ll be too many complaints. For the thought experiment let’s stick with something more arbitrary like SocSec numbers.
Don’t forget that for a state districted with a perfectly even mix, the Party that gets 59% of the vote (or even 51% of the vote) would get 100% of the seats.
Some in the thread seem to overlook that mathematical fact so let me repeat in a larger font:
for a state districted with an even mix, the Party that gets 51% of the vote would get 100% of the seats.
Still I was curious enough to check Northern California where I spent most of my life. I’m not sure where the GOP voters are concentrated in the Bay Area — there are some very rich communities, but lots of the rich are tree-hugging helicopter libtards. Could Elbridge Gerry find a way to link the redneck mountain men through the affluent suburbs like Saratoga all the way to the millionaires of Menlo Park, squashing all the GOP voters together so that the other 9 districts in the greater Bay Area would be Democratic? That after all is the hallmark of gerrymandering — a district with a super-majority for the Party opposed to the gerrymander.
I didn’t have to look hard. All ten of the Congressional Districts in the greater Bay Area elected Democratic Congress[wo]men in 2014.
We’re not in GQ, but I don’t think teaching elementary math is off-topic here. Let’s stipulate that the districting uses a random unbiased process, e.g. hashed SocSec number rather than surname. Of course we assume no other biases, e.g. weather-party correlations in turnout.
The variance of a binomial distribution is npq, or, substituting your example, (400,000)(.54)(.46) ~= 99,000. (400,0000 is an estimate of voters voting.)
Now, take the square root of that variance and divide by n=400,000 to get .00079, or about .08% — that’s the 68% confidence error bound portion, double it to get the 95% bound, 0.16%
In other words, there’s a 95% chance that the actual vote in the district defined by your example will be between 53.84% and 54.16%.
Welcome to the Law of Large Numbers.
Would the Irish have a lock on several seats beginning with “O”?
Which really just illustrates the point. As long as you have single-member districts with representatives elected on a simple plurality of votes, the most that you can hope for is that the significant distortions that such a system tends to produce will be randomly distributed. And even that’s quite tricky.
If you’re concerned about these distortions, the rational course is to move to an electoral system which doesn’t tend to produce them.
Good point! Unfortunately one of the sites I used to “research” my post omits the apostrophe when sorting those surnames. (The same Census data as Wikipedia uses is the ultimate source, but I find most government websites to be hideous and tedious. Wikipedia’s link to its census source, for example, is now broken.)
Whether to include the apostrophe in the sort order will be a major political squabble!
I’m not sure exactly what you mean here, but I think you and I may be in agreement to recommend proportional representation with party lists. Answering an objection upthread, a grassroots or democratic process could help select and sort the party lists.
Only if you feel the system should be based around parties rather than candidates. As a candidate, Sanders got more votes than O’Malley, Cruz, Webb, or Kasich. So there’s a strong argument that he has a better moral claim to a seat than they do.
That’s pretty much the whole basis of this topic. It’s not a debate between systems that are fair and systems that are unfair. It’s a debate over how you define fairness.
Note that in a “party list” system, there should be nothing to stop Sanders from running as a single-person party — though he’d want some others on the list in case in gets a landslide. (And I wonder if voters should be allowed to cast, say, 3 votes?)
The presence of multiple parties on the ballot might not debilitate America’s Time-Honored Two Party System™. For example, voters could happily choose between Tea Party and Regular GOP knowing that their respective winners would form a coalition upon election. Others would vote Libertarian knowing that now their votes do count and their Representatives would follow their supporters, voting (D) on some issues, (R) on others.
Well, Max’s system is explicitly based around parties, so if you take the view that a system based around parties is unfair then, yes, Max’s system is unfair. But that’s kind of trivial.
I think the argument only looks strong because the system is so crude. It’s designed to measure, basically, as little as possible of what voters want. The voters need to elect six representatives, yet each voter only gets to express views about one candidate, and has no say in how five out of the six seats get filled. Why would we think that was a good idea? And look how it plays out in practice; there are more than twice as many Clinton voters as Sanders voters, and yet both groups get the same representation. Surely, if you take the view that Sanders’ support entitles him to one seat, would it not follow the Clinton’s support entitles her to two?
If you want to focus your electoral system on individuals rather than parties, introduce the transferable vote. Voters number the candidates in the order of their preference. They can number as many or as few candidates as they wish. They can give their top preferences to the candidates of one party, or they can assign their preferences on any other basis they like. Candidates who get more than 1/7th of the votes (because there are six seats, only six candidates can get more than 1/7th of the votes) are elected; their surplus votes can then be redistributed to the next-preferenced candidate. If there are no surplus votes to be distributed, and seats remain unfilled, the lowest-polling candidates are eliminated and their votes are redistributed.
Under this system, on the figures we have here a candidate would need to accumulate just over 146,700 votes to be elected. Clinton and Trump would be elected on the first count. Their surplus votes would be distributed to other candidates, to increase their totals. If party loyalty holds strong - which is a decision for the voters - this will likely bring other Republican and Democratic candidates ahead of Sanders; O’Malley, say, might be elected over Sanders. If this happens, it’s because more voters prefer O’Malley to Sanders than prefer Sanders to O’Malley. This process continues until six seats are filled. Sanders can still be elected, but only if he attracts preferences from voters who gave their first preference to other candidates. (This is true for all the candidates other than Clinton and Trump.) In the end, the six candidates elected will be the ones who attract the broadest support, the ones who are acceptable to the greatest number of voters. Party identification will affect the result only if, and to the extent that, the voters decide that it matters.
His system has people voting for candidates rather than parties. The apportionment by parties is done after the voting.
A real party-based system would be where people vote for parties with the parties themselves choosing which candidates will represent the party. In such a system you could see the Republican party getting 445,000 votes but choosing to give the resulting three seats to Cruz, Kasich, and Rubio and leaving Trump out.
Which is not without its attractions. 
I think his system essentially assumes that if you vote for any Republican candidate, then you prefer all the other Republican candidates to any of the candidates who are not Republicans. My proposal essentially allows the individual voter to decide that for himself.
(You could come up with a variation on his system in which the ranking of the Republican candidates was decided not by the party, but by the number of votes each got. In fact, I think that was Max’s intention.)