# A mathematical look at gerrymandering **URL:** \ **Category:** Politics & Elections\ **Created:** [February 27, 2024, 7:56pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182 "2024-02-27T19:56:36Z")\ **Posts on this page:** 6\ **Page:** 4
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [March 3, 2024, 8:24pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/61 "2024-03-03T20:24:12Z")
### North Carolina The lower chamber North Carolina’s legislature consists of 120 members each elected in single member districts every two years. NC’s state legislative maps were redrawn in 2021 after the 2020 census, but those maps were thrown out by the NC Supreme Court in early 2022. North Carolina used remedial maps drawn by the Assembly for the 2022 elections. Furthermore, the 2022 elections flipped control of the NC Supreme Court which then revisited that body’s earlier decision for… reasons. The result was that those maps were thrown out in favor of new maps passed on party lines. This analysis is on the 2022 remedial maps, but it will be interesting to revisit this in 2025 to see what effect the new maps had. ### 2022 statehouse The 2022 elections produced a 49 D, 71 R split in the state legislature’s lower chamber. There were seven statewide races and the average two party vote share across these races went D 47.3% to R 52.7% or R+5.3% net. The lower house median district had a lean of R+6.6%, which is to say that that median district was 1.3% R leaning than the mean district. There were two seats (out of 120) that fell between the median and mean. Overall this map was pretty fair. Republicans had a slight advantage but not one that would be difficult to overcome in individual races and it looks like the lower chamber would have been up for grabs in a 50/50 election. The histogram is not symmetrical by any stretch, but there are plenty of seats around the median/mean which is means that in a 50/50 year there would be many paths for each party to pursue control of the chamber. [![Google Photos](https://lh3.googleusercontent.com/pw/AP1GczMCefPczIWC282jsaDRpzo9hW_oKgSIcMyuzllds7RRtAa6pbz-Rc3nIvn3Qob_PmT-0GROb4Pq5KHmQ_qoPWLCD1NFTrnGcf2tzBUElbCsHijTU8Y=w600-h315-p-k "New photo · Sunday, Mar 3, 2024 📸") ](https://photos.google.com/share/AF1QipNCzLvRU30c-HUhQjHqmRTL5Su6aG6UIiDm075TsCl1WAxyYQ_NwQAFWLr91kpw_Q?key=TXVkRnEyeDNTS2o2Z0tQd3ZKQmhmWnVLdkRIRUNB) ### Nerd numbers n: 120 ν: 0.0663 μ: 0.0532 σ^2: 0.1072 σ: 0.3274 skew: -0.4234 kurtosis: 2.3798 This value for kurtosis (platykurtic) also supports the idea that the chamber would be up for grabs in a 50/50 race. Overall this was a pretty fair map. Too bad it was shitcanned almost immediately once Republicans had the power to do so. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 3, 2024, 8:50pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/62 "2024-03-03T20:50:24Z")
> [@Lance\_Turbo](#): > > What if there are more areas like Vinton than there are like East Cleveland? Then the state is overall Republican and deserves to have a mostly-Republican legislature. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [March 3, 2024, 8:53pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/63 "2024-03-03T20:53:16Z")
> [@Chronos](#): > > Then the state is overall Republican and deserves to have a mostly-Republican legislature. No argument from me there. That’s not really an argument that a structural bias exists though. I’ve been pretty clear throughout that a state that has an overall lean in one direction or the other should have a legislature controlled by the party it leans toward. That’s pretty much the whole point of the thread. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 3, 2024, 9:05pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/64 "2024-03-03T21:05:37Z")
OK, so we’re agreed that a state that has more areas like Vinton than like East Cleveland should have a Republican-controlled legislature. I’m not sure why you brought up that question. But what about a state that has equal numbers of Vinton-like districts and East Cleveland-like districts? That’d be a state with a solid Democratic majority (58.7%), but the legislature would be a toss-up. Or a state with only slightly more Vinton-like districts, where the Republicans would win the legislature, despite a Democratic majority? Of course, the effect isn’t so extreme in reality, because most real districts are closer to even. But that just means that the Republican benefit from this effect is smaller than it could be, not that it doesn’t exist. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [March 3, 2024, 9:11pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/65 "2024-03-03T21:11:52Z")
Let’s summarize the three states we’ve looked at so far. Colorado’s median district is a slim 0.5% more blue leaning than its mean district. This means that in a 50/50 either party would have a legitimate shot at controlling the legislature which for purposes of this thread I’m calling ‘fair’. There are zero seats between the median and mean so the blue team doesn’t gain any extra seats due to this D+0.5% difference between the median and the mean. North Carolina’s median district was 1.3% more red leaning than its mean district. R’s have an advantage in a 50/50, but it seems like it would come down to candidate quality more than districting. The red team probably gained about two seats due to this map. This map is not quite as fair as Colorado’s but it is pretty fair. Wisconsin’s median district is 13% more red leaning than its mean district. R’s have an insurmountable advantage in a 50/50 election. They gain around 14 seats due district lines. This map is not fair. If things went D 55% R 45% statewide, the blue team probably still wouldn’t gain control of the legislature without getting extremely lucky. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [March 3, 2024, 9:24pm UTC](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182/66 "2024-03-03T21:24:45Z")
> [@Chronos](#): > > OK, so we’re agreed that a state that has more areas like Vinton than like East Cleveland should have a Republican-controlled legislature. I have been clear on that since the start. > [@Lance\_Turbo](#): > > I think everyone would agree that a fair legislative district map should reflect the will of the people. This means that if a party wins the majority of the votes statewide then that party should also win control of the legislature in cases where the entire body is on the ballot at once. > [@Chronos](#): > > I’m not sure why you brought up that question. I’m glad you asked. I brought that up because you posted: > [@Chronos](#): > > As evidenced by locales like Vinton and East Cleveland. In East Cleveland, nearly a half of the Democratic votes are wasted, while in Vinton, only a third of the Republican votes are wasted. A half is more than a third, and so more Democratic votes are wasted than Republican votes, which benefits the Republicans. A half is indeed larger than a third, but we can’t tell how many votes are wasted on each side without knowing half of what and a third of what. So that’s why I asked my question and a few others that you glossed over. I think that one would need to look at wasted votes statewide to determine if a structural bias exists. I’m not arguing that a structural bias does or does not exist, but I’m willing to be convinced. I’m asking you the questions I’m asking because your argument for the existence of a structural bias is flawed and my questions expose these flaws. Furthermore, even if you can show that a red leaning structural bias exists in Ohio, that won’t show that there is a natural tendency for red leaning structural bias. A super smart guy with a PhD in physics once said… > [@Chronos](#): > > One data point does not disprove a tendency. [Previous page](https://boards.straightdope.com/t/a-mathematical-look-at-gerrymandering/998182.md?page=3)