great uh what I would like to talk about is a little bit more about gerrymandering so we have so far talked about sort of how you can draw the lines to give one or the other party uh advantages and how to achieve different outcomes that's what we um you know the questions about Jerry mandering on the test were about that what I would like to discuss for the next little bit is how to oh got my thick pen on sorry how to detect Jerry mandering how to detect if somebody has drawn the lines in an unfair way all right and specifically I want to talk about sort of how to specifically specific sorry how to specifically measure if the map is unfair and we're going to talk about a few different ways to do this um and I have here an example of the map of Wisconsin actually this I do not believe is the current map but this was the um state of Wisconsin map in 2018 the dist districts in the great state of Wisconsin and something that you will notice when you look at the map so the blues and the Reds represent the Republicans and the Democrats and the Darkness of the shading represents sort of the concentration of such voters so for instance this is a dark red right here which indicates that this is a big majority Republican whereas this is a light red which means it's only like a slight majority Republican and there's a there 's a little scale here like this this super dark one actually the super dark ones means that um when they run the elections they there isn't even a Democratic candidate sometimes in the in districts which are so lopsided um because uh here is so many Republicans the Democrats don't even bother having a candidate at all this this can happen in some places just because it costs money to run candidates and whatever um and if they know they're going to lose sometimes they just won't even won't even even uh bother but anyway uh what we see here is this particular map here shows I would say this map shows evidence of packing and cracking I will say uh against the Democrats and I'm not I'm not trying to be a a political partisan here it's generally agreed upon people who who look at this map basically everybody will agree that this map has been specifically designed to give an advantage to the Republicans and a disadvantage to the Democrats and you can see the packing at work because most of the Blues are super dark blue what that means is that I'm not doing anything maybe my wire is loose sorry there we go all right I don't know what's going on um Mo what I was saying most of the Blues are super dark blue but most of the reds are light red what that means is the Democrat Districts The D districts are packed full of D's and if you recall the packing strategy is you load up all of the D's in like one or two districts and that means there aren't enough of them to win any of the others now in this case it's not one or two there there are many many districts here but you will notice the D's almost all of them are packed into these super dark Blues all right there are a few Light blues but not many uh compared to the Republicans it's sort of the other way around almost all of the Republicans are in light Reds versus the dark Reds so the D districts are packed full of D's and the R I would say the r voters are spread across many districts and this allows the r voters to win kind of more than they deserve or more than their more than their population would suggest is um is fair so the r voters are spread across many districts to win more right but they pack all the D's into just a few districts so even though there's a lot of them they can't win a lot of districts because they're all concentrated in those districts now uh if you look at the numbers here so uh in this election this is like I said from 2018 um there are in 2018 I'll tell you the actual results of of this this map just reading um the the numbers behind the map uh there were 99 districts and 63 were won by Republicans so the Republicans won you know something like two-thirds of the of the districts um on a whole but 53% of the voters voted for Democrats so more than half of the voters voted Democrat but because all of those Democrats were stuck in only a few different districts they had blowouts in those districts where they were but otherwise they didn't win and the Republicans were able to win most of the uh most of the districts this is totally backwards right this says most of the voters were voting for Democrats but most of the districts were won by Republicans it's it's the exact opposite of what would be a more reasonable uh outcome all right 53% of the voters voted for Democrats and 4 5 voted for Republicans but even even though they had only 45% of the voters in the state they won 2third of the uh of the districts so this is a huge effect that is this the reason this kind of lopsided result is possible is just because of the way that the uh that the map was drawn all right um yeah people have analyzed this map and you could ask uh the question how many more Democrats would be necessary in order for the Democrats to actually win a majority of the districts and uh the the um the folks who have analyzed this say that the Democrats in order to win 50% of these districts they would actually have to have 70% of the population so they would have to go way above and beyond to actually win sort of uh even 50% which is already less than their true population all right so this map uh again I'm not trying to be a partisan about this I'm not trying to be a republican hater I am a hater of this map this map is super unfair uh but it was created by Republicans and Republicans um are sort of in power in the state largely because of this map and so it's very difficult for anybody to change the map I mean it's difficult for the Democrats to change the map because they don't have enough representatives to do anything about it all right uh anyway all of the things I'm talking about certain like statistics here and in theory I hope that it's uh it should be um something that seems doable we should be able to actually sort of look at these numbers and similar types of numbers to actually specifically measure um how good the map is or how bad the map is just by the numbers all right so this is called so there's a measure of it's really a measure of packing called and this is the most well-known and people in politics talk about this the efficiency Gap this is the um most kind of uh if you read like newspaper articles about Jerry manding and such um this is the most common way that people analyze the fairness of maps in some kind of of like statistical or numerical sense it's called the efficiency Gap and it's meant to measure packing of districts all right uh and the basic concept behind the efficiency Gap is it's based on the idea of wasted votes wasted votes are votes where they have these are sort of districts these are districts where one party has way more votes than they need and this really is the problem of the Democrats in Wisconsin is that all of their voters are con concentrated into a few districts where they're getting margins of like 70 80% of the vote and that's not necessary in order to win they could have won with only you know 55% and then a lot of those Democrats could have been in another District uh making their votes counts this is what they call wasted votes it's when the party uh one or the other party has way more votes than they need in one of the districts and so those people's votes are not actually counting for anything significant because they're just being spent on blowout elections where they could more strategically or more uh valuably to the party they could be um voting in more important elections where the margins are closer all right uh this is the basic idea behind doing the efficiency Gap maybe I'll tell you sort of very particularly there's a definition of a wasted vote so I'm going to write this down and then we're going to try and do some examples where we can actually calculate uh how many votes are being Wasted by this or that party so the definition is a wasted vote is any vote which doesn't contribute to the winners victory victory and in particular this means so the the details of how this works out is so any vote for the loser counts as wasted I'm not trying to use this word wasted as like a having any moral content I'm just saying this is a mathematical term they call it a wasted vote anybody who votes for the loser that counts as a wasted vote because this is not a vote uh which contributes to the Winner's Victory all right if you're voting for The Loser that counts as a wasted vote and any vote for the loser count sets wasted and any vote beyond the victory for the winner is also wasted right the winner needs a certain amount of votes to win but if they get any extras those votes are also they also count as wasted because those extra ones weren't actually necessary in order to uh for the winner to win their election all right all right so for example let's do some very simple examples and then I have some uh a little more more interesting ones so let's say in a district with uh 100 votes say they go let's say the Democrats get 47 and the Republicans get 53 all right how many votes are being wasted by each party this is what I would like to know if it's a close race like that how many votes are being wasted by each party so in this case um the r wins right because it's 53 to 47 so the uh Republican wins in this case um how many of each party uh how many votes of each party are being wasted in this case the D wasted uh remember what I said at the top there any vote for the loser counts as wasted the D was the loser so the D in this case wasted 47 votes and the r wasted what else it says at the top there any vote beyond the victory for the winner uh can anybody say how many this is like how many extra votes they got that they didn't actually need Beyond uh what it takes to win six uh this is yeah what this does not exactly the same as the margin of Victory which would be six here um there's six more you should think this is not a bad idea but um the way that we do this is is a little different think about how many votes did the RS actually need to win and then how many sort of extra did they get can anyone say first of all how many did they need to win 51 yeah they need to to uh 51 votes to win because there's 100 votes total all right and then how many beyond that did they get they get two extra all right so R wasted two and this is because they needed ah they needed 51 to win and they got two extra all right so in this case this district is a fairly close one right like this is not a packed District this is a district which has uh fairly close to even numbers and what happens um in this kind of District so this was not a packed District not not a packed district and here the um loser wasted a lot and the winner wasted a little and that is actually kind of how it ought to be in a fair District the winner will waste uh a little bit only whatever they are beyond the margin of Victory or beyond the threshold to win uh and the loser was a lot because all the votes for the loser are wasted so this was not a pack District here the loser wasted a lot the winner wasted a little and that's actually sort of how it should be if the district is not packed if the district is more or less uh evenly split this is what you will see happen the loser Wast a lot and the winter wastes only a little all right um but what if the pack what if the district is packed so if it was packed like something like um D gets three and R gets 97 now who's wasting what in this case well again R is the winner right so R wins and all votes for the loser count as wasted so here D wasted three votes because all of the votes for the loser count as wasted and are can anybody say any masters of subtraction out there how many votes are wasted by the Republican that is how many extra votes do they get beyond what they need to win yeah 42 42 how did you get that it's 4 40 something 45 46 something like that this is how many extra did they get beyond what they need what they need to win is 51 again because there's 100 total voters here they need 51 to win they got 97 which is an extra of 46 I think so our wasted 46 that's because they need 51 they got um 97 and you know if you want to be explicit about this it's 91 uh 97 - 51 which is 46 all right that's how you figure out how many exactly they wasted the Republicans wasted 46 all right and so you can see here in a packed District the winner Wast a lot and the loser wastes a little which is the opposite of what I said here if the district is not packed the loser wasted a lot and the winner wasted a little but in this example it was packed the winner wasted a lot and the loser wasted a little so here if it's packed then the uh the loser wastes a little and the winner wastes a lot all right and that means that this business about the wasting you can use this as a measure of how packed the districts are because in um in the case when it's even versus packed the the results of the wasted votes are opposite right if you look at these two sentences together they say the opposite of each other which means you can use this kind of counting up how many are wasted you can use those numbers to tell you how packed the district is or not all right and this is the idea behind the efficiency Gap so um and the uh let's just look at an example so I have this this hardly only barely deserves to be handed out because it's a very just a very simple picture but I figured it's easier than having you all try to write this down so what you will see here is four no five districts and I would like to measure the wasted votes for each one so the efficiency Gap I'm always going to write EG from now on the efficiency Gap is a statistical measure of wasted votes for each party and you can use this to measure how packed the districts are which is a standin for how fair the districts are so it's a measure of wasted votes for each party which measures fairness of the districts and it's not hard to count up the uh efficiency Gap and that's what this example I want to use to do that and then we'll do a more I have a you know slightly more interesting looking one to do also all right so here is uh what you have on the handout so I would like to um let's measure the efficiency gap for these districts and this would be like a typical homework problem in this section or or a test question or something I would show you some districts and say measure the efficiency gap for these five districts and this will allow you to say is this being um extra Fair towards the dark ones or extra Fair uh towards the light ones or maybe it's just kind of maybe it's not giving an advantage to either one all right uh so what we have here is there are five districts of course and I'm going to make sort of a big chart here it's not super big I guess but we have the disc districts all right they are 1 two 3 four five there are five districts here and I'm going to make a bunch of uh columns in this chart um first of all I'm going to just count up how many voters from each party are in each district so in district one uh you know you have to sort of look at the look at the Dots here I see uh four dark ones and six light ones all right so I'm going to say we got four dark dark and six light in the first district and so on for the other so number two is actually the same as number one so this also has four darks and six lights number three has two dark and eight light ones number four has uh zero and 10 and number five has 10 and zero all right so these numbers are just counting up the number number of Voters in each district all right uh next I am going to indicate in each row who won each time so I wrote four and L what is doesn't make any sense four and six sorry I don't know what I was what I was thinking uh next I'm going to just indicate who's the winner each time because the the uh wasted votes depends differently on who wins so uh the winner in this case I'll just circle the winners of course the winner each time is the bigger number right okay uh I'm also now in this example this is not really a big deal but I'm also going to write down the total the total number of Voters in each district so in this example they are all tens and for typical examples that we do the total will be the same every District although this is this is true for our sort of simple examples that we're going to talk about in class um there is in real life the various districts like the five districts in the state of Connecticut they don't have exactly the same number voters in every District in real life just because we're talking about like many thousands of people in every District they don't they can't split it exactly but anyway um these are the totals in this district and I'm also going to write down the threshold the the thresh the threshold to win in each of these since the total is 10 that means you need six to win in each of those districts so I'm going to say six every time in a more complicated example these might be slightly different numbers in each district although in this one they're all the same all right now we're going to get to the the real sort of meat of it I'm going to have and these are the important columns how many votes did the D's waste and how many votes did the L's waste all right this is I suppose the hard part although it's not really hard you just have to know what you're doing the others were just writing down basic information in the chart so uh in the last two columns I'm going to say how many is wasted by each party and remember the rules about wasted which I wrote uh a few minutes ago every vote for the loser is wasted and any votes for the winner beyond the threshold are wasted so in the first row first of all every vote for the the loser is wasted that means these four for the D's are all wasted so D's wasted four here and how many are the L's wasted every vote for the loser is wasted and every vote for the winner beyond the threshold is wasted in this case the L's wasted zero because they actually didn't get any votes beyond the threshold to win they got exactly what they needed which was six all right the threshold is six they got six that is zero extra that's what this zero means all right if you want to be very specific about it this column for the winner is always this number minus the threshold which in that case is zero all right the next row is exactly the same all the numbers in row two are the same as Row one so again the D is wasted four that's because every vote for the loser is wasted and the L's wasted zero because they got no extra votes beyond the threshold all right the next row again the D's are the losers and every vote for the loser is wasted so here the D's wasted too and the L's someone want to say how many are wasted by the L's this would be how many they got extra beyond the threshold two is the answer yeah the they got eight they only needed six so that's two extra and those count as wasted for the L's all right next line we have D's got zero L's got 10 every vote for the loser is wasted so these zero become Zero D wasted and uh what do you say for the L four four yeah the L's got 10 but they only needed six so that's four extra so the L's wasted four on that one and then the last one is similar but it's the other way around so the last one the L's lost every vote for the loser is wasted so the L votes here are are all wasted but it's it's zero the 10 was four extra so it's like so all right so those last two columns that's like I said that's kind of the hard part I hope it doesn't seem it's not that hard you just have to know what you're doing and be a little careful about where the numbers go all right uh this is pretty much everything that you need to do to figure out the efficiency Gap uh how do you say the answer so the efficiency Gap is a specific number and the way that you sort of calculate your final answer here is it's all about who is wasting more votes than the other party so we are going to add up the total of the wasted votes the L's wasted a total of six the D's wasted uh looks like 14 right so the D's are wasting many more votes than the L's that suggests that the map is sort of biased against the D's and in favor of the L's because the D's are wasting more now the efficiency Gap is typically written as some kind of a percentage and it's written um as usual you know since we're not using calculators on our tests or whatever I would like you to just I would expect you to just write it as a fraction we are also going to add up so the fraction here I'm going to add up the total of the totals so this is 50 total votes that's what the the total of the totals is 50 total votes 14 are dewed six are L wasted right in a typical election you know each of the two parties is going to waste some the big thing the what's interesting is that the D's are wasting a lot more than the L's in this case which means that the map is biased against the D's and so the way that we write down our final answer we say the efficiency Gap is this fraction it's the difference divided by the total so the this this fraction the denominator is always the total number of votes and the numerator is the distance uh the difference between who's wasting more versus who's wasting less all right and we say in favor of the L that's because D is wasting more and so this map benefits the L and it hurts the D right this is my final answer so can I just say the fraction just so we're all on the same page it looks like up top is the difference of the wasted right in this case it was 14 and six and the difference I mean you subtract you know the bigger one minus the smaller one and then and then the bottom is the total number of votes all right this is how you do the fraction and then you always say so together with that you say in favor of whatever and what goes here is the uh the one with fewer wasted right that's the one that's benefiting is the one that is La uh wasting fewer all right and if you like of course if you're doing this on the on the homework or something you can write this as a percentage and when you read about the efficiency Gap in real life it's usually written as a percentage um I did this in my calculator this fraction here this is 8 you know if you actually do the subtraction 8 over 50 which is 16% and so you can look at various maps in real life and you can just compare their efficiency gaps one with another and see which ones are more fair uh big number here is bad so like efficiency gap of zero that is like the theoretically lowest that it could be efficiency gap of 0% indicates no Advantage for either party and this is this is sort of good right this is how the maps ought to be that they the map itself doesn't give a benefit to one or the other of the parties but then a high efficiency Gap uh is is indicates unfair Maps high efficiency Gap indicates an unfair map right this is how the efficiency Gap weeks any uh any question about that example I got another one for us to try all right we got 15 minutes I think that's enough time to try this one so this is oops sorry this is another one this is one is maybe a little bit more interesting uh maybe we can do the this this uh paper has two different examples maybe we'll do the first one all together together and then I'll have you guys try the second one I think if you know what you're doing this uh efficiency Gap thing is not that hard you just make the make the big table make sure everything goes where it ought to go all right so we have two different examples here let's do the first one Al together and then I'll have you guys try the second one on your own some okay so what we have here again sort of the the lights and the darks I hope you can tell the difference uh between the shadings it's probably easier to tell on your on your page there um if you look at the two the two pictures on the paper this one I intend for the first one to be a little more fair the first one is a is a is a very natural just kind of even division whereas the second one you can see some evidence of packing um in the way that I drew the shapes in the second one so uh anyway let's just see how it goes so this time I have four districts one two 3 4 um I'm going to try to make the same chart that we did before you have to just sort of count stuff up so in the first district we have 1 2 3 4 5 6 7 8 Nine dark ones and 1 2 3 4 5 six seven light ones all right uh each of these boxes have 16 total in them so that might help you do the counting in District Two over here the dark ones are 1 two 3 4 5 6 7 8 nine so this again is nine and seven in District three I have 1 two 3 4 5 six seven dark and nine light it's that that way and then in District Four we have 1 4 5 6 7even this is seven dark and nine light that way all right so these are the counts from now on actually you don't have to look at the the picture anymore everything else is just so fairly routine so I'm going to write down the uh the total in each one was it that was the next column I wrote right yeah so the total in each one was 16 for all of them that means the threshold what's the threshold here that's how many you need to win in each one I would say nine I think somebody said nine uh half of 16 would be eight that will be a tie if you got eight uh if you want to win you got to get nine so the threshold is nine here in each of them uh all right and then I can say the D wasted and the L wasted maybe I like to circle the winner each time that's just the kind of guy I am um and remember every vote for the loser counts as wasted so you might you might want to just uh immediately draw in all the loser votes all these sevens are wasted so I have L wasting seven here and seven here because those were the loser votes and the D is wasting seven and seven here because those were the loser votes and then how many uh wasted for the winner is I I suppose slightly more complicated but not really that much how many is dwting here that means again how many extra did they get beyond the threshold what do you say show me the fingers I see some fingers like this fight the power zero extra right the threshold here to win was nine they got exactly nine that is no extra votes were obtained by the D's they got exactly how many they needed no extras all right uh and so and so on actually all of these are going to be zeros because they're all the same nine versus seven all right this is the whole chart let's say the difference I mean say the answer the answer remember the way we write this as fractions or whatever you add up the total wasted for each of the two parties in this case there are 14 and 14 you also add the total of the totals there's uh four 16s there adds up to 64 I happen to know and then we make our fraction so the efficiency Gap is remember how you get the fraction the bottom is the total of the totals which is 64 and the numerator is the difference of the wasted now in this case we have 14 and 14 which just makes zero in the numerator so this is zero out of 64 which as a percentage I happen to know is zero any fraction where the top is zero the whole thing is just zero all right so the efficiency Gap is zero that indicates that this map at least as far as efficiency Gap goes is totally fair there's no um there's no Advantage for one or the other based on wasted votes all right so this indicates this map is totally fair at least according to this efficiency Gap all right of course efficiency Gap is not the only thing that you could consider when you're trying to judge if they're fair or not but as far as the efficiency Gap goes this uh this division is completely Fair all right in our remaining 10 minutes I would like for you all to try the second one so you will want to create a chart like that based on the other picture on there and that one will be a little marching you're not going to get zero as the answer come on now here's the picture your chart should look something like that sorry I ran out of room on the side there I got a little messy that's fine there we go all right I'm going to come and see how you're doing I count the dots okay than every I'll give you another couple minutes maybe all write down to numbers here sure all right can we talk about these we got five minutes to uh conclude here so in the first district I see only two L's and there must be 14 D's then in the second I see seven and nine in the third I see six and 10 and in the fourth I see five and 11 is that right anyone agree with that yeah so this unfortunately if you mess up these counts then the whole rest of it is going to be screwed but um hopefully you counted them up there are 16 in each that's how I did them and the threshold then what do you say nine yeah half of 16 would be eight one more than half is what you need to win which would be nine yeah that's the same as the first picture there all right and now the important part is the wasted votes for each of the two parties I i' like to write down so first of all I Circle the winners just cuz it helps me keep it all straight and every vote for the loser is always wasted so all of those numbers which are not circled they just get copied over to the wasted columns so that's like that right two wasted for the L's in the first row and then those other loser votes are wasted for the D's in the other rows and then let's fill in the winner wasted votes where you have to do a little subtraction I mean if you want to be uh specific about it it's always going to be this circled number minus the threshold that's what these um these numbers over here should be so it's going to be 14 minus 9 is 5 that's because they needed nine but they got 14 which is five extra and then I have 9us 9 is zero they hit the threshold exactly so there was no wasted votes there then I have 10 that's one extra and 11 that's two extra so I hope that you got these same numbers that I got any questions about thems all right and how do we finish it off so that was the hard part I guess uh just to actually finish it off you add these up so that's five this one adds to 23 I believe the total of the totals is 64 and then I say the efficiency Gap is 23 minus 5 over 64 that is to say 18 over 64 which you can put in your calculator if you want to I'm not sure if I did I did I got 28% and you should always say in favor of which one is it in favor of L yeah that's because the D's are wasting much more than the L's so that means this map is uh advantaging the L and disadvantaging the D's all right that's how we do it we'll do some more examples next time