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so there's a video going around by a

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doctor shiva ayadarya

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and uh in it he puts up this graph here

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and it's a

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as a metric of something that he plots

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based on

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the votes in kent county michigan and is

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confused as to why

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this line slopes down so what i did is i

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set up a kind of a

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simulation of of voting possibilities

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to explain why that happens and as you

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can see i've kind of duplicated

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the line sloping down here now he has

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this other thing here where he says the

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line kinks off to the side but really

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that's just a

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a very arbitrary way of drawing a line

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through here you could very easily just

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draw a straight line

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through the entire thing as i have here

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uh so

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what's actually going on here well i set

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up this simulator so

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this square here represents all of the

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voters on

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one side there's the people who normally

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vote republican on the other side

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there's the people who normally vote

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democrat

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and we can move uh between the two

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so we can kind of simulate different

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precincts where for example the

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republican vote is very low like over

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here

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very low and the republican vote is very

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high

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and that gives you this this graph of

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different precincts throughout

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michigan some of them are more democrats

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some of them are more republican

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uh in kent county so what's actually

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what is this graph what is it

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representing well it's a little

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a little confusing based on his

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description but i eventually figured it

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out

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he's taking on the x-axis here

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what he calls the straight republican

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party score

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which is the percentage of people who

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just voted for republican straight

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ticket

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divided by the total number of people

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who voted for straight tickets which is

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the republican straight ticket plus the

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democrat straight ticket

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and we're ignoring all of the parties

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for now because they're pretty small

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in this analysis so it's essentially

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this rectangle here divided by this

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larger rectangle the red plus blue

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rectangle

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uh then against that is plotting

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uh the difference between that and

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the same thing for individual voters

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people who

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chose to vote for individual parties in

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each race so they could vote say

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for one party for the senate and another

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party for the president

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so it's the ratio of this rectangle here

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the republican individual

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uh trump voters uh the trump the

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individual trump voters to the

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individual biden voters

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uh over here so is this rectangle

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divided by this rectangle but it's not

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just plotting these two it's plotting

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the difference between them

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so we can see if i put that back and

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move from left to right

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we have this difference here between the

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two and you can see it's plotted over

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here

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now i had area's key mistake is that

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he assumed that all people who were

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republicans would vote for trump because

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republicans all love trump

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so much of course this isn't true if it

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was true you get what he

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says he should expect which is a flat

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line centered around zero

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because the the proportions of these two

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things never actually changes it's

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always the exact same proportions this

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to this and this to this exact same

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proportions

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of course if you add something into the

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mix like uh republicans who vote for

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biden republican individual voters vote

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for biden

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and democrat individual voters who vote

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for trump

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and this changes things now if we

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go through the various proportions

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you'll see we get a sloped line

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and it's always going to slow down it

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doesn't actually matter

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whether you've got like all republicans

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or

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all democrats switching it's always

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going to slow down

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the reason is because that this ratio

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here always goes from zero to one

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whereas uh

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this one goes from different values but

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the point is

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that if you introduce something like

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this which is an expected thing we

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expect people to do this you get this

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slope would this downward sloping line

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and you can see

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this downward sloping line is similar to

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what we get in

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in this graph and you can adjust the

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amounts of people i think perhaps

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more republicans would actually vote for

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biden than democrats would vote for

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trump

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and that changes the graph to be more

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like the one we see in the picture here

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of course it's more complicated than

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this this is a fairly straight linear

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thing

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the proportion of people who vote

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republican straight tickets might not be

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the same

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as the democrats they might be more

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or it could be the other way around

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or it could be in fact that

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it's skewed so that the more people vote

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republican the more likely

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they are to vote a straight ticket and

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vice versa so it could end up something

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a bit more

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like this which is even more of a

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so i think this kind of illustrates a

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couple of things uh first of all

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you know this graph here the fact that

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he's confused about how he could be

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sloped down

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is he actually confused or is it a bit

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misleading i don't know i

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tend to assume that he's just a bit

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confused

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but perhaps he has a preference

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to express here and he's expressing it

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by maybe deliberately misleading i don't

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know

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it's just a speculation on my part and

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the other point is that it's

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it's actually quite complicated uh it

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was kind of difficult at first uh

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to follow his explanation of where these

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numbers actually came from

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and it took me a while to replicate the

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graph which i i did eventually replicate

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the exact same graph here's is my

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version of it it's basically the

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the same one uh and it's not intuitively

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obvious as to why the line would slope

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down i thought

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initially that if we had the these

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flipped around then it would the line

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would go up but of course that doesn't

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doesn't actually happen the line goes

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down no matter which way around you have

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it so it's actually

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an unintuitive metric and it's also kind

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of um

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in some ways kind of a pointless metric

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because it doesn't really tell you

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anything because there's so many other

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variables like

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how does the split between uh

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split ticket voters people who vote one

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party for one one season one for another

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how does that vary

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based on the percentage of people uh

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voting one way or the other

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i have it skewing here uh for the

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the amount of straight versus individual

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but

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you know that that too is uh is unknown

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as to how much

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that's an actual factor uh but it didn't

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really take very much

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for to replicate the the results as we

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uh

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we see them more or less the same here

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as they are in the graph below so there

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you go

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there's there's no real significance to

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this other than showing that some people