# How would presidential elections change if electoral votes were allocated by congressional district ?

First published on Quora.

This is the system currently used in Maine and Nebraska. In Maine and Nebraska the statewide winner gets the two electoral votes (EVs) that correspond to the senators and then the remaining votes are determined by the winner of each congressional district.

The Electoral College already has a “small state bias” that skews for the time being in favor of the Republicans, since the smaller states tend to be more Republican than the country as a whole. I haven’t checked the numbers, but California has the same population as something like the smallest 20 states combined. That’s two EVs for the statewide win in California compared to forty for the statewide wins in these other states. It’s this bias that is responsible for the two “electoral inversions” we had in 2000 and 2016. That is to say, the two elections where the winner of the Electoral College did not match the winner of the popular vote.

Choosing the remaining EVs by congressional district would further skew things in the Republican direction. This is due to the extreme partisan gerrymander that took place after the 2010 election. To put this into perspective, the Democrats won the “national congressional vote” (NCV) in 2018 by something around 7 percentage points. This will give them a majority of between 14 and 19 seats when the remaining races are determined. By contrast, the Republicans won the 2014 NCV by 5.4 percent in 2014 and that gave them a majority of 30 seats. Worse, in 2012 the Democrats won the NCV by 1.2% but the Republicans maintained a majority in the House of 16 seats.

So, at least until the the congressional districts are redrawn in the wake of the 2020 Census, the current small state bias that favors republicans would be exacerbated. I don’t know if it would be impossible for a Democrat to win the presidency under such a system, but it would certainly be more difficult and there would be many instances where this system would elect the Republican even if the American people preferred the Democrat.

Still, it’s easy to imagine a worse system. During the run-up to the 2012 election, I recall Nebraska debating a return to a winner-take-all system so that President Obama could not win an EV from Nebraska like he did in 2008. At at about the same time the republican-controlled Pennsylvania legislature debated switching to allocating EVs by congressional district to help Governor Romney. Imagine such a system implemented nationwide, with all the red states using winner-take-all and all the blue states allocating by congressional district or vice-versa. Such a system would virtually guarantee one-party control of the presidency.

References (all accessed 19 November 2018):

House Election Results: Democrats Take Control

RealClearPolitics – Election Other – 2014 Generic Congressional Vote

RealClearPolitics – Election Other – 2012 Generic Congressional Vote

114th United States Congress – Wikipedia

113th United States Congress – Ballotpedia

# What if Captain America became President?

First Published on Quora, 14 October 2019.

It’s worth pointing out here that this very idea has already been played around with in the comics. In Captain America 250 (October 1980) Steve is approached by the New Populist Party and asked to be their candidate for president. He gives it serious thought and spends most of the issue debating the pros and cons with his friends, Avengers and otherwise. The ending of the issue is bittersweet; Steve, of course, decides not to run for president and the enthusiasm that had been building within the NPP turns to a profound disappointment.

About six months later, Marvel itself answered this question in What If? #26. Of course we don’t really know whether WI#26 tells us what “really” would have happened, but it’s at least as valid as what anybody else would have said. And in some sense, that’s the ultimate answer to the question at hand. It really depends on who gets to write the story.

Cap #250 is a classic. What if #26 is pretty good. Both are worth checking out and are available on Marvel Unlimited.

To give my own opinion, there’s two things I think are worth addressing, how Steve would have governed and how the public would have been likely to respond.

Politically, I think Steve is likely to be a New Dealer. He was born in 1920 and came of age around 1940; FDR was popular and won a fairly lopsided electoral victory that year, although not nearly as lopsided as 1936. I think what we’ve seen from Steve over the years bares this out, from Englehart’s run in the 70’s to his reason for stepping out of the role in “Captain America No More” to his stance in Civil War and beyond (Hydra-Steve not withstanding). In foreign policy I think he would be an excellent diplomat, able to find common ground with other nations and move forward productively. He would certainly be more apt to use military force than Carter, but probably not nearly so apt as either of the Bushes. He would be relentlessly ethical.

But I think that the public’s response to Steve as president would be more indicative of his legacy as Commander-in-Chief than his political positions.

If he had been elected President in 1980 when “Cap for President” first hit the stands, conservative or liberal, I think President Rogers would have been a transformational  figure. Six years out from Watergate and a bit over a year after Carter’s malaise speech, the American Electorate was in flux. “Reagan Democrats” were becoming a thing while there was a candidate for the Republican nomination, John Anderson, who was arguably more liberal than the Democrats’ eventual nominee. If there’s one constant in all the portrayals of Steve Rogers, it’s in his ability to lead and inspire. Cap as president in the early 1980’s would have changed the political landscape for a generation or more.

On the other hand, had Steve been elected in the current political climate, I don’t think any of that would have mattered. Ed Brubaker (I’m pretty sure, I haven’t been able to locate the quote) made a relevant remark about the time Steve “died” in the aftermath of Civil War. He said that it was tricky to write Cap. One side of the political spectrum mainly wanted to see Cap beating up terrorists, while the other side mainly wants to see him giving speeches about rights and fairness. If anything, this aspect of has gotten more extreme over the past 11 years. Steve as president in the 21st Century probably presides over a lackluster presidency with one side of the aisle lauding his accomplishments and the other condemning his inadequacies, justly or unjustly.

And that, I think says much more about the state of politics in America today than it does about Captain America.

References:

Captain America #250 (October 1980)

What If? # 26

Captain America – Wikipedia

# Peter Parker’s Playlist

I just took a stab at answering the following question on Quora, and I thought I would share it here as well.

What would Spider-Man/Peter Parker’s music playlist be?

No definitive playlist, but some thoughts. The only mention I recall of Peter Parker’s music taste is from Marvel Team-Up Annual #4 from 1981.

Purple Man has Peter climb a lamppost to distract him and has him sing. His choice of music? Elvis Costello. Specifically “Oliver’s Army” from Armed Forces.

Extrapolating from this, here’s my guess. Peter probably listens to well regarded artists who are slightly out of the mainstream. Elvis Costello is established. Perhaps also artists like the Velvet Underground, Big Star, Nick Lowe or The Talking Heads.

Popular and mainstream artists might be less likely. Pulling from the same time period, maybe not Madonna, Michael Jackson or U2. These are mostly 1980’s examples since that’s when the comic came out, but you could extend the same thinking to other decades. It feels to me like it would hold true.

The one thing we can say for sure, is that Peter isn’t just listening to the top 40; he’s done some research and I suspect his tastes are fairly eclectic. It wouldn’t surprise me if he listened to some Big Band music if that was what he heard growing up with Aunt May and Uncle Ben.

It would be interesting

to see what other references to music we could find in the comics.

Update: Blaine Savini, a member of Old Guys who Love Old Comics on Facebook, pointed  out that we also learn in the Comics the Peter likes Ella Fitzgerald.  This is from Amazing Spider-Man #136, September 1974.

The Album in question is likely Ella in London (4 1/2 Stars, allmusic.com) which is the only 1974 issue listed in her discography on ellafitzgerald.com. It contains songs by George and Ira Gershwin, Duke Ellington and Cole Porter.

Notice that MJ clearly implies that Peter doesn’t listen to much in the way of popular music.  He mentions that he’s a junior in college in this issue, if that means he’s 21, he would have been Spider-Man for about 6 years at this point.  In 1964 we would have been 11.

But,well regarded, check.  Out of the matinstream, check.  Ella Fitzgerald and Elvis Costello: Eclectic, check.

References:

# Writing a Combinatorial Proof

This started life as a post on Quora, answering the question:

For any positive integer $n$, how do you write a combinatorial proof of the identity

$\displaystyle {2n \choose n} = \sum_{i = 0}^{n} {n \choose i} {n \choose n-i}$?

To write a combinatorial proof, the idea is to describe how each side of the equation is actually counting the same set of objects.

Now, if you have a set of $2n$ objects, $\displaystyle {2n \choose n}$ (that is $2n$ choose $n$) is the number of subsets of that set which contain exactly $n$ of them.

Now pretend that you’ve taken your $2n$ objects and put them into two boxes with $n$ objects in each. Think about what each of your terms on the other side of the equation, $\displaystyle {n \choose i}{n \choose n-i}$ represent. Then consider what you get when you add all of these together. You should be able to explain that this really does count the same thing as $\displaystyle {2n \choose n}$.

Now when I wrote the above, I wondered if this was a homework question someone had posted to Quora.  I didn’t fill in all the details since, while I’m happy to help someone with their homework, I don’t want to do it for them.

But in case anyone wants to see a worked out example, here’s the standard initial example of a combinatorial proof.  This is the identity that makes Pascal’s Triangle work as nicely as it does.

Theorem: $\displaystyle {n \choose k} = {n-1 \choose k} + {n-1 \choose k-1}$.

Proof: Let’s start by thinking about the expression on the left.  If we have a set with $n$ objects in it, $\displaystyle {n \choose k}$ is the number of ways we can select a subset of $k$ objects.  To say that another way, it’s the number of ways we can pick $k$ objects out of our set without caring what order they’re in.

Now suppose one of our objects has decided to wear a hat.  If we’re looking to select a subset with $k$ objects, we can decide to include or exclude the one wearing the hat.

Say we don’t want to include the guy with the hat.  In that case, all $k$ objects, have to be selected from the $n-1$ objects that aren’t wearing hats.  We can do this in $\displaystyle {n-1 \choose k}$ different ways.

Now suppose we decide to include the one with the hat.  Well then, to get $k$ objects altogether, we need to select $k-1$ more from the set.  There’s $\displaystyle {n-1 \choose k-1}$ ways to get the rest of the objects that you need.

Putting these two together we see that $\displaystyle {n-1 \choose k} + {n-1 \choose k-1}$ is also the number of ways to select a subset of $k$ objects from a set containing $n$ things.

Therefore, our identity must be true.

If you’d like to try one on your own, $\displaystyle 2^n = \sum_{i = 0}^{n} {n \choose i}$ is another nice example.

# How do you prove a conjecture is false?

First posted to Quora on Friday, 7 September 2018

That depends on the nature of the statement.

If you have a universal statement, which is to say a statement that all of the things in some category share some property, you merely have to provide a counter-example.

So if you wanted to disprove the statement, “all prime numbers are odd” you’d merely have to point out that 2 is even and the statement cannot be true.

Disproving an existential statement is usually more work. These statements say that there is at least one thing that has a particular property. To disprove an existential statement, you need a general argument that that property can never happen.

So to prove that the statement “There is a pair of even integers whose sum is odd” is false, you must prove that the sum of any two even integers must be even.

Those are the cases “all” and “some.” The cases “none” and “some are not” are similar.

To disprove a statement like “None of the items in set A have property B” you simply have to find one that does. If you want to show a statement like “Some of the items in set A do not have property B” is false you need a general argument that everything in A has property B.

In any case, disproving a statement is equivalent to proving its negation.