Judging for Ourselves

References to and comparisons with Hitler’s rise may be valid, however, I think a more accurate comparison can be drawn with Romania’s pre-WWII  “Iron Guard” movement  and its leader Corneliu Codreanu.   This became the basis for Eugene Ionesco’s “Rhinoceros”, a play that depicted the transition of a group of ordinary people into a herd of these animals, one by one, each with their own rationale for accepting them and then becoming one themselves.   We read this in high school (mid-70s) and it comes to mind whenever I see people I thought I knew and even respected begin to embrace right-wing authoritarianism, something I thought they abhorred as much as I.

Right-wing fascism has reared its ugly head many times throughout history, wearing many masks.   The players, populations, and languages differ, but, the circumstances and warning signs are nearly always the same:

The good news is that, notwithstanding claims of “the death of liberalism” that fascists and their apologists seem often chant these days, it is in fact fascism, authoritarianism that is typically short-lived.   Like its economic concubine, speculative capitalism, it survives on the necessarily increasing output and consumption of it’s own excrement, and soon meets its end by starvation, or sepsis from having swallowed too much of its own shit.   Democracies, or at least regimes that recognise their power as being derived from the compliance (or complacency) of the governed survive for centuries; authoritarian regimes rarely last more than a few decades.

I’d be willing to bet that the articles of impeachment against Trump were drafted even before he took office — possibly even before the election.   Both Putin and the Republicans saw him as a “useful idiot” and they’ll continue to pull his strings until the FBI and other investigative agencies have all of the ducks lined up to bring him down.  At which point, Trump will either be convicted and removed, or he’ll resign, or 25A will be invoked.  In any case, Pence will be installed and, whereas Trump was a useful idiot, we’ll now have to deal with a complete moron until 2020.   With any luck enough of the benighted fly-over (by then they’ll be more aptly-named fucked-over) states will have seen the folly of voting for Trump and use their votes to say “fuck you” right back.

In the mean time, however, we’ll see a rise in anti-anyone-who-ain’t-white-christians-like-us violence and threats to persons and American Democracy itself.  The last, best defense, there, will be the courts.  My greatest fear, is that we’ll start to see judges assassinated, as has happened when such regimes have taken over in Latin America, for example.   We can worry ourselves over the circus going on in Washington and state capitols across the country, but such assassinations are, to me, far more worrisome.   Two of our government’s three branches have been weakened by three decades of relentless, right-wing undermining of people and principles, leaving the judiciary to stand against it, alone.  Unless and until we see that start to happen, I have great confidence in the ability of our constitution and the democracy that it implements to endure and prevail.

Horse lookin’ at you, kid

I have been on a horse precisely three times in my life. This photo was taken on the first such occasion. About five minutes afterward, the horse, named Winnie1, was running around the paddock at what seemed like about 100 mph with me hanging off to one side, held there only by my foot, caught in the opposite stirrup. I was four or five at the time.  My aunt  (whose horse it was) and uncle (the guy in the photo NOT on the horse) quickly ran over, got the horse under control and spent the rest of the day attempting, with varying degrees of success, to calm me down — or, at least get that silent, open-mouthed scream look off of my face before my parents showed up to take me home.

I did not get back on a horse again until I was maybe 20.  A friend from school owned a horse and asked if I’d like to come along with her to feed and brush it.  She also planned to ride her a bit around the paddock. I reckoned there’d be no harm (to me) in that, so, I went along. The horse was nice and calm (turns out it was faking, plotting when and how it would make its attempt on my life) and lulled me into a false sense of trust. My friend finished her short ride, and knowing my apprehension of horses, asked if I’d like to just sit in the saddle for a bit.  Sure.   Why not.

I was still alive and well after a whole two minutes on horseback, so she (my friend) asked if I’d like to have a short walk with her (the horse) around the paddock.  “Uh … ok.”  After all, I thought, I was little when that other horse nearly killed me.   I’m a full-grown adult now.  I’m big enough to control this animal.  And if not,  I’d at least be able to get in a couple of good hits before this one did me in.

Five minutes later, there I was hanging on for dear life as that fuckin’ horse went racing around the paddock at what seemed like around 100 mph.   “Pull on the reins and say ‘Whoa!'”, my friend yelled.  I pulled and pulled on the reins, to no effect. “Whoa!!”. Nothing. “Stop!! Fermo!! Halt!! стоите!!”  The horse was evidently deaf in addition to being homicidal.

Still moving at break-neck speed,  the horse turned and headed straight for the (closed) paddock gate.  Just when I thought my fear of injury or death couldn’t be any greater, my friend opened up a whole new world of pants-shitting terror for me when I heard her hollering, “Don’t let her jump!!!!”.

I decided the only chance I had of getting off alive was to jump off while the horse was in motion.  I got my feet out of the stirrups and vaulted2 as best I could off the horse, still holding on to the horn on the saddle.  My feet no sooner hit the ground than the horse stopped dead in its tracks, maybe a meter or two from the gate. It swung it’s head around to look at me with a murderous glint in its eye that said, quite unambiguously, “Next time, asshole.”

The third (and so far, last) time was on a visit to Turkey around 14 years ago. We were on the island of Heybeliada, in the Sea of Marmara near Istanbul. There are no cars there; only horses and horse-drawn carts. My companion had never been on a horse and was dying to try it. There was a guy there with several horses for hire and he was happy to lead the horse by its tether for those who wanted to ride but were untrained. I figured, what could go wrong? So, we hired a couple of them and he led us for two or three kilometers under a perfect blue sky along one of the lovely, quiet, car-less green avenues that follow the island’s shoreline.

Our guide saw that both horses were behaving well, and my friend seemed to take to riding like a duck to water. He saw that I had taken to riding like a duck to bowling.   Still, the horse was well-behaved as it continued clip-clopping along, so he decided to let go of the tethers.  Both of them.   My friend and her horse kept right on going, the horse happily obeying her gentle tugs this way or that on the reins, the two of them making shallow S-turns as they ambled along.  My horse plodded along lazily, disinterested, slightly behind hers.   I just held the reins nice and steady, making every effort to not remind the beast that it still had me on its back.   Several blessedly uneventful minutes passed and I started to think that maybe horses didn’t have it in for me after all.

Of course, he was just biding his time, waiting until the man wasn’t looking, at which point he turned right around and headed off toward … I don’t know where … a quiet spot to murder me, perhaps.  In any case, the man soon noticed I’d been kidnapped and quickly came back for us.  He gave me an apologetic smile as he took up the tether, and continued to lead the horse, with me still on it, for the remainder of our hired time.

I’m not kidding when I say they want to kill me.

To be fair, I have had equine encounters that were not life-threatening.  One could even go as far as to say that they were pleasant.   While visiting a long-time friend in Arizona some years ago, she introduced me to her horse, Mage.   We eyed each other cautiously at first, but it wasn’t long before she was letting me pat her on the forehead and taking a carrot from my hand3.  By the end of our visit, Mage and I were getting on famously.  The trick, I found, is in knowing where you and the horse stand with one another.  I stand on one side of the paddock fence, and the horse stands on the other.  No miscommunication, and no one gets hurt.

My most recent encounter was with a neighbor’s two Australian miniatures.   These look either like fat ponies or rather well-built donkeys. Regardless, they turned out to have the sweetest most gentle temperament of any animal I’ve been close to that’s larger than, say, a great dane.4  Still, I kept to my side, they kept to theirs, and we all got along just fine and all walked away with no injuries.   I hear they’d be great for keeping what passes for a lawn in our garden under control.   I’m even tempted to see if one day we might get one.  Trouble is, these adorable little creatures live for 40 or more years.   Given my present age the odds are that, for them, it would simply be a waiting game.

Epilogue

It seems there is now research to support my suspicions that horses are out to get me.

Selectoral College

For the third time in a century we have another election in which the candidate who won the popular vote did not gain enough electoral votes to win the presidency.  This probably leaves you scratching your  head, wondering how that’s even possible?    After all, the number of electors each state has is based on the size of that state’s population, right?  If a candidate gets the most votes in that state, that candidate wins all of the electors for that state.   If you sum up all those votes the winning candidate should have the biggest total in both the popular vote and the electoral vote counts.   Right?  Yet, we have two recent examples where the candidate who won the popular vote LOST the electoral vote.  (Gore in 2000, and Clinton this year.)

You don’t need to have a degree in math or political science to understand how this can happen.   It looks complicated because there are so many states involved and the outcomes in those states are determined not just by votes cast, but by the percentage of voters who actually vote.   If we look at a simpler system, and just assume everyone who can vote does, electoral math – and weird outcomes like we’ve just seen – are much easier to understand.

An Example

Let’s imagine a country that has just 6 states.   One state has a population of 100, the other five have populations of 10 each.   Each state is allotted one electoral vote for every 10 people.  (We round up to the next 10, so a state with 13 people would be treated as though it had 20 and thus get 2 electoral votes.)  Electors are awarded on a winner-take-all basis:  whoever wins the most votes in that state, even if only by a single popular vote, wins all of the electoral votes.

State Population Electors
Big State 100 10
Small State 1 10 1
Small State 2 10 1
Small State 3 10 1
Small State 4 10 1
Small State 5 10 1

Now, suppose you have an election to decide between candidate Jim and candidate Nancy for the next president.   Even if all of the Small States vote unanimously for Jim, giving him 50 popular votes, he’ll only get 5 electoral votes.   But if Jim loses in the Big State, even by only a few votes, Nancy gets all 10 of that state’s electoral votes, and thus beats Jim.  All Nancy needs to do to win is get 51 votes (Jim would presumably get the  other 49.)

Candidate Big State Tally Small State Tally Popular Total Electoral Total
Nancy 51 0 51 10
Jim 49 50 99 5

Nancy’s electoral tally is 10, but Jim’s is only 5.  Yet, the popular vote CLEARLY favored Jim, giving him a total of 99 (50 from the Small States plus 49 from the Big State) with Nancy only receiving 51.  Nancy wins with the most electoral votes even though she lost the poplar vote.  Jim could lose by a very wide margin in the Big State — as much as 26 to 74 — and still win the popular vote (76 to 74), but lose the electoral college the way we’ve laid this out.  This system is quite obviously biased in favor of the state with the most (voting) people.

Unbiasing the Bias

Let’s see if we can fix that the same way representation in the US’s legislative branch (Congress) was fixed.   We’ll start by giving every state just one more electoral vote.  We end up with Big State having 11 votes and each Small State having 2.  Together the small states have 10 votes, which is better than before but still not enough to overcome Big State’s voting “power”.

So, let’s give every state two additional electoral votes and see what happens.

State Population Electors
Big State 100 12
Small State 1 10 3
Small State 2 10 3
Small State 3 10 3
Small State 4 10 3
Small State 5 10 3

Now each Small State has 3 electoral votes for a total of 15, and  the Big State has 12.   Recalculating the tallies …

Candidate Big State Tally Small State Tally Popular Total Electoral Total
Nancy 51 0 51 12
Jim 49 50 99 15

Nancy now has 12 electoral votes, but Jim has 15, so Jim wins both the popular vote and the electoral college.  We can all agree this is a fair and decisive outcome.

Or, is it?

In fact, this doesn’t eliminate the bias at all; it just shifts it to the smaller states.   Sure, it gives the Big State 20% more voting “power”, but it gives each of the Small States 200% more voting power.

Let’s go back to our example and change the vote counts so that Nancy gets 80 votes in the large state and Jim only 20.  Nancy still gets no votes in the Small States like before and Jim gets all of the popular votes there and so wins those electoral votes.

Candidate Big State Tally Small State Tally Popular Total Electoral Total
Nancy 80 0 80 12
Jim 20 50 70 15

Nancy wins the overall popular vote with a tally of 80 to Jim’s 70 (20 from Big State plus 5 x 10 from the Small States), but loses the electoral college to Jim with only 12 votes to his 15.   In fact, Nancy could completely trounce Jim in the Big State, even winning it unanimously in the popular vote, and get 4 votes in every small state,  giving her a whopping 120 votes to Jim’s 30.  Jim would still win the most electoral votes and thus win the election.

A more recent, up-close-and-personal example

Our example isn’t all that far off from what the electoral map actually looked like in the first US election, held in 17881.  In that election, John Hancock (Federalist) soundly defeated George Clinton (anti-Federalist).  This map shows how the distribution of slave states and free states or industrial vs agrarian states was more or less even for both candidates.   Worth noting, 51 out of the 96 total electoral votes rested with just 5 of the `13 states.  That is, more than half the electoral college — clearly enough to carry any election — rested with less than half of the states.    If electoral votes were simply one-state-one-vote, the 8 smaller states would have the greater power.   Left to a one-(land-owning)-man-one-vote system, the more populous states have the upper hand.   Rather than pick one or the other, the Framers of the Constitution came up with a system that combined these two extremes.

Electoral Map of 1st US election, 1988.
Electoral map of 1788 — first US election. Hancock vs Clinton.

In the 2016 election cycle, Donald Trump won the most electoral votes and thus won the presidency even though Hillary Clinton won the popular vote by nearly three million more than Trump.   Let’s look at how electoral math  figured into this by looking at one of the two, electorally-large blue bastions, New York, which has 29 electoral votes, and a handful of small (by population), red states that have a total of 29 electoral votes between them.  The following table2 depicts just such a collection.

Red State Clinton Trump Electoral
Idaho 189,765 409,055 4
Iowa 653,669 800,983 6
Montana 177,709 279,240 3
Nebraska 284,494 495,961 5
South Dakota 117,548 227,721 3
West Virginia 188,794 489,371 5
Wyoming 557,93 174,419 3
Totals 1,667,772 2,876,750 29

Both the popular vote and electoral vote tallies indicate Trump to be the clear winner among these states.   New York, on the other hand went unambiguously for Clinton with 4,547,562 votes to Trump’s 2,814,589.  Clinton absolutely demolished Trump in New York’s popular vote and thus gained its 29 electoral votes.   But, take a look at what happens when you add the New York popular vote with that of the red states:

State(s) Clinton Trump
Blue (NY) 4,547,562 2,814,589
Red 1,667,772 2,876,750
Totals 6,215,334 5,691,339

In the overall totals, Clinton wins over half a million more votes than Trump in this subset of states — a margin of about 4.4% —  yet they come out dead even in the electoral count.

Let’s throw in just one more small red state — Alaska, for example, which has only three electoral votes — Clinton still beats Trump by nearly half a million votes, yet loses the electoral count 32 to 29.   Or, try this with Maine, which splits its electoral votes:  Two went to Clinton, one to Trump.   Clinton wins this electoral match-up by just one point, which hardly reflects the popular tally in which she wins by over a half million.

What are those “bonus” electoral votes really worth?

Suppose we paired up as many red and blue states as we could and subtracted two electoral votes from each of these states.   In our example (before throwing in Alaska), we would discount New York’s two “bonus” electoral votes along with another two votes from one of the red states.  That leaves 12 bonus from the other six red states.  Now, divide the difference in the popular vote count (around 500,000) by these remaining 12 electoral votes and you find that they are worth just under 44,000 popular votes EACH.  (This number would vary, of course, depending on actual voter turn out in a given election.)  In other words, without this electoral bonus, for Trump to have matched Clinton in terms of the popular vote in these red states, he would have had to win an additional 87,000+ votes in each state, on average.   If you subtract that number from the vote tallies for Trump in each of the red states and then recalculate the totals (including New York), Clinton beats Trump by more than a million popular votes, yet still ties him in the electoral count, 27-273.

I said on average rather generously.  In fact, electoral votes aren’t “averaged”, so if we want to be truly strict about this, we’ll insist that Trump would have needed at least 87,000 more votes per state, for each of those six states.   Where the popular margin was clearly in his favor, as it was in this sample, he still wins both the popular and electoral counts.  If we include Alaska and apply this arithmetic,  we have roughly 34,000 popular votes per bonus electoral vote.  Subtracting twice this number (~68,000) as we did before, from Alaska’s popular count for Trump actually has Clinton winning Alaska in both the popular vote and electoral counts, 30-27.

If we apply this same arithmetic to all 50 states, Trump’s electoral edge of 77 electoral votes versus Clinton’s popular margin of 2,865,075 means each of those “bonus” electoral votes had the equivalent of 37,200 popular votes for Trump.  Since he didn’t have to actually win those votes, he in effect won the election at a discount of sorts.

Is there a better way?

One solution that is regularly (and often) proposed is to do away with the electoral college completely and have just a popular vote.  This would work fine when there is a clear choice or when a large enough part of the electorate is behind one of the candidates to make the vote clearly decisive.  When voters are more or less evenly split, the system becomes highly vulnerable to ballot-box stuffing, voter intimidation and other types of fraud, or even counting errors or the rare loss of ballots from just one polling station.   The electoral system makes this sort of rigging extremely difficult, and is highly fault-tolerant against slip-ups whether they are deliberate or accidental.   It is also unlikely to produce a tie, in which case the Constitution says the election is decided by a vote in the House of Representatives.   This has happened twice, the last time being nearly 200 years ago.  In every election since the electoral college has delivered a very clear decision.

Another solution is to eliminate the additional two electoral votes per state.   This sounds especially appealing when you realise that the whole reason we even do this relates indirectly to slavery being legal early in our history.  I’m not going to go into the specifics of this, here.  It’s sufficient to say that taking away those two electors from each state just puts us back to the first scenario where states with larger populations have the electoral edge.   (Click here for a more detailed explanation of the link between slavery and the electoral college.)

Vote-splitting — allocating a states electoral votes in proportion to the popular vote — is yet another popular idea.   Where there are only two candidates this amounts to nothing more than the system I described at the beginning of the example.  Furthermore, suppose a state had only two electoral votes.  How would you split these between two candidates when one of them had a significant majority in the popular vote?   If there were more candidates, there would still be two major ones, leaving the other, minor candidates to function as little more than spoilers.  It doesn’t really solve the problem; it merely “kicks the can” down the road a bit further.  (You can begin to see why the Framers left this up to the states.)

You Can’t Fix “Stupid” … or  “Lazy”

I believe that the real problem isn’t the electoral college; it is the electorate — the voting public — themselves.   Any system that puts such important decisions to a vote as we do REQUIRES participation in that system for it to work properly.   That means that eligible voters MUST VOTE, at the very least.    When too few show up, the system becomes unstable, “wobbly” and decisions like electing a new president become about as random as flipping a coin.   The electoral result will still be quite definite, but it is just as likely to disagree with the popular vote as it is to agree with it.

The electoral college is designed to ensure a decisive victory one way or the other.   In fact, it quite purposely punishes poor voter turn-out by often handing the election to the least popular candidate.  And, for those who say, “But I did vote!  For a third-party candidate.”, I would answer that the electoral college also punishes poor understanding and willful ignorance.   To vote in the general election you must understand or at least accept that, like it or not, there are two main candidates and only one of them will win.  Voting for a third party candidate because you think you shouldn’t have to choose between the “lesser of two evils” will almost certainly result in your vote helping to elect the greater of the two.

Summing it Up

This example is a simplified version of  precisely what happened in this year’s election, as well as 2000’s and 1960’s.   Instead of just six states, we have 50 (plus DC) and there are far more combinations of state populations and electoral vote tallies.   But, the underlying mathematics is the same.    You only need to know how to add numbers and compare them to see which is larger.  It is tempting to say that anyone who can’t understand such basic arithmetic probably shouldn’t be voting.    It is much more accurate to say that those who don’t vote can’t count.

 

Babette’s Feast

This is a fun little puzzle inspired by the movie Babette’s Feast and my solution provided me with an opportunity to learn how to use the MathTex plugin for WordPress to render mathematical expressions.

The Problem:

For her feast, Babette invited many people to be seated around a round table. She prepared a table plan but all the guests arrived and took a seat so that everyone was sitting in front of somebody else’s place. Is it possible to turn the table so that at least 2 guests are sitting in the right place?

The Solution:

The short answer is, Yes, it is possible. Another way to phrase this is to ask, Does there exist an arrangement of guests around the table such that prior to rotating the table, no guest is found at his or her assigned seat, and following a rotation of the table (guests remaining where they are) at least 2 guests are at their assigned seat? Consider two specific cases. (Note that the number of guests is always the same as the number of assigned seats. For simplicity, we’ll assume the table is round, and we’ll also assume that both the guests and the seating are equally distributed around the table so the space between any two seats is the same for all seats around the table.)

Case 1: Just two guests, each initially at each other’s assigned place, π radians apart. Rotate the table through π radians and both guests are now seated at their assigned seats. (Somewhat trivial, and yet it looks like it might be a nice base case for a proof by induction.)

Case 2: More than two guests, each seated one place to the left of their assigned seat. Rotate the table clockwise one place and every guest is now seated at their assigned seat.

But, the problem is harder than that, isn’t it? We want to know if, for ANY given seating arrangement and distribution of guests where no guest is at his or her assigned seat, if it is possible to rotate the table to where at least 2 guests are now at their assigned place.

Let’s define the distance d_{gp}  between a guest g_i  and his/her place p_i  be the minimum number of places to the left or to the right the table would need to rotate for that guest to find themselves in front of their assigned place. Note that  d_{gp}  is never more than \frac{n}{2}  where  n is the number of guests.

If every guest were maximally distant from their place, the sum of these distances would be bounded above by n\left( \frac{n}{2} \right)  or \frac{n^2}{2} .  The actual sum of the distances is given by

\displaystyle\sum_{i=1}^n \frac{n^2}{{|g_i - p_i|}} \leq \frac{n^2}{2}

Rearranging this a bit gives us

 2\leq\frac{1}{\sum_{i=1}^n \frac{1}{{|g_i - p_i|}}

Notice two things: First, this is only defined if there is at least one misalignment. Since we’re not interested in the fully-aligned case this isn’t a problem. The second, and more important thing to notice is that the minimum actual distance will never be less than 2. This makes intuitive sense if you look at case 1, above. But, consider yet another case where n > 2 and all of the guests are in their proper seats. The minimum misalignment possible is achieved by picking any two guests seated next to each other and having them swap seats. The distance between all other guests and their respective places will be zero, but for each of these two guests it will be 1. 2 x 1 = 2, i.e. our lower bound. Since the left-hand side is a constant, this holds for all n > 1.

Keeping this same arrangement in mind, observe that no matter how many times we rotate the table, in either direction, we cannot return these two to their original (i.e. correct) places. We can misalign all of the other guests by rotating just one seat to the left or to the right, leaving at least one of the two misalligned seats still misaligned. To put this another way, we have constructed two subsets of seats – the misaligned subset, and its complement, the aligned subset. Moreover, there can never be just one misaligned pair; there must always be two.

Now, consider the two sequences {g} and {s} which represent arbitrary but otherwise fixed orderings of our guests and their seats. Suppose the first element of {g}, g_i  aligns with the first element of {s}, s_i . If we examine the rest of {g} vs {s} we’ll either find a match … or we won’t. If we find another match, we have our two guests seated at their assigned places and we can start the first round of aperitifs.

But, if the first elements do not match, the drinks must wait. We rotate {s} so that s_{i+1}  becomes s_i , for i in [1,n], moving s_1  to s_n . We apply multiple rotations until an s_1  aligns with g_1 , and look for a second matching pair. Again, if we find a second matching set, we’re done. Drinks are on. If there isn’t a match (put the decanter down, colonel) we still have more work to do. Rotate {s} again until s_2  aligns with g_2  and look again. But, notice that our search space has shrunk by 1. We can continue doing this all the way down until we are looking at g_{n-1}  matching an s_{n-1}  (after some number of rotations) and a g_n  that must match s_n . Why must it? Recall that even in the most minimal misalignment of guests vs seats, there will be at least TWO mismatches. Consequently, by rotating through all of the matches, then mismatching them by rotating, we are isolating those mismatches. And these aren’t just any mismatches. These are mismatches that are NOT swaps. In fact, they are in the complement of the set of mismatches resulting from swaps, making them mismatches by rotation. Since all we have done is rotate the elements within {g} and {s}, and not change their order, we have accomplished what we set out to do: we have rotated the seats (i.e. places), keeping the guests stationary, until at least two of the guests find themselves at their assigned place.

Now then, Let’s EAT!!