Tuesday, September 5, 2017

Electoral College

Those who support maintaining the institution of the Electoral College as it is today defend it on several grounds. These are primarily that the electoral college

  • ensures that a president must win by appealing to citizens across demographics; merely winning those votes from urban centers will not be enough if they ignore the concerns of those in more rural areas and states.
  • serves as a check on the power of more populous states and prevents a "tyranny of the majority". 
  • maintains the integrity of the United States as a representative republic. 
  • preserves the intentions of the Founding Fathers with respect to the function of the government
  • prevents the election from being decided by only a few states

Citizens of different regions may differ significantly in their political concerns and be impacted differently by legislation. If the president only needed to win the popular vote, the argument goes, then he would be able to ignore or sacrifice the considerations of these less populous rural areas for the sake of the more populous areas. The electoral college ensures that the president has widespread acceptance across these demographics. 

My question with respect to this argument is: why limit our concern to only geographic demographics? Different ethnic groups may also differ significantly in their political concerns. If our worry is that a purely popular vote will allow the concerns of some demographics to overshadow others why shouldn't we also require a president to have widespread appeal across different ethnic demographics? Or religious ones? Educational, economic, or age-related ones? Limiting it to geographic concerns seems entirely arbitrary.

Does the EC serve as a check on the power of more populous states? Maybe. But there is already a check on the power of states by virtue of the Senate where all states are afforded equal representation. The very fact that the House is (ostensibly) proportional to population is in contrast to this. Also in this case the EC isn't merely a check on power, but in fact allows the minority party to actively do something, namely elect a president. That goes beyond just a check on the more populous states. 

We are a representative republic by virtue of our legislatures where bills are proposed and voted on by our representatives. None of this however has to do with how our representatives themselves are elected, which is in fact by popular vote. How would electing our highest representative in the same manner somehow undermine or contradict our government being a representative republic? I don't see it.

Reading The Federalist Papers as well as Madison's comments of the Federal Convention I fail to see how the implementation of the EC had absolutely anything to do with protecting rural areas from being eclipsed by urban areas. (this would hardly be a concern seeing as how at the time well over 90% of the population was rural.) It in every way appears that Madison saw it as an unfortunate concession for the sake of ratifying the constitution which was seen as preferable to falling back to the Articles of Confederation. While Hamilton supported the Electoral College, it wasn't for the sake of protecting smaller states and he still desired that it be proportional to population.

Often a worry that "only a few states will decide the election" is expressed when the idea of a popular vote comes up. Two points. 1. This is already the case with the EC. Rather than having a few populous states deciding the election it simply shifts to a few swing states deciding the election and candidates spending a disproportionate time campaigning there. The EC does nothing to alleviate this worry. 2. If we change to a purely popular vote then it is not "states" that decide anything; it is the people that make up those sates that decide. Those state lines are completely meaningless with respect to a popular vote. One may as well draw an arbitrary line around a densely populated area of Wyoming and one around a less dense area of California and make the argument "why should this city in Wyoming have more voting power than this city in California?". 

As it stands I think I support a national popular vote or at least expanding the House by the Wyoming rule to more accurately reflect the population. This better encompasses the equality among voters and holds true to the principle of one man one vote while the winner takes all approach of the current makeup of the EC serves to reduce voter turnout and make the value of a vote dependent on where it is cast.



Sunday, September 3, 2017

Basic Big O Notation Rough Draft

Measuring the "time" it takes for a machine to compute a particular algorithm brings with it several difficulties. It's not as simple as simply passing an algorithm to a computer and clocking the time it takes for the computer to complete the instructions. Different hardware and software may implement algorithms and operations in distinct matters; computers and structures differ in their use of cache, differ in the number and speed of their processors and the size of their ram, their use of ssd vs hdd etc. This makes it impractical to truly understand the speed of an algorithm itself as distinct from the architecture implementing it. Therefore, to measure the speed of an algorithm we refer to the number of operations, using Big O notation, rather than a simplistic measure of actual clock speed.

Imagine we have an array of elements that we wish to print. To do this we iterate over the array one element at a time, adding the next integer to the previous total. If we were to double the number of elements in the array we would double the number of operations we have to perform. This is known as linear speed (due to the fact that the number of operations increase directly with the size of the input) and in Big O notation is signified by O(n). Contrast this with adding two random elements in the array. Due to the fact that arrays are preallocated, access to it's elements is random and an index can be accessed directly, regardless of the total number of elements in the array. As such, all things being equal, it would take no more time to implement this sum if we were to double the size of the array. This time is known as constant speed(since the time taken is independent of the size of the input) and is signified by O(1).

There are of course all kinds of time complexities, such as exponential and poly-logarithmic times, and these follow naturally from what is defined here.