Wednesday, February 27, 2013

The Inevitability of the Unlikely


This was originally posted to the now-defunct Thursday Think Tank Blog by Garbanzo

Do you remember anything from that statistics class you took years ago? If you do, it's probably the "bell curve", aka the "normal distribution". That's a good thing to remember, because the bell curve is a really useful tool for understanding some aspects in the real world. If you were really paying attention, you remember all that stuff about mean and standard deviation, and maybe even skew and central limit theorem.

Attack of the 50 ft woman!




Like me, I'm sure you're concerned about the possibility of a gigantic swimsuit clad supermodel rampaging through our cities. After all, it's happened twice in the movies, once in 1953, and again in 1993. Just how likely is this scenario? Let's look at the height of women, over the age of 20. The statistics are based on the U.S. National Health Statistics Report - October 22, 2008.


As you can see the average height of adult females is around 64 inches, or about 5'4". The laws of statistics tell us that 99.7 percent of women will be between 4'3" and 6'4". Well, what do you suppose the odds are of a woman being 20 feet tall? See if you can find it on the graph - that's about 243 inches. (50 ft didn't fit)




That's right - the chances are infinitesimally small (around 1.0E-399). So, what are the chances of being attacked by a 50 foot woman - zero actually. There are real biological reasons that a human can't grow to be 50 feet tall. She would collapse and suffocate under her own weight. Maybe the 50 foot woman could live in the ocean, eating krill and sticking her nose out of the water to breathe. Water might support her colossal mass like it does for whales, but she could not survive on land. In any case, she wouldn't be much of a menace. 

Like many natural systems systems constrained by biological and physical limits, human height matches the bell curve pretty well


Why Volkswagen was the world's most valuable company: for a few minutes.

Some things don't fit well under a bell curve. There are lots of examples, including executive compensation, attendance of rock concerts, and lottery payouts. What these examples have in common is that a few rare events have an unprecedented impact.



A good example is the stock price of the German auto company Volkswagen. In early 2008, the company stock was trading for around €120 a share. The executives at rival German auto maker Porsche, decided to  take control of Volkswagen. They started by buying all the VW stock they could get their hands on. They also bought stock options to guarantee a reasonable price for shares once the news of the takeover became public. Porsche acquired 43% of all VW stock, and had options for another 32% - controlling a total of 75%. Another 20% was not for sale - leaving only 5% of VW shares on the market.

Stock options are complicated, but allow me to simplify the problem: Options are a type of contract promising to sell stocks in the future, for an agreed price. The seller doesn't have to own any shares when they sell the option - it's just a promise. Some of these sellers are betting that they can buy the stocks in the future more cheaply than they can now. They can make a lot of money if prices go down - or lose a lot if they go up.

Here's how it all went crazy: Porsche called up the people who owed them options, and said  "Gib mir meine Bestände!" ("Give me my stocks, now!" )
 The option sellers had to rush out and buy 32% of all VW stock - oops! Only 5% of the stock was for sale. This is called a "short squeeze".


Price history of Volkswagen shares (VOW). Hint: This is not a bell curve.
The buyers were desperate; sellers raised prices - the price shot up to over €1000 a share for a few minutes. Guess who had the most stock to sell? Why Porsche, of course. Porsche sold €1000 shares to the option sellers, so the option sellers could sell it back to them for €120 a share. Not a bad deal for Porsche Automobil Holding SE. (Ironically, some options traders had to sell their Porsche and buy a Volkswagen.)

Life in Mediocristan and Extremistan


The height of women, and the price of VW stock are examples of what economist Nassim Nicholas Taleb  humorously refers to as Mediocristan and Extremistan. These two fictional countries represent the predictable world of things like height, and the insanely unpredictable world of stock prices.



Map of the "Stans"

In Mediocrastan, everything fits under a bell curve. In Mediocrastan rare events are rare - and when they do occur, they can be explained. Yao Defen of China is seven-feet-eight-inches tall. Despite being the tallest woman in the world she belongs in Mediocristan. She she is a mere 90 inches on our graph above (+5 sigma).

Residents of Extremistan include Bill Gates and the price of VW stock on October 23, 2008, and most lottery grand prize winners. Bill Gates is has a net worth of $63 Billion, as compared to the mean U.S. net worth of $556,300*. If Bill Gates's height were proportional to his wealth, he would stand at a height of about 100 miles.

"In Extremistan, rare events are common"

How can this be? Any single rare event is, by definition, rare. But when you take all the possible rare events that can occur, chances of one of them occurring are high. For example, the odds of being struck by lightning are 1 in 280,000. The odds of being killed in an air-crash are 1 in 335,000. Both are pretty long odds. But, when you also add in the possibility of being eaten by a shark, hit by a meteor, bit by a black mamba, eaten by piranhas, run over by a bulldozer, and a thousand other rare events, the odds start adding up.

You probably knew someone who was killed by a rare event - maybe several. The odds of that event were tiny, but given all the possible rare events, and all the people you have known, the chances are pretty high.

Useful information:
  • Rare events are common, you just never know which event!
  • Options trading is riskier than you may think
  • The bell curve does not apply to everything
  • Bill Gates is 100 miles tall, financially speaking
Congratulations you're one of those rare people who can read a whole blog post about statistics. Many of the ideas in this post are misrepresentations of The Black Swan: The Impact of the Highly Improbable, by Nassim Nicholas Taleb


*$556,300 is the average U.S. net worth, including Bill Gates and Warren Buffet. Median is $120,300.

Tuesday, February 26, 2013

Founder's Follies VIII: Got to Draw the Line Somewhere


This is the eighth installment of Chredon's analysis of the making of the Constitution, and where the Founders went wrong. For background, see the previous issues:

Issue I: The Founders' World - Historical context of the Constitution
Issue II: The Confederate Period - The failure of the Articles of Confederation
Issue III: Washington and Madison - The Father of our Country and the Father of the Constitution
Issue IV: The Constitutional Convention - The Primary Issues at Philadelphia Convention

Other Topics of Discussion:

Issue V: Bobbing for Senators - Was the Seventeenth Amendment Really a Good Idea?
Issue VI: The Two-Party System - Wise Creation, or Dismal Unintended Consequence?
Issue VII: Reverse Democracy - Should Representatives Choose their Voters.

In Issue VII, Reverse Democracy, we looked at Gerrymandering - the process by which our State Legislatures get to decide who will represent us in the US House by drawing Congressional districts for partisan victories. This was, perhaps, an oversight on the part of the Founders. 

The question remains - can this be fixed?

Well, it could be fixed. It would not require a Constitutional amendment to get rid of gerrymandering for seats in the House - all it would take is for the House to either stop requiring single-member districts (leaving the states free to experiment with other options for electing Representatives) or for them to change the rules by which such districts are drawn so that they can no longer be drawn for partisan advantage. But don't count on Congress to do what is necessary to fix it. After all, gerrymandering protects the incumbents. You shouldn't expect them to change the rules to their own detriment.

Nor would I bet on a Constitutional Amendment to fix it. It would require two-thirds of both Houses of Congress to pass the Amendment. If you can't get a simple majority to change the rules, I doubt you can get a two-thirds super-majority to do so, either. And as for calling a Constitutional Convention, no thanks - nobody wants to open that can of worms.

However, the Constitution may contains the wording needed to get a Supreme Court ruling to end partisan gerrymandering. In Article I, Section 2, we find this:
The House of Representatives shall be composed of members chosen every second year by the people of the several states
I think a case could be made that partisan gerrymandering violates this wording, since the vote of the people is pointless when the state legislatures have already chosen the party that will win the district. Sadly, no group is attempting to challenge gerrymandering on these grounds.

The Fourteenth Amendment, Section 1, says this:
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States
I think it could be equally argued that partisan gerrymandering is a case of the states enforcing a law (specifically, the Apportionment Act of 1967) that abridges the privileges of the citizens. Whether either of these is a legally-valid argument is a question for lawyers - I have no skill at counting the angels that dance on the head of a pin. But I would certainly like to see someone (the ACLU, perhaps) give it a try.


But if we take away Congress' power to decide how districts must be drawn, to whom should it be given? One suggestion would be to leave it in the hands of the states themselves, which, of course, was the original intent of the Founders.

Unfortunately, if we leave the apportionment process in the hands of the states, the leaders of the state parties will use it for partisan advantage in ways that might be even worse than our current system. For example, a state with a 60% majority for any party might choose to elect every Representative in a state-wide at-large vote. That would nearly guarantee that all of that state's representatives would be of the majority party and the 40% of voters from other parties would be totally unrepresented. States that had a more balanced electorate might use our current system. But none would choose a system that might give a third party a chance to win a seat, or that would guarantee that representation in Congress was proportional to that of the population.

So this is a situation in which we must be very careful. The solution to the current gerrymandering problem could be worse than what we have now.

What Are the Options?

The United States is not the only nation to have faced this issue. Many groups in the US advocate for methods that are used in other countries. Some propose new ways of drawing districts. Other do away with districts altogether. In the best methods, the goal is to have Congress match the electorate in terms of partisan participation. (If 10% of voters are Libertarians, 10% of the House should be Libertarians.)

Here are a few changes that have been proposed.

Different Voting Methods

Cumulative Voting: There are no districts. All people running for Representative are listed together on the ballot, and voters get a number of votes equal to the number of candidates. They can put as many votes on each candidate as they like - spread them out or concentrate them all on one. Votes are counted and the top recipients get the seats.

Single Transferable Vote: There are no districts. All candidates are listed together on the ballot, and voters choose their top N candidates in order, where N is the number of open seats. Each candidate needs to receive a number of votes equal to the number of voters divided by the number of seats. Everyone's top choice is counted. If any candidates receive more votes than needed, their remaining votes are split among the #2 candidates on the ballot by the proportion of their appearance. This is repeated until splitting a winning candidate's excess votes no longer creates a new winner. Then, you take the candidate with the fewest votes and distribute them to the highest-choice candidate who is not already a winner. This method of voting is used in many places around the world.

The problem with these two ideas is that in a state like California, where there are 53 Representatives, it would be unreasonable to expect voters to know enough about 200 or more potential candidates to make an informed choice. Also, in states like New York and Illinois, where one major city holds the vast majority of the state population, city voters would take a disproportional number of seats, leaving rural voters unrepresented.

Different District Allocation Methods

If we don't want to radically change the voting method, then the alternative is to change how we draw the districts. Since I used North Carolina's 12th district as an example of bad gerrymandering, I'll use NC as the examples below. For reference, here are the current districts.
  


Shortest Straight Line: Since NC has 13 Congressional Districts, the state is divided, using the shortest straight line possible, such that 7/13ths of the population is on one side and 6/13ths on the other. Then each of these regions are divided, again using the shortest straight line possible, and again and again, until you have a number of equally-populated regions. Here is the result, courtesy of Range Voting :



Minimum Centroid Distance: The state is divided into districts such that the total distance of each person in the state to the center of their district is minimized. Here is the result, courtesy of Brian Olsen's Redistricting:




The problem with these two methods is that the districts created will often divide even small communities into two or more districts, denying the idea of people with similar local interests voting for the same candidates. (This is a problem with the current system as well.)


Fewest Split Counties: In this method, the result that splits the fewest counties is selected. Since there will obviously be multiple options, you choose the one that splits a county most evenly. Here is an example, courtesy of Daily Kos:



Here is another that I drew myself using Dave's Redistricting Application.



FairVote.org proposes a hybrid system, where larger states are divided into regions with similar numbers of representatives (up to 5) and then does a Single Transferable Vote process within the regions. Here is a suggestion of how NC might be divided into regions:



In this plan, the eastern and western regions receive four Representatives each, while the center section, which contains the densely-populated Charlotte, Raleigh, Durham, and Greensboro metro areas receive five. All three mega-districts have recent voting records in which neither party received more than 58% of the vote, which leads to a greater chance the vote will be split 7/6, which is in line with the state's 53/47 partisan split. (Current gerrymandered districts split the state 10/3 with no swing districts at all.)

As you can tell by the descriptions, none of these methods take partisan factors into consideration. Districts are either drawn by a computer algorithm and left as they are drawn, or drawn based on county divisions. In either case, they are drawn without regard to partisan considerations.

In Conclusion

With apologies to Patriot, Governor, and Vice-President Gerry, your accidental namesake is one of the banes of the nation. The idea that membership in the House of Representatives should be chosen by the Representatives themselves, working through their allies in the states, is reprehensible and goes against every ideal of democratic government. Solutions exist, but convincing our current Representatives to take advantage of them will be difficult, given that the current plan protects incumbents.

Chredon would like to acknowledge the contributions of FairVote.org for background information on this article and Dave's Redistricting Application for the maps drawn and included above.

Monday, February 18, 2013

Founder's Follies VII: Reverse Democracy


This is the seventh installment of Chredon's analysis of the making of the Constitution, and where the Founders went wrong. For background, see the previous issues:

Issue I: The Founders' World - Historical context of the Constitution
Issue II: The Confederate Period - The failure of the Articles of Confederation
Issue III: Washington and Madison - The Father of our Country and the Father of the Constitution
Issue IV: The Constitutional Convention - The Primary Issues at Philadelphia Convention

Other Topics of Discussion:

Issue V: Bobbing for Senators - Was the Seventeenth Amendment Really a Good Idea?
Issue VI: The Two-Party System - Wise Creation, or Dismal Unintended Consequence?



Elbridge Gerry
 This article is devoted to Founding Father Elbridge Gerry. Largely forgotten to history, Elbridge Gerry had quite an illustrious career as an early patriot and legislator. He used his personal wealth and connections to supply the Continental Army as it held Boston under siege. He is one of only six men who were present for both the Second Continental Congress, during which he signed the Declaration of Independence, and the Philadelphia Convention, during which he helped draft the Constitution. He was instrumental in the creation of the Bill of Rights, primarily by refusing to sign the Constitution until after the Bill had been attached. He later went on to serve in the House of Representatives, as Governor of Massachusetts, and as the fifth Vice-President of the United States under James Madison.

But in our modern politics, his name is remembered mostly for one thing - gerrymandering.

The Gerry-mander
In 1812, while he was Governor of Massachusetts, the legislature of that state drew some controversial Congressional districts designed to give more Representatives of Gerry's Democratic-Republican Party while leaving fewer for the Federalist Party, despite the population being almost evenly split. A Federalist-leaning newspaper published a famous picture of one of the districts which wound through the northern and western edges of Essex County and resembled a salamander. The paper dubbed it the 'Gerry-mander,' though there is no evidence that Governor Gerry had any hand in drawing the lines. It was still a fairly radical idea, and the Federalists used attacks on the process to oust Gerry in the next election.

(Historical Note: Governor Gerry's last name is pronounced with a hard G, as in Golf. Our modern pronunciation of the word 'gerrymander' tends to use a soft G, as in Giant.)

I titled this Founders' Follies issue Reverse Democracy because that is what gerrymandering is. In a representative democracy, such as we theoretically have here in the USA, voters are supposed to choose their representatives. Gerrymandering makes it possible for representatives to choose their voters. This is done in practically every state in the Union, since it allows the political party that holds a majority in the state legislature to align the state's districts in order to give advantages to their party in the House of Representatives. Gerrymandering is also used in the apportionment of state representatives' districts, thereby guaranteeing continued party majorities in the state legislatures.

The impact of this process is that the vast majority of Americans don't really have any choice in who represents them in the House. According to FairVote.org, of the 435 House seats, 195 are safe for Republicans, 166 are safe for Democrats, and only 74 are really in play. The same is true for any state that has districts drawn for elections of state representatives. Unless you are one of the 15-20% of voters who live in a swing district, your vote is pointless. And with every passing census, the ability to draw safe districts increases as computer technology advances and information about individual households becomes more readily available to partisan redistricting efforts. (After the 2000 census, there were 89 swing districts, fifteen more than today.)

But wait, you say. Doesn't the House change hands every few years? It may seem so in the past election or two, but historically, it does not change that often and it usually takes a seismic event to turn it. Since 1900, control of the House has changed 10 times out of 57 elections. In the history of the United States, through 112 Congresses, it has changed 26 times. And the pattern is clear - there are long periods of single-party control, broken up by several back-and-forth elections as policies and parties are in flux. Except for the 80th and 83rd Congress just after World War II, the Democrats controlled the House from 1931 until 1995. Since the Civil War, House control has changed hands only 14 times.

Brief Description of Gerrymandering - Skip if you are already familiar

(NOTE: I updated this from my original. I found a brief and very clear description of the process at electoral-vote.com that was much better than my original.)

Here is a brief primer on how the process works.

Imagine a state with 1.5 million Democrats and 1.5 million Republicans and 6 seats in the House. A fair map would be something like this, with 250,000 Democrats and 250,000 Republicans in each of the six districts. Each icon represents 100,000 voters.





But a Republican legislature that wanted to maximize its representation in the House might draw the boundaries differently, for example like this.



In this map, districts 1-5 have 300,000 Republicans and 200,000 Democrats, so the Republican candidate can probably win, assuming he doesn't spend the whole campaign talking about rape. But we have 500,000 Democrats left over, so they get stuffed into district 6, which probably needs a strange shape to include them all. If the map looks like this, the Republicans can easily win five of the districts and won't bother to even field a candidate in district 6. With voting totals available on a precinct level, computer software can produce statewide maps that maximize the partisan advantage for one side. Here are some actual district maps drawn in 2010.

Illinois Congressional District 4, which includes a narrow strip of land along I294, creates a majority-Hispanic district.

North Carolina District 12, which winds across the central portions of the state,  to create a predominantly liberal African-American district.

California District 23, which winds along the Pacific coastline, creates a district with an extremely high proportion of Democrats, allowing multiple Republican districts inland.

These are only a few of the more oddly-shaped districts. Gerrymandered districts don't have to look so crazy, though. Some highly-partisan districts look perfectly sane.

The Problem with Gerrymandering

The main issues that people have with gerrymandering are:

  1. It disenfranchises voters by making elections meaningless. The winner is chosen by the party who drew the districts, not the citizens who cast the votes.
  2. Voters feel powerless. After all, why bother to vote if the outcome is already chosen?
  3. Incumbents are nearly impossible to remove, no matter how bad they are.
  4. Districts do not reflect groups with common interests.
  5. Districts are drawn without regard to existing political structures, like counties or cities.
  6. The partisan make-up of Congress does not match the partisan make-up of the people.
  7. Third party candidates have no chance of winning.


Is this a Founder's Folly?

Did the Founders make a mistake? That's hard to say. Their only mistake is that they did not anticipate the strength of national political parties nor did they see how the institutions as they created them would inevitably lead to a two-party system. Madison believed that in a nation so wide and diverse, it was practically impossible that any party would ever emerge that was not regional in nature. Given that they were so far apart, these regional parties would never have common-enough interests that they would ever combine. Thus, no national parties would ever emerge. Madison said:

The lesson we are to draw from the whole is that where a majority are united by a common sentiment, and have an opportunity, the rights of the minor party become insecure. In a Republican Government, the majority if united have always an opportunity. The only remedy is to enlarge the sphere, and thereby divide the community into so great a number of interests and parties, that in the first place a majority will not be likely at the same moment to have a common interest separate from that of the whole or of the minority; and in the second place that in case they should have such an interest, they may not be apt to unite in the pursuit of it.

This is one of the few times when Madison was dead wrong. He did not envision the 'common interest' of controlling the national legislature as something parties might desire. You don't need nation-spanning cable TV networks to form a national party. In fact, Madison was ignoring the nation's recent history. Had the United States not just won a war against Britain that was begun because small groups of like-minded patriots were able to organize all across the continent?

Another problem is that the House has the power to tell the states how they are to handle elections - though they were never supposed to use it except in extraordinary circumstances. Article I, Section 4 of the Constitution states:

The times, places and manner of holding elections for Senators and Representatives, shall be prescribed in each state by the legislature thereof; but the Congress may at any time by law make or alter such regulations, except as to the places of choosing Senators.

This really is the key phrase of the Constitution where the redistricting process is concerned. The Constitution gave the state legislatures the power to choose how their Representatives would be chosen, but then gave Congress the power to pass laws to override the states' plans. And override them they did. Apportionment Acts began as early as 1790. (In fact, the Apportionment Act of 1790 was the first bill to be hit with a Presidential veto.)

According to Alexander Hamilton In The Federalist Papers, #52, the goal of the construction within the Constitution was to give the power of selection to the states, with the national government given power to overrule the states in those cases where their method of selection was harmful to the Republic.

A discretionary power over elections ought to exist somewhere. It will, I presume, be as readily conceded, that there were only three ways in which this power could have been reasonably modified and disposed: that it must either have been lodged wholly in the national legislature, or wholly in the State legislatures, or primarily in the latter and ultimately in the former. The last mode has, with reason, been preferred by the convention. They have submitted the regulation of elections for the federal government, in the first instance, to the local administrations; which, in ordinary cases, and when no improper views prevail, may be both more convenient and more satisfactory; but they have reserved to the national authority a right to interpose, whenever extraordinary circumstances might render that interposition necessary to its safety.
According to Madison's notes on the Constitutional Convention, the only reason that the House was given any power at all over the methods by which the election would be conducted was to prevent abuse that might arise should the state decide to choose Representatives in some way that violated the will of the people. Madison himself said:

The legislatures of the states ought not to have the uncontrolled right of regulating the times, places, and manner, of holding elections. These were words of great latitude. It was impossible to foresee all the abuses that might be made of the discretionary power. Whether the electors should vote by ballot, or viva voce, should assemble at this place or that place, should be divided into districts, or all meet at one place, should all vote for all the representatives, or all in a district vote for a number allotted to the district,—these, and many other points, would depend on the legislatures, and might materially affect the appointments.

Madison did, however, note that it seemed to make no sense to question the ability of the state legislatures to properly devise the method by which Representatives would be chosen while at the same time trusting them to select Senators and to devise methods of choosing Electors for the office of President.

This provision, then, was to be a fail-safe measure to prevent the states from doing something that violated the spirit of Republican democracy. There were several nightmare scenarios suggested, such as a state simply not holding elections at all, in effect withdrawing from the Union. Or a state might decide that all votes had to be cast in person at a single meeting, which would be held in the most populous city of the state, thus guaranteeing that one city the majority of the representatives.

But the provision was almost immediately used, not as a fail-safe, but as a way for the national legislature to impose regulations and restrictions on state elections that today violate the spirit of Republican democracy. Early attempts to do so were challenged, but upheld by the Supreme Court. This is one of many cases where the letter of the law is not in keeping with the spirit of the law, and the letter of the law won out.

Thus, the House would pass, with each Census, rules covering the apportionment of the House members. In some years, single-member districts (such as we have today) were mandated. In other years, there were no districts and all states were free to elect their Representatives however they wanted. In some years, laws required districts to be contiguous or to have equal population. These went back and forth often. It was not until 1967 that Congress passed the laws by which districts are currently allocated, requiring contiguous borders, equal population, and some districts drawn for the purpose of gaining racial parity in Congress equal to the state population.


While Madison and the Framers couldn't envision the power of national parties and how gerrymandering would subvert the electoral process, even the Congress of 1967 could not envision the power of today's computing systems and the massive amounts of data on individuals available to them. Gerrymandering has become much more of a science than an art. With the House requiring single-member districts and the states free to draw them as they wish, the status quo could remain with us indefinitely.

In the next issue, Got to Draw the Line Somewhere, I will take a look at some potential solutions for the gerrymandering issue and how they could be implemented.

Founder's Follies VI: The Two-Party System



This is the sixth installment of Chredon's analysis of the making of the Constitution, and where the Founders went wrong. For background, see the previous issues:

Issue I: The Founders' World - Historical context of the Constitution
Issue II: The Confederate Period - The failure of the Articles of Confederation
Issue III: Washington and Madison - The Father of our Country and the Father of the Constitution
Issue IV: The Constitutional Convention - The Primary Issues at Philadelphia Convention

Other Topics of Discussion:

Issue V: Bobbing for Senators - Was the Seventeenth Amendment Really a Good Idea?


A Google search of the phrase 'the US two-party system' returns approximate 286 million hits. A search of 'the loch ness monster' returns only 3 million. I mention this because, like Nessie, the US two-party system doesn't really exist.

Except that it does. Sort of.

There is no Constitutional mandate that our government have only two parties. It has merely worked out that way. And oddly, it has worked out that way for over two hundred years. So the question for the Constitutional scholar is this - is the de facto two party system merely the inevitable result of the all-too-human proclivity to choose sides? Or is it inherent in the very fabric of our Constitution and the institutions that surround it?

Historically, we have always divided into two camps here in America. When Thomas Jefferson proposed a smaller Committee of the States, he lamented that the new group  “quarreled very soon, split into two parties, and abandoned their post.” While writing the Constitution, Madison commented that when it came to determining the size and method of electing the two houses of Congress, the states split into two camps, large states and small. But when it came time to discuss the powers that the states would give up to the Federal government, the convention split along north-south lines.

During the period in which the Constitution was being ratified, we had Federalists and Anti-Federalists.

After it was ratified, we had the Federalist Party (led by John Adams) and the Democratic-Republican Party (led by Thomas Jefferson). 

Throughout the history of the United States, though parties have come and gone upon occasion, we have almost always had two, and usually only two, significant political parties. There have been, on very rare occasions, a third-party candidate who received a few Electoral College votes for President. But none of them lasted longer than a single Presidential election cycle. The Populist movement had a brief but unsuccessful heyday between 1880 and 1912, and an anti-Civil Right movement in the South saw a couple of third parties win a handful of electoral college votes in the 1950s and 1960s. The last third party to win any electoral college votes for President was the Libertarian Party in 1972, when John Hospers got a single vote. 

Duverger's Law tells us that the two-party system is inherent in the way our political structures are formed. Two fundamental elements of our voting system are the one-person, one-vote idea, and the idea of majority rule. In that sort of an environment, people must band together to try to get a little more than 50% of any vote in order to win. Thus, weak parties will merge with more powerful ones in order to get the votes needed for victory, or voters will flee smaller parties with no chance of victory and join larger parties capable of achieving the 50% requirement.

Of course, not all elections require a majority. Some are first-past-the-post, meaning that the person with the most votes wins, even if they have less than a majority. Some places would require a run-off in these cases, but some don't - sort of like the way Mitt Romney was winning the GOP primary getting 35% of the vote (to his opponents' 25% or less).

A moment of reflection on this concept will convince you that the two-party system is inevitable. But it is inevitable because of the way we vote.

Imagine that your state is voting for a Senator. You have five candidates from five different parties, the Democrats, Republicans, Libertarians, Green, and Constitution Parties. Imagine that the Democratic and Republican candidates have the support of 35% of the voters each, and the other three parties have 10% each. Unsure of the victory, what would the Democrats and Republicans do? Obviously, they would reach out to the other three parties and try to form a coalition to get to 50%. The major party that is able to get two of the minor parties on board would be the winner. Seeing that their own candidate has no chance at victory, would the supporters of the three minor parties vote their preference anyway? Or would they opt not to 'waste' their vote on a lost cause and instead support the major party candidate whose views most closely match their own? After all, to stay with your own party would be to risk splitting the vote such that the viewpoint you most oppose has the greater chance of victory. Few will risk that.

So how could we possibly get viable smaller parties in the United States? We would have to change how elections work - specifically, we would have to change BACK to the ways the Founders designed it.

If you read the Constitution, it says nothing about dividing the states into Congressional districts and having one representative from each. It says, simply "The House of Representatives shall be composed of members chosen every second year by the people of the several states." So as long as they were chosen by direct popular election, there was no limit to how that choice could be made. In the early years of the Republic, Representatives were generally chosen by at-large voting (no districts), though each office would have only two candidates. Congress eventually mandated single-member districts by rules passed in 1842. But those rules changed back and forth for over 100 years. A 1967 law required congressional districts and outlawed any sort of at-large voting. (This was done over fear that southern states might revert to at-large voting as a way to suppress minority votes.) 

Since this law was passed, there has never been more than one member of a third party serving in Congress at any time, nor more than one or two Independents.

Today, many groups are advocating new voting systems, like Range Voting or Instant Runoff Voting in an attempt to give voters more choices in their representation, or to at least get around the wasted vote issue, or the problem of a first-past-the-post election being won by someone with only 25% of the vote. But while these methods will make it easier to get a third-party candidate onto the ballot and convince people to make them their top selection, it still doesn't end the process of having to choose only one person for one office. To really get third-party options into the House (and eventually the Senate and higher), you have to get rid of the single-district vote and go back to at-large votes for larger pools of people.

Imagine, if you will, a state with three House members. Instead of having three contests, one for each seat, with most contests having just two contestants and a couple of third-party candidate, all contestants go into one pool. Using Instant Runoff Voting, all the voters rank the 8 candidates in order of preference. Count up how many #1 votes each candidate got and rank them in order.

Now, take the person who came in eighth. Eliminate that candidate and distribute his votes to the voters' #2 choice. Now take the candidate who came in seventh and do the same, then sixth, and so on until there are only three left - these are the three winners.

The results are much more likely to reflect the will of the people. A third-party candidate could potentially take one of the seats (and even more likely in a state with more Representatives). And the distribution along party lines is more likely to be consistent with the party affiliation of the voters (as opposed to the results of voting in gerrymandered districts).

Once that was in place, we would begin to see changes in the makeup of Congress. Changes that might make it necessary to build coalitions inside the House, a wider range of ideologies represented, and potentially a return to bipartisan agreements instead of stubborn party-line votes.

Until then, we're stuck with an entrenched two-party system that does more to entrench itself every day.