** Disclaimer, this article is very technical. But if you are up for wrestling the material, I think what follows, reveals a pretty interesting set of considerations.

My goal is to uncover some of the realities of democratic voting. To set the stage for what I am trying to do here, think about the voting method we currently have. Think about the way candidates campaign, think about primary elections, the electoral college, etc. There is obviously a lot that goes into how we elect our leaders but because America is assumed as a democracy, the thought is that American citizens play a part in this process.

Political scientists think we need our party system in order to generate public opinion into big government. My belief in regards to this is that the American party system is, essentially, big government.

In other words, I disagree.

I think the two-party system we have in America has made it such that, on the one hand, American voters have no rational basis for grounding their views on political matters. It is easier for people to associate with one of the two identified parties rather than form a real reason to believe in any of the tents they advocate for. On the other hand, the particular problem with the party system is how it has made voters irrational. So much so, that they assume themselves as rational while partaking in irrationality.

OK, buckle up, things are about to get tricky!

Kenneth Arrow’s impossibility theorem illustrates the logical inconsistencies that arise from democratic voting. The theorem unravels to depict that a clear order of preferences is impossible to determine while adhering to the principles he sets of fair voting procedures. The crux is that it illustrates a paradox in social-choice, especially in reference to voting.

To illustrate Arrow’s notion of impossibility. Imagine that three people, Jane, Alison, and Ethan, are able to choose from three possible choices—A. Bernie Sanders, B. Hillary Clinton, and C. Donald Trump—for candidacy in the presidential election. Of course they each can only vote for one candidate. Yet in deciphering this choice they must rank their preferences respective to their desired outcomes (i.e their 1st, 2nd, and 3rd choice).

When pushing individual preference sets into a societal preference set, the first task is establishing a universal domain. The universal domain generates a set of all possible preferences. The idea behind the universal domain is to achieve a social welfare function; or otherwise, a rule for generating a set of preferences for society reflective of each set of possible individual preferences. If the universal domain, X, is the set of all possible ranking preferences of presidential candidates. The ranked preference set we get from the universal domain is through establishing X n. This establishes all the possible preference sets, by means of considering: the candidates, the voters, and all the possible rankings of their preferences.

In continuation of the previous example, i.e Jane, Alison, and Ethan voting for president. Imagine that all three agents must rank their preferences. They each have different rankings to encompass the variations in public opinion. For example:

A>B>C, B>C>A, C>A>B

Now, in the same vane each individual’s ‘preference set’ had to be transitive. The group preference set also has to be transitive. Thus, here, we must look to the preferences of ranking pairs chosen by each person. The first question that raised is, how many people prefer option A to B?

A>B>C, B>C>A, C>A>B

From the three rankings, two of the three prefer A to B. Meaning that the majority have this preference ranking. To establish transitivity, the second question raised is how many people prefer B to C?

A>B>C, B>C>A, C>A>B

Again, two people, which means the majority, have this preference. Logically then, it follows that the majority of this three-person community prefers option A to C, A to B, and B to C. This next question, however, will uncover the paradox. Namely, how many people rank option C before A?

A>B>C, B>C>A, C>A>B

Two people, the majority, have again, voted C over A. Yet that means that the majority prefers both A to C and C to A, which is quite, impossible.

This is the very paradox Arrow’s theorem uncovers.

Our system does a good job of fooling us into believing that we are free. All while we are always irrationally constrained to two choices. Now, is it really the case that the two-party system is the only way America can sufficiently establish public opinion within its government? Or, is that merely the way political scientist have come to understand this issue?