Political Analysis: Median Voter Theorem and Voting Systems

In this final, though not very conclusive, post on political analysis, we’re talking voting, voting systems, and ice cream.

The Median voter theorem helps explain the importance of the swing voter. For the MVT there are four elements:

  1. A set of n voters where n is odd (apparently an even number can work too, but we didn’t really talk about it, and, as in Minecraft, odd numbers just work better.)
  2. Unidimensional policy space (i.e. right vs. left, socialist vs. capitalist, more funding vs. less funding)
  3. Voters have quadratic or “single-peaked” preferences that can be represented by the equation U[x] = [x1 – x’]2. So they have one ideal point (x’) and whichever option falls closer to their ideal point is what they’ll vote for.
  4. The group makes decisions by majority rule (and we’ll talk about alternatives to this in a  bit.)

The theorem states that, if every voter in the group has an ideal point, the voter with the median ideal point is an indicator of how the group will vote.

To apply this, here’s an example:

The International Space Committee is voting between two bills to send colonists to Mars. There are seven seats on the committee. Three of them are hardliners who think colonization is a waster of resources, and their ideal point is 0 colonists. On the other end of the spectrum is a sci-fi fan who wants to send a hundred colonists. Then in the middle we have someone who wants to send three colonists, someone who wants to send five, and someone who wants to send twelve. Read More »

Political Analysis: Coalitions

In this penultimate post taken from my Intro to Political Analysis class notes, we’re talking about coalitions—and how to predict which coalitions will form. 

The fundamental building block of politics is the mass political party. The first mass political party was formed in the US. After the “corrupt bargain” of the election of 1824, Jackson’s supporters formed a mass political party, fully recognized as the Democrats by 1840.

But we won’t be really talking about the US, because we don’t have coalitions, because of our party system. Party systems (as with any systems, according to systemic theory) can be categorized as the one, the few, and the many.

The one would be places like China and Cuba, with only one party.

The US’s two-party system would be considered “the few.”

And the many is what you see in parliamentary countries (like most of Europe.) This is the kind of system we’ll focus on.Read More »

Political Analysis: The Decentralized Solution

Last week I wrote about the prisoner’s dilemma, and a centralized, Hobbesian solution to that—essentially, to get people to cooperate you have to bring in an outside authority, like a monarch. This is the decentralized solution.

The decentralized solution to the prisoner’s dilemma has three elements:

  1. The game is repeated an unknown number of times
  2. The strategy is reciprocity—if A cooperates, B does too. If A defects, B does too.
  3. The shadow of the future is sufficiently long.

That “unknown” bit is important. If people know the game’s gonna end, and they know when, there’s no reason to develop trust with the other person. “Unknown” can mean infinite iterations, or just a percentage chance each time that the game will be replayed.

So if you’re going to play forever (or potentially forever), two basics strategies are always defecting (“All-D”), or always cooperating (“All-C.”) These strategies are useful for reference points, but they aren’t actually practical, because they aren’t reciprocal strategy—they’re not based on what the other person is doing. And in a normal-form game, what the other person does, combined with what you do, determines your payoff.

One reciprocal strategy is “Tit-for-Tat”—whatever the player did last turn, do that this turn.

We’re going to focus on the “Grim Trigger” strategy. God, that sounds badass. With Grim Trigger, you start out by always cooperating, but if the other player ever defects, you switch to All-D.Read More »

Political Analysis: The Prisoner’s Dilemma

Now for a classic of political analysis—the prisoner’s dilemma.

“Rational individuals select actions to achieve their most preferred outcomes. If two rational individuals can do better by acting collectively, then they will do so, because they are rational.”

Annnnh! Wrong! That is the rock pile method, and it’s false, and we can see this with the prisoner’s dilemma.

A lot of people teach the Prisoner’s Dilemma, and a lot of them get it wrong. “If you’ve heard of it or had a class that covered it, get a lobotomy to eliminate that part of the brain,” says Professor Dion.

I’ll get to some misconceptions in a moment, but first, here’s the story of the prisoner’s dilemma: two accomplices in a crime are taken in for questioning. The police have enough to convict the two on a small charge, but they want to get them on this bigger crime. The two criminals are separated, and each is offered a deal—rat on the other guy (“defect”) and you’ll get to walk free, and the other guy will get a really harsh sentence. They’re also told that this deal is being presented to both of them. What ends up happening? They both defect, of course. If they expect the other person to say nothing (to “cooperate”), it’s best to defect, because then they’ll walk free. And if they expect the other person to rat on them, it’s also best to defect, because while they’ll still get a harsh sentence, it won’t be as harsh, because it’s split between them.

So, here’s the Canonical prisoner’s dilemma, shown as a normal-form game.

PD-canonicalRead More »

Political Analysis: Condorcet Jury Theorem

Last post I introduced the concept of aggregation in political analysis, and how you can’t always make inferences about members of a group based on the character of the group as a whole—or visa versa. This post will go further into that, and also why democracy works.

In college, it’s easy to forget how much smarter you are than everyone, because you’re surrounded by people as smart or smarter than you—but really, a lot of people are highly ignorant. [NOTE FROM THE NOTE-TAKER: This is how Professor Dion introduced the topic, not me just throwing in my own color. But it is kind of true.]

For example, only 74% of Americans believe that the Earth orbits around the sun. As for politics, in 2010 only 54% knew the controlling party of the House of Representatives.

So, is democracy doomed? The idea with democracy is that an individual is the best judge of their own interests, and will elect a good representative for themself. But if people are ignorant, will they really?Read More »

Political Analysis: Aggregation and the Ecological Fallacy

Well, with little planned in the way of textual posts (although I have plenty planned for other types of posts), now is as good a time as any to start posting the second half of my political analysis notes. I already posted the notes from the first half of the semester, which you can find grouped together here. Those posts are all about power. These coming posts will be from the second half of the semester, and will focus on aggregation. So, let’s begin.

The Latin word “grex” means “flock,” and “ad” (which becomes “agg” in aggregation) means “to,” so “aggregation” is assembling a flock. It’s clear how power pertains to politics—but how does aggregation relate to it?

Well, let’s start with another question: Why war?

Maybe it’s a spiritual problem, as the Dalai Lama would assert—a problem of misunderstanding and hatred.

Other people believe it is a diversionary tactic—leaders need support of the selectorate (the critical sectors of the voting society.) So when there are domestic problems, the leader will create a foreign policy crisis to distract the electorate and unify them against the common enemy.

Then there’s the strategic theory. The strategic theory says you need two states for a war, so it can be modeled as a game. And as we’ve seen, if people don’t trust each other, they’ll end up with suboptimal results—war. Another strategic theory is that war comes about when there is incomplete information—both sides are unsure if they can win an armed conflict, so they have to duke it out to find out, rather than relying on the validity of each other’s threats.

Finally, there’s systemic theory. Systemic theories don’t look at individual states or dyads (pairings), they look at the system. There are three types of systems—the one, the few, and the many.

The one, or unipolar, is a system with a single strong state, like the Aztec Empire in Mesoamerica, or the US since 1989. Also Childhood’s End.

The few, or bipolar, is a system with two powerful states, like Athens vs. Sparta, or the Cold War.

The many, or multipolar, is a system with more than two powerful states, usually a lot more than two. Examples are the concert of Europe, the Warring States Period of China, or A Song of Ice and Fire.

And if you want to determine if a war will happen, or why a war will happen, you have to determine what kind of system is present.

Hobbes said unipolar systems are best, because everyone will be subject to one power which will ensure that there’s no infighting. We’ll talk more about this later.

Neorealism disagrees with this, arguing that bipolar systems are better, because the two powers will be in competition, and both will work harder to ensure that what they control is peaceful.

And Wilsonian idealism champions multipolar systems, and a peaceful league of nations.

So, why all these theories? Which one is right?

That’s tough, because they’re all explaining war at different levels. The spiritual explanation looks at individuals, where diversionary theory looks at a single nation, strategic theory focuses on dyads, and systemic theory looks at the whole big mess.

So how do you link these levels together? How do you aggregate them? This, to some extent, is our question.

The Ecological Fallacy

The most basic form of aggregation is just to put everything together. Put together a bunch of individuals, you get a nation. Put together a couple nations, you get a dyad. Put together a bunch of dyads, you have a system. That’s what Professor Dion calls the “rock pile” method. If you put together a bunch of rocks, you get a rock pile. So if you have put together a bunch of dumb people, you’ll get a dumb group. If a majority of republicans are elected into congress, you’ll get a congress that votes republican.

But this isn’t actually the case. When you put a bunch of individuals together, things get weird.

To explore this, we’ll look at another question, similar to “why war?”: Who voted for the Nazis?

The problem is, they used secret ballots, and this information isn’t readily available. We could look at precincts and see how they voted, and what their demographics were. From that we can find a rough correlation between certain groups and voting patterns. This is perfect, right—or as close to it?

Not necessarily, because it’s an ecological fallacy. That name is a bit misleading, so I’ll explain. It comes from sociologists applying biological sciences to individuals—moving from individuals to whole groups, just like biologists moved from species to ecological systems to better understand the individuals. So sociologists applied this ecological approach, using the same sort of precinct analysis above, but this method was proven ineffective and inaccurate.

To summarize, the ecological fallacy involves using information from one level of analysis to make inferences about another level of analysis.

An example:

A Berkley graduate admission study in the 70s found that 46% of men were admitted, while only 36% of women were admitted. An ecologically fallacious argument would be that the school is biased against women. But by looking at each department, they found that some departments actually heavily favored women, while others just slightly favored men. So what happened?

Men applied to departments with high acceptance rates for everyone, while women applied more often to departments with lower acceptance rates. So it wasn’t that UC Berkley was discriminating against women—it was a problem of analysis on one level versus another.

Next post will look at a more accurate use of aggregation—the Condorcet Jury Theorem.

Political Analysis: Expectations

Now we come to the final topic from my notes on political analysis—at least from the first half of the class. I’ll probably do another series of posts at the end of this semester, but for now, this is the final word on power.

“How many divisions does the Pope have?”

Thus spake Joseph Stalin in response to Churchill’s concerns about the Vatican’s views.

So far in this discussion of power, we’ve focused on hard power—threats, bargains, consequences—the kind of stuff that Stalin could respect. But what about the Pope? Does he not have power just because his only divisions are brightly dressed swiss pikemen?

It turns out (sorry Stalin) that there is such a thing as soft power, and to talk about soft power we have to talk about expectations, and to talk about expectations, we’re going to talk about John Maynard Keynes and beauty contests.Read More »

Political Analysis: Games

This post we’ll be talking about games—contrary to what people often say in dramas, this is a game.

An extensive-form game is a tree of decisions branching out, with actors forming the nodes in the branches, and the branches representing choices that the actors can make. The assumption is always that each actor is making rational choices, trying to get their best outcome, at every point.

To determine the outcome of an extensive-form game, you work from the ends backward to the beginning, using backwards induction. To demonstrate, here’s this game:

EFG-volunteerRead More »

Political Analysis: Choice

Now we’re talking about choice—why do people choose to do things? Why do they take bribes?

If we suppose an individual faced with a set of actions to choose from, and all of the actions are linked to clear outcomes, there are two principles of rational choice.

Principle One: The individual has a consistent set of preferences for outcomes. There are two types of preference ordering: strict and weak. Strict ordering is like a total dominance hierarchy. No matter what, between two outcomes the individual will always have a preference. Weak ordering is like a partial dominance hierarchy, and an individual can have outcomes that are tied in preference. Unlike a partial dominance hierarchy however, the ordering will never be ambiguous—choices will always be tied or ranked, never unknown (as they were in the black male/white female scenario.)

Principle Two: The individual chooses an action to achieve the most preferred outcomes. Sometimes the choice is easy. Sometimes the link between action and outcome isn’t clear. Sometimes the outcome depends on chance, or someone else’s choice.

Well this seems pretty obvious, so what use is it? It’s useful because by understanding what a person’s preferences are, it’s possible to predict more complex decisions involving the interaction of multiple preferences.Read More »

Political Analysis: Networks

In this continuing series of posts taken from the notes for my Intro to Political Analysis class, we’ll look now at networks and what they tell us about power.

Networks are composed of nodes and ties. Nodes are like points. Each represents an actor. An actor can be any individual, institution, nation-state, or social group with a distinct personality. It can even be a chemical.

Ties are like lines connecting nodes. They can represent any relationship—economic, romantic, religious, chemical. These ties have characteristics, like strength, direction, and elements. Strength can be dichotomous (binary) or cardinal (being represented by a number on a scale.) A tie can be undirected (two-way) or directed (one-way, and assymetric.) The elements of a tie can be univalent (just one relationship), or multivalent (with multiple strands of relationships.)

This is what a total (left) and partial (right) dominance hierarchy look like drawn as networks. The arrows point to the dominators (so A has the most dominance in both networks.)


Read More »

Political Analysis: Dominance

I just had my midterm for my Intro to Political Analysis class, taught by the eccentric, chalk-wielding, duck-loving Professor Douglas Dion, and in preparation for it I typed up all of my notes. Over the years I’ve found that the best way for me to remember notes, and be able to easily study them afterward, is by writing them down in full sentences and paragraphs. Sometimes they even end up being readable and well organized, and I think this is one of those cases. So, here is the first post in a probably four-part series of my notes on political analysis from the first quarter of the Spring semester, and specifically, power. This post in particular is taken from lectures on dominance theory.

The word “politics” comes from a treatise by Aristotle, deriving from the word “polis.” A practical definition is: the theory or practice of government. It can also mean a person’s ideology (i.e., “what are your politics?”) It could be a term for the acquisition of power or status. From all these definitions, politics might seem a mess, which is why we need analysis—another Greek derivation, from a term that means “to unravel.”

Read More »