SarahC:
One thing we do know is that if we project all the opinions onto a set of dimensions that we like -- for example, the old standby of liberal/conservative and authoritarian/libertarian -- we can start to measure "political diversity." People who describe themselves as Democrats, for example, span a much wider range of views than people who describe themselves as "Republicans." Implicitly, we're putting a Euclidean distance on a high-dimensional space, projected onto a few dimensions.
Trouble is, any concrete definition of this distance will be arbitrary. Even with a single dimension, it is only possible to construct an ordinal scale, and there is no objective way to define distance. With multiple dimensions, there is the additional problem of how to make different dimensions commensurable. By varying these arbitrary parameters, any such calculation can be manipulated to reach very different conclusions.
An assertion that people in one group have a wider range of views than those in another can be defended only insofar as common-sense clearly leads to such a conclusion. If this is not the case, then the answer given by all this flashy math will be determined by your own preconceptions you put into the model, not some objective truth.
If we used some kind of resource distribution to acquire the information; i.e. "you have a budget how much do you spend on what" you would (in addition to learning how little people know about economics) have some pretty solid numbers to work with in defining a metric.
The issues of budget allocation are only a subset of people's political opinions. But even with concrete budget numbers, the metric still cannot be objective.
Suppose you have three people who advocate, respectively, a $700B military budget, a $350B military budget, and a $0 budget (i.e. complete abolition of the armed forces). Clearly, common sense tells us that the first two people have a large difference of opinion, but it pales in comparison with the extremism of the third one's position, and it makes no sense to claim that the distances 1-2 and 2-3 are equal, even though the difference in numbers is the same. So again you have to introduce some arbitrary scaling to define this distance.
Moreover, the differences of opinion on different budget items cannot be compared directly based on just the amounts of money allocated. The budged of the FDA is only a few billion, but abolishing the FDA is a far more radical proposition that cutting back, say, the military budget by ten times what the FDA now gets. Again, you have to introduce some arbitrary criteria to compare these numbers.
So, ultimately, you'll end up producing arbitrary numbers no matter what.
Both of your examples are ultimately arguments in favor of reasoning about ratios of budgets: going from $350B to $700B is a 100% increase, while going from $0 to $350B isn't even defined. Perhaps $175B and $350B would be at a similar distance from each other.
Similarly, taking away a few billion from the FDA and a few billion are incomparable; however, reducing the FDA budget by 50% and reducing the military budget by 50% might be approximately equally radical suggestions.
So maybe we should be talking about log-budgets instead. Is there any example where such a calculation would produce counter-intuitive results?
I think you misunderstand, though. Just label the three budget options A, B, and C. There's no need to rank them. There's no need even to know what the question was about.
If you have a long questionnaire and many respondents, you have a big matrix, each column being a person's responses to all the questions. These are labeled arbitrarily. Zero or one or something. Looking at the covariance matrix tells you which answers are correlated with which other answers; clusters and outliers appear. "Radicalness" is defined simply as low correlation with other columns: low likelihood of giving the same multiple-choice answers as other people did.
There's arbitrariness in the choice of questions, but it's not quite as arbitrary as you think.
I understand the general approach; my response was to this concrete budget-based proposal. However, you say:
There's arbitrariness in the choice of questions, but it's not quite as arbitrary as you think.
It is in fact extremely arbitrary. You're avoiding the arbitrariness necessary for defining a normed vector space of political positions by offloading the same arbitrariness to the choice of questions in this model. Both approaches would likely correctly identify extreme outliers that are far from the mainstream, but the measured amount of variation within clustered groups would be, in both cases, an equally arbitrary reflection of the model author's preconceptions.
To take an extreme example, you could have a hundred questions, ninety of which deal with various intricacies of Christian theology, while the rest deal with human universals. If you administered them to a representative sample of the world's population, your model would tell you that the opinions of Christians span a much wider range of views than the opinions of non-Christians. The same principle applies -- perhaps less obviously, but no less powerfully -- to any other conceivable questionnaire.
This comment (I think) makes your point clearer to me. The problem isn't so much in the "send your directed graph to a metric space" as it is "choose a basis of your metric space."
I think there is a sense in which you could find "less arbitrary" choices, but I don't think an algorithm exists among humans to find one reliably so I think you're right.
I wouldn't go so far as to say that you'll produce arbitrary numbers no matter what. But I think you're right that the method of measurement and analysis can make a huge difference to the observed result--it's a volatile combination of statistics and qualitative politics. However, wasn't part of the point of the post that this model is insufficient in the first place?
It's all arbitrary here to some degree -- it's just messing around with the numbers. (Incidentally I wasn't trying to imply that "political diversity" was a virtue.)
If you pick the axes to mean something, then they'll be defined "to taste," of course. If you don't bother about giving them English-word labels, just let them be the first two components in PCA or something.
Honestly, I'm just messing around here. For crying out loud, it's not meant to be Truth.
In part 2, I sort of glossed over the technical stuff, but I was not talking about making up political dimensions like "more anti-war" and rating the answers to poll questions by hand. That is way too arbitrary for my taste. I'm talking about plain old dimensionality reduction. I had something like PCA in mind (if we were careful we might use a different method, but this is just illustrative.)
If you don't know about Principal Components Analysis, it's an important notion.
Tutorial with a practical example
The principle is that if you decide a priori what the "coordinates" are, you might pick wrong. You might not explain the variability in the data very well. Amazon.com doesn't have a pre-set category called "horror" and recommend you horror movies based on the fact that you've watched other horror movies. Amazon gauges "similarity" based on coordinates that arise naturally from the data (and maybe don't easily correspond to a property that can be given an English name.)
Maybe I'll write a top-level post explaining this sometime, if it isn't common knowledge.
Principal component analysis of UK political views, from a few years back: http://politicalsurvey2005.com/themap.pdf
(Response composed while reading, so it's a little disorganized, and most of it wasn't written after I'd read the whole post. If something seems like a tangent to or misunderstanding of what you wrote, please assume that it is, but if it's interesting feel free to remark on it anyway.)
I find the interaction between
Generally, if a politician supports one "Republican" position, he'll support most of the other "Republican" positions.
and
Suddenly, it's not one-dimensional any more. There are people who like low taxes and also like gay marriage.
noteworthy. Is the contrast that when making policy, people follow the party line, but when polled about their real opinions, they stray more? Or is it that politicians whose job security depends on pleasing a certain group of people will play it safe, and private individuals are freer to express their varied views? Or are those the same thing, in practice? It seems like you're comparing apple politicians to orange citizens, but I might be missing something.
People who describe themselves as Democrats, for example, span a much wider range of views than people who describe themselves as "Republicans."
Interesting! I didn't know that. It doesn't surprise me, but I wouldn't have trusted my intuition about it--it's easy for me to see more variety among Democrats because I live in an area that has lots of them. (I actually have unusually specific data about that, because I've been a poll worker and thus have skimmed through the entire list of party affiliations for a nearby district. IIRC there were more Green Party members than Republicans.)
If you support spending more on X, you must either support less spending on some other thing Y, or support raising taxes, or support running a higher deficit.
That depends on whether you're polling people about practical policy or about what they wish could/would occur. These are two very different questions. I may very much want to increase the budget for education, but simultaneously understand that it's not feasible to do so at the moment.
You cannot simultaneously be in favor of reducing carbon emissions, and be in favor of a set of policies that, on net, increase carbon emissions. Or, you can, but you'd have to be either ignorant or confused.
Similarly, if poll questions took into account the link between these policies, we'd rob ourselves of data about how many respondants are ignorant or confused. I think you underestimate the significance of the fact that people DO hold conflicting positions, sometimes strongly, and this puts the people who actually have to make feasible policy in an awkward position.
Or is that the point? That popularizing the second model encourages people to hold incompatible positions, whereas encouraging the use of the third encourages more practicality? I'm not sure I would try to push people to hold beliefs about politics or policies that are internally consistent. If I tell you that I want two things of which I cannot plausibly have both, I've told you more about my preferences than I would have if I'd just told you what compromise I would settle for. As the situation changes in the future, it might become possible to reconcile my two previously incompatible preferences, and it's useful to know that I'd support that.
That said, I really like your description of a graph of policy preferences. I think it's very useful for the purpose you describe--identifying root differences--and not just in politics. Two people who disagree strongly about which of two anime shows is better are more similar than two people who disagree about whether animated television is inherently childish and a waste of time. Seen in a certain light, this is also very much like the ancestral/derived trait analogy I used in the OKC post a while back: "ancestral" preferences would be the influential nodes, and "derived" ones the leaf nodes. I wonder where else interesting one can go with that pattern.
"Hi, I actually support monarchy,"
This made me laugh because I imagine it being used as a greeting. ("Hello, I'm Jesse." "Hi, I actually support monarchy.")
I think both your conclusion and your example of it are excellent, but I feel like the final point deserves more words than it got. I'm left wondering about specific major instances and ramifications of making the error you describe. (Is there already a name for it? If not, can we call it the space squid fallacy? Is there some bureau that decides these things?)
I'll reply to a few of your points.
I think that there's such a thing as party discipline among politicians, such that breaking with one's party is a career risk, but ordinary folks can believe whatever they want to believe with little cost.
I don't want to eliminate polling and replace it with something else. Polling describes people's opinions; my "graph" describes the logical and causal relationships between policies. They describe different things. Also, making a graph for all of politics is impossible -- you'd have to be Laplace's Demon to do that. I could imagine making a very small toy example on a very specific project.
I agree that the graph setup is useful for analyzing disagreements and value differences in general, not just political ones.
The "fallacy" isn't exactly a fallacy in reasoning, but it's instrumentally irrational. One example would be infighting between very similar groups: "People's Front of Judaea" versus "Judaean People's Front." It's tempting to spend all your time fighting your friends -- but if you focus on fighting over which anime shows are best, you won't get across the message to people outside your subculture that anime in general is a good medium.
It's tempting to spend all your time fighting your friends -- but if you focus on fighting over which anime shows are best, you won't get across the message to people outside your subculture that anime in general is a good medium.
Indeed. The value of which depends on why you're arguing, I suppose--you might be artists trying to gain acceptance, but you might just be trying to decide what to watch tonight.
The main problem I see with your discussion is that it fails to distinguish between the face value of beliefs and their implicit signaling value. If you try to disentangle the internal logical structure of a typical (smart and well-informed) person's political and ideological beliefs, you will not find a neat logical network of axioms, facts, and their implications, but a jumbled mess of extremely vague propositions whose logical connection with their concrete positions is tenuous at best, and with a bunch of seemingly random unprincipled exceptions. The entire structure will reflect status- and affiliation-signaling considerations far more than logical and factual accuracy.
For example, you list "democracy with universal suffrage is the best form of government" as a core influential belief that might determine a wide range of someone's positions. But if you try to analyze what this belief says, you'll see that it's in fact extremely vague, and implies nothing concrete without an entire hairball of implicit beliefs, preferences, and values that are normally associated with this proposition in our culture, with signaling implications hopelessly entangled with reasoning all along the way.
Without undertaking the tremendously difficult task of disentangling this hairball, your approach will still lead to people talking past each other. (Or worse, understanding the implicit conflict instinctively and responding accordingly.)
Sure. This is sort of idealized, Spock-politics. Issues of irrationality and signaling are a whole other kettle of fish. They've also been extensively discussed on this site.
The thing is, a network of axioms, facts, and their implications is hard enough to understand. If we wanted to understand the differences between different people's beliefs, on any subject, we'd need to tackle a very scary mathematical/computational problem.
I am aware that the mere mention of politics gets on your nerves. They are, however, a good example of a sort of belief that
Just about everybody has. Lots of salient examples available that everyone will recognize.
Differs a lot from person to person.
People (at least the smart and well-informed ones) spend time trying to reconcile and make coherent.
So you hate politics. What else do almost all people have opinions about, where the opinions vary, and people bother with implications and internal coherence?
No, I don't hate politics. In fact, I enjoy discussing it if it's done the right way; those things that get on my nerves, I simply ignore. With posts like this one, I see some potential for an interesting discussion, but for this to happen, it is necessary to clarify some misconceptions and make sure we stick to reality, not false idealizations and metaphysical fictions.
The trouble here is that analyzing the structure of people's political beliefs while ignoring signaling and related considerations is like trying to analyze the structure of the atom nucleus while ignoring the strong interaction. It is simply too large a step away from reality to allow for any accurate discussion.
It's easiest to see this if you just ask people to state some of the core principles underlying their political and ideological beliefs, and then do some Socratic questioning about their various implications. It's very easy to get them into a self-contradiction, or to demonstrate that a straightforward deduction from these principles leads to something they'd never subscribe to. At the end, you'll get a stream of annoyed and incoherent special pleading and rationalizations aimed to uphold the positions your interlocutor deems to be desirable and respectable, not a coherent logical structure where you might start locating the root of your disagreements.
Pew has used cluster analysis of Americans' responses to political survey questions to divide them into 9 political categories. Here's the first page of their report and here's the methodology section.
People who describe themselves as Democrats, for example, span a much wider range of views than people who describe themselves as "Republicans."
And yet it was NPR who fired Juan Williams for appearing on Fox, not Fox for appearing on NPR. Now, one theory is that NPR is admirable, Fox is disreputable, so of course NPR has good reason to be more concerned about Fox cooties than Fox does to be concerned a out NPR cooties. But another theory is that NPR is much more ideologically narrow and intolerant of dissent than Fox. Which is the truth? Well, if we ask an academic, who is probably on average to the left of Chavez, he will probably tell you that the big problem with NPR is that they are just way too broad-minded and that it is high time they got rid of that bigot. So, what sources are telling you that democrats are more diverse than republicans? Are you talking about academic studies?
God, am I doomed to be misunderstood?
Who said that Democrats were more tolerant? And who said anything about a news network of any kind being reasonable?
Even if the "wider range of views" I wrote about was absolutely, authoritatively true, it wouldn't have to do what you're talking about. And in fact I don't believe it's authoritatively true -- I think I've seen a study somewhere, that's all. It's a vague memory. Call it false if you want.
Who said that Democrats were more tolerant?
Do you believe there is no relationship between whether a group tolerates dissent from a narrowly defined ideology within the group, and how wide a range of views one finds within the group? Really? Let's consider an example.
Suppose you encounter a group that tolerates no dissent from big-endianism, a group which expels members who dissent from big-endianism. Do you believe that this group contains both big-endians and little-endians? Really? How so? It does not tolerate - in the sense of expels - non-big-endians.
It seems to me to be pretty obvious that there is not only a connection, there is a strong relationship between tolerance and variety. Maybe not a necessary one, but then, hardly anything is necessary. if you point a loaded gun at my head and pull the trigger, it is not logically necessary that I will be killed. An extremely unlikely quantum event might occur which intervenes, rendering your action harmless. Nevertheless, the lack of absolute logical necessity hardly means there is no connection.
And who said anything about a news network of any kind being reasonable?
Well, that's a new one. So out of the blue you are going to throw in the idea that news networks are somehow peculiarly unreasonable, all so that I can't use an example of a Democrat-aligned and a Rebublican-aligned news network as evidence for questioning your view. Because unless there is something peculiarly unreasonable about news networks, then you have given no argument for rejecting my evidence. Since you have objected to my evidence, I can only interpret this as presupposing that there is something special about news networks which makes them inapplicable to the question.
I don't see it. I don't see any reason to think anything other than that a Democrate-aligned news network and a Republican-aligned news network will exhibit, more often than not, in microcosm, the behavior of their respective groups. So unless you give me a better answer than that, I can't accept your rejection.
There are, of course, objections you can make. For example, it is after all just one event, an anecdote. However, I think it's significant that NPR firing Juan Williams seems intuitively quite expected, and Fox firing Juan Williams seems intuitively unlikely. So we have not just the event itself, but our intuitive feeling, which the event serves to elicit and to highlight. Now, one view of this is that we expect liberals to be intolerant of the slightest dissent, and we expect conservatives to be tolerant of significant dissent. The anecdote, then, serves primarily to elicit this intuition, which I feel and which perhaps some readers will feel, and this intuition in turn goes against the gist of what you were saying - does so despite the distinctions you have made (between tolerance for dissent and variety of views, between a network and the population at large) for the reasons that I have given.
And in fact I don't believe it's authoritatively true -- I think I've seen a study somewhere, that's all. It's a vague memory. Call it false if you want.
Call it false if I want? I don't even know what to make of that. I gave an argument for X, and your response is "believe X if you want"? That sounds like saying "whatever" - it's a brush-off, rather than a genuine response. But if what you want to do is brush me off, why respond at all?
Constant, I really don't care.
Maybe you're right. Maybe you're wrong. I don't know who's more tolerant. I agree that firing Juan Williams is pretty intolerant.
Look, I wrote a shitty little post and blasted it off into the ether. There wasn't any research to it, I made statements without justification, etc, etc. Who's more tolerant was not the point -- hell, I don't even know if I had a point. It just sounded cool.
So I'm not super-invested in my claims, that's all. I'm not going to spend a bunch of time dredging up evidence to show that Democrats are tolerant -- because honestly, I don't necessarily believe they are. And honestly I'm not interested in the issue. If you want to think of this as "conceding the point" then I concede the point.
This was a "noise" post. I basically secrete long, ranty essays the way a spider secretes spiderweb. Sometimes I make the mistake of showing them to other people. Jesus Katy, people get touchy about the topic. So sue me, I'm neurotypical, I'm a product of my time and class, and I rant about politics just like everyone else. It's just shooting the shit.
I can't tell how you were feeling at the time you wrote something. I am going to respond to what you wrote, not to how you were feeling at the time you wrote it. And I am going to take however long of a comment to respond to it that I feel is needed to fully make the point. Sometimes that takes a brief comment, sometimes a long one, depending on the difficulty and subtlety of the subject matter.
There is nothing "touchy" - oversensitive, easily offended - about rebutting a claim per se. In calling me "touchy" for rebutting a claim, you seem to be implying that anyone who rebuts that claim is easily offended. Really? You claim that Democrats are more diverse than Republicans, and anyone who rebuts that claim is easily offended?
That hardly makes any sense. But what's left, in determining whether a response to something you wrote is a symptom of oversensitivity? Is the topic so unimportant that making any claim at all about it one way or another is itself a sign of oversensitivity? But you made a claim about the topic yourself. Does that make you oversensitive?
Or is it the fact that you made the claim while in a state of mind of uncaring, and then I responded, that shows that I am too easily offended? So to avoid being classed as having a chip on my shoulder requires that I (a) read your mind, and (b) avoid rebutting claims if my mindreading powers have discerned that you were not serious when you made the claims.
There is nothing "touchy" - oversensitive, easily offended - about rebutting a claim per se. In calling me "touchy" for rebutting a claim, you seem to be implying that anyone who rebuts that claim is easily offended.
There's an alternate reading of SarahC's reaction.
Your comment addressed 2 percent of her article that was not essential to the main thrust of article and interpreted this portion of the article in a way that made it look as though you suspected her of partisanship. Your choice of focus suggested to me that her comparison of Democrats and Republicans put you on the defensive.
Miscommunication is common on the internet as the communication aids of body language / facial expression / tone of voice that humans evolved are absent. I recognize that my initial reading of your comment may have been inaccurate.
Since statements made on the internet are easily misinterpreted, I think it's a good idea to probe as to whether one's initial interpretation is correct when responding to somebody's statement.
In particular, I think that you would have been more likely to provoke a positive reaction from the poster if your initial comment had been something like
"Do you have a strong belief about Democrats being more diverse than Republicans or was your reference just an offhand comment? If so, can you give supporting references?"
On the flip side, I think that she could have better communicated with you in her response to your comment. Concretely, I would guess that she would have been more likely to receive a favorable response from you had she responded with:
"I was not claiming that Democrats are more tolerant than Republicans. My remark that Democrats are more diverse than Republicans is based on a vague memory of a study which I can no longer find. I will cut out the reference accordingly as my evidence on this point is very weak and is not crucial to the main thrust of the article."
Is this right?
Your comment addressed 2 percent of her article that was not essential to the main thrust of article
It hardly seems unusual or wrong for tangential discussions to form.
and interpreted this portion of the article in a way that made it look as though you suspected her of partisanship.
I stated almost straight out that I believed her source was probably academic and therefore probably biased in a way that flattered Democrats. Academics contribute to Democrats over Republicans by something close to 90% to 10%. They are an amazingly heavily Democratic bunch of people. I said nothing about her.
The bias is not a matter of dishonesty. Look at the Juan Williams example. If you think that NPR is more reputable than Fox, are you being dishonest? If you think that NPR is more intolerant than Fox, are you being dishonest? I don't see any obvious dishonesty either way. But it's a hugely different perspective, which interprets the same event - the firing of Juan Williams - in two very different ways.
She objected that tolerance is not variety, that networks are not the population at large. But the point is a very general point. Bias greatly affects what we measure. Suppose you are trying to measure relative tolerance at NPR and Fox. If you think that NPR is reputable and Fox is disreputable, then you have no reason to interpret Juan Williams's firing as an indication that NPR is more intolerant than Fox. It makes sense that disreputable Fox should seek out reputable people, and that reputable NPR should disassociate itself from disreputable people.
So your perspective is going to greatly affect your result when you attempt to measure degree of tolerance. Yes, tolerance is not variety, but it's a general point. (And anyway, tolerance is closely related to variety.)
Your choice of focus suggested to me that her comparison of Democrats and Republicans put you on the defensive.
I don't even know what to make of this. "On the defensive" means, what? Any action in either a military conflict or a intellectual disagreement could be called a "defense" (e.g. of one's own position). Do you mean that my choice of focus suggested to you that I am touchy about the topic? That I am overly sensitive (the meaning of touchy)? Is that what you mean by "defensive"?
Well, I don't really see why the choice of topic would suggest to you that I am overly sensitive to the topic. That I am sensitive enough to respond - sure. But is that over sensitive? Maybe it is being more sensitive than she is. She does, after all, say she doesn't care. If she's the model of the correct degree of sensitivity, then I am over-sensitive. But what if she is under-sensitive and I am just right?
In particular, I think that you would have been more likely to provoke a positive reaction from the poster if ...
I would guess that she would have been more likely to receive a favorable response from you had she...
I'm not sure what to make of this. If I take issue with something, then I will take issue with it. Is this what you call an "unfavorable response"? Are you saying that, had she refrained from saying something that I took issue with, then I would not have taken issue with it? I suppose so. But where's the fun in that? And anyway, how can she possibly know what I will take issue with and what I won't? Isn't the point of discussion to discover what other people take issue with?
Are we supposed to avoid argument? Avoid disagreement?
As it happens, she said something I took issue with. In your revision of her comments, you eliminated stuff I took issue with. But you're doing this with hindsight. That's cheating. You already know that I don't take issue with it, because I didn't take issue with it.
She didn't say "more diverse", she said "span a much wider range of views". These are not the same. When you say "more diverse", people think of ethnic, racial, gender, religious and geographic diversity, which people love to cheer for, but which are all irrelevant to the topic of this article. "Wider range of views," as used here, means more different positions advocated. That's neither inherently good nor inherently bad.
One common characterization of the liberal/conservative spectrum is that conservatives favor stability, and liberals favor change. In the space of possible answers to a question, the status quo is one answer, and change is every other answer. So liberals span a wider range of views, and the Democratic party identifies as liberal.
The rest of what you wrote on this thread seems to flow from this bit of confusion. You also talk a bit about "tolerance", which is an orthogonal issue; a group may all agree and be tolerant of disagreement, or all disagree and be tolerant, or all agree and be intolerant, or all disagree and be intolerant. SarahC made no claim as to which of these categories either party falls into, and neither will I.
Suppose you wanted to describe the political landscape efficiently. That is, you want to describe the range of existing political positions, and develop some way of evaluating which political positions are "similar." (I'm American, so I'm going to think in terms of the US.) There are three ways you could go about this and they are radically different.
1. Politicians' voting.
Because we have a two-party system, politicians (and some other political players, like Supreme Court justices) make decisions on a single, left-right axis. You can explain almost all the variation with one dimension: "More Republican" or "More Democrat." Generally, if a politician supports one "Republican" position, he'll support most of the other "Republican" positions. Studies have been done here (too lazy to look them up right now) supporting this phenomenon at all levels of politics.
2. Individuals' opinions on poll questions.
Here, we do something different. We ask poll questions about a variety of issues and see what people think. Suddenly, it's not one-dimensional any more. There are people who like low taxes and also like gay marriage. There are people who are anti-abortion and anti-war. The fact that individual opinions don't line up along a left-right axis is what's behind ideas like the Nolan Chart -- although it doesn't imply that the "real" way to explain opinions is necessarily two-dimensional. How many dimensions actually do efficiently explain all the different kinds of opinions? I don't know, and that's a statistical puzzle in itself, although I do know of techniques (like multi-dimensional scaling) that purport to estimate the "right" number of dimensions.
One thing we do know is that if we project all the opinions onto a set of dimensions that we like -- for example, the old standby of liberal/conservative and authoritarian/libertarian -- we can start to measure "political diversity." People who describe themselves as Democrats, for example, span a much wider range of views than people who describe themselves as "Republicans." Implicitly, we're putting a Euclidean distance on a high-dimensional space, projected onto a few dimensions.
3. Logical and causal implications of policies.
Just as politicians' voting doesn't capture what regular people think, it could also be argued that people's opinions on poll questions also don't capture something important about politics. Namely, some policies logically imply one another. If you support raising spending on the war in Afghanistan for 2011, you must also support continuing the war in Afghanistan in 2011. If you support spending more on X, you must either support less spending on some other thing Y, or support raising taxes, or support running a higher deficit. Simply asking people about their opinions on a variety of questions doesn't capture this structure.
Additionally, some policies have consequences for other policies. You cannot simultaneously be in favor of reducing carbon emissions, and be in favor of a set of policies that, on net, increase carbon emissions. Or, you can, but you'd have to be either ignorant or confused.
And some philosophical claims imply policies. If you believe "Congress should not do anything except the enumerated powers in the Constitution" then that implies you have to oppose all the things Congress does that are not enumerated powers.
In part 2, every policy position was just a coordinate in a high-dimensional vector space. Now, in part 3, it's suddenly not so simple. You have a directed graph of implications. It's very hard to get a handle on this graph. But just as this graph is more intractable, it's also more informative. In the part 2 model, a person could easily support a variety of inconsistent positions, and, in fact, people do. In part 3, some of your policy choices are determined by your other policy choices -- not just by correlation but by necessity.
What can we say about one policy node that implies a lot about other policy nodes? Well, it's very influential. If you could examine a single person's directed graph of the policy universe, with nodes colored red for "oppose" and green for "support," then the choke-points, those nodes that imply the choice of color for lots of other nodes, are core beliefs. A pacifist's graph, for example, is heavily influenced by the "War is wrong" node, because that logically implies his position on all specific wars.
Obviously this doesn't have to be binary; you could have degrees of support and opposition, that imply updating the degrees of daughter nodes. Increasing your support of "End all wars" should increase your support of all nodes "End war X," but increasing your support of "Go to war to defend allies" should decrease your support of "End war Y" if an ally was attacked in war Y.
This gives us a different way of defining which policies are similar to each other. Policies that are close "cousins" on a tree are similar; "End the war in Iraq," and "End the Korean war" are close because they're both implied by "End all wars", but "End the war in Iraq" and "End the war in Afghanistan" are even closer because they're both implied by "End the War on Terror" (which is implied by "End all wars.")
Three kinds of similarity are not the same
Points that are close on the left-right spectrum of politicians' decisions are not necessarily all that close in the higher-dimensional space of people's opinions on poll questions. I also hypothesize that points that are closely correlated in people's poll answers are not necessarily close in the part 3 sense of being close cousins on a tree of implications. That is, I would guess that people may tend to hold opinion B whenever they hold opinion A, even when A and B actually have nothing to do with each other.
How different is your debating partner?
I think part 3 is a good model for having political conversations -- better than part 1 or part 2. How "different" a person's politics feel from your own, once you've had a discussion with him, is not so much a matter of which party he votes for, or what his opinions are on a laundry list of issues. No: a person feels really "different" when you and he have opposite opinions on one of your influential nodes, something really far back on the tree. If one of your influential nodes is "Democracy with universal suffrage is the best form of government" and you're talking to someone who says, "Hi, I actually support monarchy," then that person is really different from you. A person who agrees with you up until the last branch on the tree is pretty similar to you, no matter how vehemently you disagree about that last branch, because you both can draw upon the same assumptions from farther up the tree.
The personal lesson is that it's useful to be clear with yourself about levels of difference. People can spend a lot of time arguing or even hating people who are very similar, and completely forget that there's a higher level on the tree. My politics are pretty different from Sarah Palin's; but I'd be Sarah Palin's ally against Louis XIV, I'd be Louis XIV's ally against Aurangzeb, and I'd be Aurangzeb's ally against a giant space squid intent on annihilating Earth -- Aurangzeb may have wanted to get rid of all the Hindus in India, but we've got more in common with each other than with a planeticidal space squid. Squids aside, it's rather ridiculous when people identify their "greatest enemy" or "greatest threat" as a person with only slightly different political views.