Tag Archives: Academic Life

The professional world of political science — the job market, research methodology, peer review, academic writing, the role of formal theory in the discipline, and occasional dispatches from the trenches.

Let Me Confirm Your Belief That Your Irrationality Is Rational

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This opinion piece in the New York Times, entitled “Why We Make Bad Decisions,” by Noreena Hertz, explores the implications of a well-established psychological/behavioral phenomenon known as confirmation bias.  In a nutshell, confirmation bias describes the general tendency to overweigh information in line with one’s prior beliefs and/or give too little weight to information contradicting those beliefs or attitudes.

This phenomena is clearly relevant to politics in a wide array of settings.  Voters may ignore “negative” information about their own favored party or give too much credence to “negative” information about other parties.  Individuals may selectively pay more attention to positive information about the policies they favor or ignore information that reflects poorly upon those policies.

Well, as is my usual approach, I wanted to briefly point out that observing such a bias may not be irrational.  I have two explanations for this behavior. The first demonstrates why positive and negative information should be evaluated differently in certain (common) contexts.  The second explanation demonstrates why individuals should stop exerting effort on updating their beliefs (i.e., paying attention to information) in certain (again, common) choice situations.

Both explanations rely on a simple presumption about beliefs: I will presume, as typical, that an individual’s beliefs are important only insofar as they affect the individual’s behavior. This is an important presumption, and it is definitely contestable, albeit not in standard social science models.  I will touch upon it again in the conclusion of the post.

Before continuing, note that I am not arguing that Hertz is “wrong.”  To the degree that one is confronted with “pure and costless information” in a single decision-maker situation, there is absolutely no reason to do anything other than faithfully revise your beliefs as far as possible according to Bayes’s Rule.  This is a mathematical fact.  That said, situations in which information is pure and costless and one’s decisions and incentives are in no way contaminated by strategic considerations are pretty few and far between.

That said, let’s move on to the explanations.

The first explanation is demonstrated by the following example. Suppose you have decided to get your yard reseeded: the bare spots have gotten unbearable, and something must be done.  Now suppose that you head down to the local nursery to get some seed and, while jawing with the sales person, he or she says “you know, buying sod is a much faster way to get a beautiful lawn.”  Should you believe this statement? Yes.

Should you change your beliefs about the effectiveness of seed and sod? Well, that’s not clear. In particular, you need to consider the source of the information and his or her motivations.  Sod is much more expensive than seed, and the sales person is presumably motivated to increase the amount of money you spend.  Accordingly, you should give less weight to the information—particularly in terms of whether you should put the seed back and buy sod instead.  Furthermore, once you realize that you should probably not act upon the information in terms of changing your choice, it is not even clear that you should process/pay attention to anything that the sales person says about the relative value of sod over seed.[1]

The second explanation is based on the following example.  Suppose that you have spent many months studying (say) two different houses, and you will buy one and exactly one.  Eventually, you have enough evidence to conclude with near-certainty that house A is the best one to buy.  At some point, your belief about the relative values of the two houses (if you are good Bayesian decision theorist) will be sufficiently certain that you would not pay any nontrivial cost for additional information.  Incorporating and processing information is costly insofar as it requires mental effort.  Even if it doesn’t, belief revision is important only to the degree that it will affect your decision.  But rarely is decision revision costless.  That is, most decisions about (say) personal health and finances are ongoing: changing one’s habits and diet, rearranging one’s asset allocation and consumption—these all require effort.  Put these two together, and it is clear that in some cases, ignoring information that is contrary to one’s beliefs may actually be rational.[2]

Finally, before concluding, I want to quickly mention that beliefs can be directly valuable in a “psychological” sense.  To be quick about it, suppose that you enjoy believing that your future will be bright.  Say you took an exam yesterday and will find out the results in 2 weeks.  You enjoy thinking that you did well, and you dislike negative disappointment.  In such cases, it is often optimal for you to have beliefs of the following form:

1. Walk out of the exam thinking you did INCREDIBLY WELL.
2. Keep thinking this.  No reason to find out anything about it, even if you can, until the end.
3. In the moments before you find out, recalibrate those beliefs downward.[3]

The same logic applies in situations in which the decision is a fait accompli for other reasons.  That is, suppose you have to buy a given house.  If you enjoy thinking that “the future is bright” even a little bit, then you have no immediate incentive to update upon/pay attention to information that disconfirms your “apparent prior beliefs” (i.e., the beliefs that would justify buying the house if you had a choice).

The link between this and the apparently pathological belief revision by (say) smokers/drinkers/drug users/UNC football fans and others “addicted” to arguably unhealthy lifestyles is clear: if you know—for whatever reason—that your decision is invariant to your beliefs, there is no reason to hold rational ones.  Indeed, there is probably a clear argument on “psychological” grounds that you should update in ways consistent with confirmation bias.

With that, I leave you with this and this.

__________________

[1] Of course, the opposite is true if the sales person tells you, “oh, you are definitely doing the right thing not buying sod.” In this case, the information is more credible because of the source’s motivations, so that this would rationally be given at least as much credence as if it were provided by a “neutral” source, and would therefore similarly look like confirmation bias.  In politics, this is known as the “it takes a Nixon to go to China” logic.

[2] You could call this a “tune in, update, and drop out” kind of logic.  And, it is beyond the scope of this post, but it is also a justification for apparent overconfidence in some strategic situations.  In particular, committing to not updating on the viability of a joint venture can bolster members’ incentives to contribute individually to the team production components of the venture.  In other words, if I am less worried that you might be listening to evidence that could make you doubt the value of the venture, I am in some situations less worried about my own individual effort being in vain because of you happening to have heard, on your own, that the venture might be less profitable than we all believed when we started out.  There is a link to NFL quarterbacks and head coaches in here somewhere.

[3] Years ago, I wrote a paper with George Loewenstein and Niklas Karlsson, on exactly this behavioral optimization problem.  The basic idea is that irrational beliefs (and irrational belief revision) is even “more easily made optimal/rational” if one allows for beliefs to matter on their own, which I rule out in the two explanations, but clearly is descriptively realistic.

My Research Is Kind Of Obscene…But I Knew It Only When I Blogged It.

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My last post dealt with my personal conundrum about how best to deal with the problem of “I know these data are interesting, but I don’t (yet) have a theory to understand/explain/”test with” them.  I got some very nice responses from colleagues and virtual friends.  Thank you.  (I have no idea why I get no comments on the blog, but from years of lurking/surfing I am actually “O.K.” with this second best outcome.  In short, I am under no delusion that, if you read this, you probably know how to talk with me “offline,” and truly appreciate when you do, even (or perhaps especially) when you disagree with what I post.)

All that said, I thought it useful to delve a little more into the problem I face(d) here.  (We’ll come back at the end to why I added a (d) to that.)

Simply put, the data I have represent how policy is made at the federal level in the United States.  By “represent how policy is made at the federal level,” I mean “are federal policy, per se.” My questions are multiple and somewhat in-the-weeds, but for the purpose of the post, I’ll focus on the question: “why do some issues get dealt with at a given point in time and others do not?”

The most basic theoretical problem I have with this enterprise is one of measurement.  (It’s the most basic one I have because it is the most basic theoretical problem in empirical analysis, full stop.)

To make this concrete: consider the notions of “issue” and “get dealt with.”  Suppose, for simplicity, that we take a law duly enacted under Artice I, Section 7 of the US Constitution.  What are the issues that law deals with?  Now, note that there are many practical ways to answer this question, but all of them—to my knowledge—are based on one of three approaches:

  1. Human coding: (very) smart and fair individuals (say) read the bill and accompanying contextual data (debates, press coverage, etc.) and assign the law to a topic.
  2. Ascription based on source: for example, if the bill was dealt with by the Senate Foreign Relations Committee, then it must have at least partially dealt with foreign relations, or
  3. Automated (or semi-automated) text processing approaches: essentially, very fast computers cluster bills/laws with similar words and/or semantic structures.

The two main problems (for my purposes) with approaches in class (1) is that human coding is (a) slow/expensive (implying that most preexisting codings are subject to selection effects due to the natural desire to maximize speed/minimize cost—e.g., it many researchers focus largely or solely on bills that were enacted or at least got to the floor of one chamber) and (b) inevitably designed to test preexisting theories or match preexisting ancillary data sources.

The main problem with approaches in class (2) is that I am interested (for example) in how institutions (i.e., sources) are aligned vis-a-vis what the human coders would call the “issues” of the true (i.e., latent) policy space.  Thus, to use the institutions that generate policy instruments as the basis for coding the issues dealt with by those policy instruments is very close to tautological for my purposes.

So, I was/am playing with the NKOTB of approaches, those in class (3).  The progress I have made there is classically ironic in the sense that that the more I learned/discovered, the less I knew.  Put another way, I increasingly realized that the validity of any conclusions I could reach would be necessarily predicated on the assumptions undergirding those approaches.  These assumptions, to put it mildly, are orthogonal to traditional methodologically individualistic social science.  (For example, what is the social science justification for viewing documents as “bags of words” or “term frequency inverse document frequency”—look it up—as a measure of the relative importance of a law in identifying the latent issues of the 112th Congress?  [crickets])

This is not an attack on any of these methods—I am so very interested in these questions, I’m happy to grasp at straws if need be, but I’d rather find a lifeboat.

So, again, I return to the question: how do I measure (i.e., discriminate between) what voters/congressmen/judges/presidents would call a topic/issue from the instruments that I will then derive face-melting models demonstrating the incentives of voters/congressmen/judges/presidents to conflate/combine/obfuscate those topics when drafting/amending/interpreting those very same instruments?  Wait for it…you knew it was coming…it’s a top-down version of the Gibbard-Satterthwaite theorem.

Thus, before concluding, I will pose “the big question”: is it impossible for us to actually gauge the match between politics in practice and the latent structure of policy?  In other words, when we talk about “strange bedfellows” in terms of political actors, we mean based on that they are typically in opposition, but in the case in question, they are allied.  How can we detect the analogue with political issues: how can we discern when a bill contains both apples and oranges, if one took/had the time to read it? [1]  …Still thinking about that.

To conclude, let me return quickly to why I implied that the problem is no longer pertinent (“face(d)”)?  Well, in short order, my previous blog post cleared my head and forced me to think about the problem from a third-person version of my own perspective.  As a result, I have had a (truly) very fun 36 hours or so of active modeling: change a word or two in a google search here and there, and…SHAZAM!…I have plenty of new ideas about what could be the right models for the problem.  And, as I said in my last post, modeling is truly what I do.  So, stay tuned…I really think there’s some cool stuff that’s about to drop.

With that, I leave you with this.

_________________________

Footnotes:

[1] There is a political science term for this, due to William Riker: heresthetics: in somewhat ironic self-promotion terms, Scott Moser, Maggie Penn, and I have published on the topic in the Journal of Theoretical Politics.

Which Comes First, Theory or Data?

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It’s kind of a trick question, exactly the type of gambit that drives both research and blog posts. (The answer, it seems, is “both should magically emerge simultaneously.”)

Anyway…I’ve been in a bit of a funk lately, and not the twerking kind.  Both the seasonal goings-on and my mind doing laps on a vexing problem have left me a bit, ummm, unmotivated to post.  Without further delay, let’s make petroleum jelly out of petroleum…here’s my intellectual/professional quandary/blogging impediment in the form of a blog post.

1. I have a lot of data (BIG data) that I just know is important.  Basically, it is (a big part of) the substance of federal policymaking.

2. I don’t know any theories that really speak to it.

3. Well, I have some, but they are both intractable as presently formulated and I don’t know how best to simplify them to get results.  I have strong hunches about how I could do so, but I’d like to choose the simplifications that are most appropriate for the questions I want to answer.  (In a nutshell, the questions I want to answer are “why are some issues raised and acted upon while others are set aside,” and “how are people and resources deployed across multiple issues at a given point in time?”)

So…what to do?  (If you think about it for a moment, my conundrum is very meta.)

From a “math of math of politics” angle, the real rub is exemplified by the astute question raised by one of my colleagues when I described something I was doing/wanted to do with this big data.

“But what’s the theory?”

I have been told by other colleagues that theory is not necessary—though highly desirable—for empirical social science.  I fundamentally and, if I say so myself, quite correctly disagree with this assertion on theoretical grounds.  (See what I did there?)  But, the more practical rectitude of my assertion that there is no empirical analysis without some kind of theory—in terms of interpreting, publishing, and communicating empirical analysis—is also illustrated by my (empirically focused) colleague’s question.

More “math of math of politics” is raised by the fact that my absolute advantage in terms of scholarly production is in theory (really, modeling), rather than “pure” empirical analysis.  So, maybe I should take a hint and take a leap, “doing the models” that I can do, and letting others sort them out.  After all, I’m tenured, and therefore have the freedom to take the time to do this—the bulk of “the time” in this case (in my expectation, at least) will be navigating what I expect will be a bumpy road to publication and communication of the models.  I foresee plenty of (in-the-weeds) speedbumps in pursuing a “pure theory” approach to the questions I am interested in.

The irony, of course, is that one might think that tenure is at least partly there to motivate me to “take risks” in the sense of really trying to do things right.  In this case, the right path in terms of getting people to listen to the ultimate analysis might involve developing models that, at least now, can not be motivated by empirical verisimilitude.

So, what to do, I ask you.  Most of you are social scientists, and I am honestly befuddled by the proper way to aggregate/trade-off the two competing intellectual incentives: should I patiently, doggedly, and perhaps inefficiently chase the (as now unknown) “right analysis,” or do the analysis that will be more readily heard and may accordingly grease the wheels for ultimate production and communication of the right analysis?

With that, I leave you with this.

There is no Networking without “two” and “work” or, Incentives & Smelt at APSA!

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As Labor Day weekend approaches, scores of scholars are steeling themselves for the “networking experience” that is the annual meeting of the American Political Science Association.  Of course, the main value of networking is establishing relationships.  For example, meeting new people can lead to coauthorships, useful information about grants/jobs/conferences, invitations to give talks, and so forth.

Like it or not, networking is important: to be truly successful in social science (and any academic or creative field), your ideas have to reach and influence others, and the constraints of time and attention lead to a variant on “the squeaky wheel gets the grease” in this, and all, professions.  Networking both exposes others to your ideas and, in the best case, helps you generate (sometimes, but not always, in overt cooperation with others) new ones.

All that said, I wanted to make three quick points about what this aspect of the role of networking implies, from a strategic (but not cynical) standpoint, about how one should network.

1. To the degree that one wants to create a relationship through networking, it is better, ceteris paribus, that the relationship have a longer expected duration.  Nobody washes a rented car (see: Breaking Bad), and in terms of dyadic relationships, the length of the relationship is bounded above by the shorter of the two scholars’, ahem, “time horizons.”

2. To the degree that one wants to generate, produce, and publish influential ideas, it is better, ceteris paribus, to create relationships with those who have stronger incentives (e.g., getting a job, getting tenure, being promoted, etc.) than with those who have lower extrinsic incentives to “get stuff out the door.”

3. To the degree that one wants to avoid conflicts of interest in terms of shirking, credit-claiming, and so forth, it is better (as in the repeated prisoners’ dilemma) that both parties have long time horizons so as to increase the (both intrinsic and extrinsic) salience of potential future punishment/comeuppance for transgressions.

All three of these factors suggest that, if you’re a young scholar considering who to spend time with in Chicago in two weeks, don’t forget to meet other young scholars.  Share your ideas, buy a round of smelt, and remember why you’re doing this.  Similarly, it is also important to remember the famous line from Seinfeld:

When you’re in your thirties it’s very hard to make a new friend. Whatever the 
group is that you’ve got now that’s who you’re going with. You’re not 
interviewing, you’re not looking at any new people, you’re not interested in 
seeing any applications. They don’t know the places. They don’t know the food. 
They don’t know the activities. If I meet a guy in a club, in the gym or 
someplace I’m sure you’re a very nice person you seem to have a lot of 
potential, but we’re just not hiring right now.

With that, I leave you with this.

DON’T PANIC. Theory and Empirics Are Both Alive & Well…at least in political science.

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Paul Krugman recently wrote a post about how/why formal theory has fallen behind empirical work in prestige/prominence in economics.  I agree with Krugman that the decline (if one thinks it has occurred) is not due to behavioral social science (Kahneman & Tversky’s voluminous body of work being the most notable of this field).  Krugman argues that this can’t be because people had long known that the axioms of decision-making that undergird much of formal theory in the social sciences:

“…anyone sensible had long known that the axioms of rational choice didn’t hold in the real world, and those who didn’t care weren’t going to be persuaded by one man’s work.”

Well, I agree with this statement (for example, Adam Smith was famously well-aware of this (see The Theory of Moral Sentiments).  But I disagree that this is why behavioral economics did not “cause” the decline of theory.  Mostly, this is because behavioral economics (and behavioral economists) have been looking for a theory to unify their disparate findings.  For example, Kahneman & Tversky are arguably most famous for prospect theory. That is, Kahneman & Tversky were not merely throwing hand grenades—they were at least partially occupied with the classical task of inductive theorizing.

I don’t have any dog in the fight about the relative position of theory and empirics in economics.  And by that, I mean, I am not even sure that dogs are involved in the skirmish or even if there is skirmish worth keeping tabs on.  And, in many ways, I’m an economist.  Well, I am an economist to those who distrust economists and “just maybe an economist” to economists.  (See what I did there?)

In political science, which I proudly call my home, theory is definitely not “dead” (Krugman’s title is “What Killed Theory?”).  Rather, I like to think that, most days of the week, theory and empirics reside quite amicably side-by-side in our big tent of a discipline.  Sure, theorists make jokes about empiricists and empiricists make (typically funnier) jokes about theorists, but this is simply incentive compatibility: every empiricist chose not to be a theorist, and every theorist chose not to be an empiricist.  (Of course, many political scientists are a little bit of both, but rarely at the same time, if only because the jokes become oh so much more poignant.)  As a theorist, I (honestly) love empirical work—particularly descriptive and qualitative work that gives me fodder for new models, but also “causal” findings and quantitative conclusions that I can “get all contrarian on.”[1]

What has happened in political science during the last 20 years is a decline (in terms of number of articles published) of what one might call “pure,” or “technical,” theory.  In a nutshell, I—and others—think of social science theory as being usefully broken into two categories: pure and applied.  Pure theory (tends to) focus on the technical aspects of the model and accordingly ask more “general” questions.  The “purest” theory is inherently “untestable” outside of the theory itself: Arrow’s theorem, the Gibbard-Satterthwaite theorem, Nash’s theorem, May’s theorem, etc. all reach very general conclusions about a theoretical construct (Arrow’s theorem describes all aggregation rules (for 3 or more alternatives), Gibbard-Satterthwaite describes all choice functions (for 3 or more alternatives), Nash’s theorem describes all finite games, and May’s theorem describes all social choice functions between two alternatives, etc.).  This type of theory is hard in a specific sense: useful/explicable results are notoriously hard to obtain.  A fundamental reality of theorizing is that the expected number of results one can obtain from a model is proportional to the number of assumptions one makes.  Without belaboring the point, this difficulty is part of the reason such theory has become less prevalent in political science.  (However, as a “shameless” plug, I will note that Elizabeth Maggie Penn, Sean Gailmard, and I recently published just such a theory, entitled “Manipulation and Single-Peakedness: A General Result,” in the American Journal of Political Science (ungated version here).)

Applied theory, on the other hand, involves making more assumptions and, as a price, exerting the effort to motivate the model as descriptive or illustrative of something that either does or “could” happen.  I’ve talked about my view of the proper role of theory before.  I’ll keep it brief here and say that this type of theorizing is very much alive in political science.  Because “applied” sounds pejorative, I like to refer to this practice as “modeling,” which sounds sexier (and the Brits spell it “modelling,” possibly because their models tend to involve “maths” rather than “math”).

Relevant to Krugman’s point at least as it might be extended to political science, modern political models include some that are “behavioral” in spirit (bounded rationality, etc.) and some are more classical (common knowledge of the game, rationality, etc.) To me at least, that ‘s a distinction without a difference: the quality of a theory/model is per se independent of its assumptions.  Rather, the quality is based on what it teaches me or makes me see in new ways.  This is why “rational actor” models are useful: for example, some rational actor models can explain apparently irrational behavior.  This is important for those who see the “irrational” behavior in question and start to make conclusions about policy and institutions based on their potentially flawed inference that people are irrational per se.  Similarly, behavioral models can generate predictions and possibility results that outperform (and/or are more easily understood than) rational actor models of the same phenomenon.  I like to think of rational actor models as being like the Cantor Set (or perhaps the Banach-Tarski paradox) and behavioral models as being like Taylor polynomials.

In other words, and regardless of whether you are comparing behavioral and rational actor models or pure and applied theory, neither is better or worse than the other from an a priori perspective, just like it is nonsense to assert that a hammer is “better” than a screwdriver: it depends on whether you need to smack something or twist it.  (AND WHAT IF YOU NEED TO DO BOTH? A.K.A. “A Theory of Revise & Resubmits.”)

As a final note, it is important to note (as we are seeing in the “big data” revolution—inter alia, here and here) that the process of “…theory with empirics with theory…” is one of complements, not substitutes: the value of new theory/data increases as data/theory gets ahead of it, and conversely, the value of additional data/theories declines as theory/data lag behind.  Krugman sort of tells this story in his post, but at least doesn’t explicitly extend to the conclusion: theory and empirics have tended, and will probably continue, to cycle “in and out of fashion.”  I am fortunate that, at least right now, the big tent of political science includes active work in both areas.

With that, I leave you with this.

_________________________________________

Footnotes.

[1] I used to do empirical work, until a court (of my peers) ordered me, in the interests of both society and data everywhere, to cease and desist.

 

“Strength & Numbers”: Is a Weak Argument Better Than A Strong One?

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Thanks to Kevin Collins, I saw this forthcoming article (described succinctly here) by Omair Akhtar, David Paunesku, and Zakary L. Tormala.  In a nutshell, the article, entitled “The Ironic Effect of Argument Strength on Supportive Advocacy,” reports four studies that suggest “that under some conditions…in particular, presenting weak rather than strong arguments might stimulate greater advocacy and action.”

This caught my attention because I think a lot about information and, in particular lately, “advice” in politics.  One of the central questions (in my mind at least) in political interactions is when communication can be credible/persuasive.  I was additionally attracted, given my contrarian nature, to the article because of statements such as this:

[These findings] suggest, counterintuitively, that it might sometimes behoove advocacy groups to expose their supporters to weak arguments from others—especially if those supporters are initially uncertain about their attitudes or about their ability to make the case for them. (p. 11)

Is this actually counterintuitive? I would argue, unsurprisingly since I’m writing this post, “no.”  Why not?

I have two simple models that indicate two different intuitions for this finding, both in a “collective action” tradition.  In addition to sharing a mathematical instantiation, also common to the motivations behind both of these models is the fact that the article’s findings/results are largely confined to individuals who already supported the position being advocated.  For example, weak “pro-Obama” arguments were more motivating than strong “pro-Obama” arguments among individuals who supported Obama prior to exposure to the arguments. (The effect of argument strength was insignificant and actually in the opposite direction among those who did not support Obama prior to exposure.)

My focus on collective action in this post is justified because the 4 studies reported in the paper each examined advocacy for a collective choice (either an election of a candidate and adoption of a public policy). Thus, in all studies, advocacy can potentially have an instrumental purpose: secure the individual’s desired collective choice.  Accordingly, suppose that an individual i is predisposed to support/vote for President Obama.  To keep it simple, suppose that advocacy is costly—if advocacy is less likely to affect the outcome of the election, then individual i will be less likely to perceive advocacy as being “worth it.”

Collective Action: Complementary Strength and Numbers. The question is how individual i should react to hearing a pro-Obama argument from a “random voter.”  If the argument is weak, should individual i—who, remember, already supports Obama—view advocacy as more or less likely to affect the outcome?

Well, suppose for simplicity that the election outcome is perceived to be a function like this:

f(q,n) \equiv \Pr[\rm{Obama\; Wins}] = \frac{ q * n }{1+ q * n},

where q>0 is the quality of the best argument that can be made for Obama (a content-based persuasive effect), and n>0 is the number of advocates for Obama (a “sample size”-based persuasive effect).  Then, being a bit sloppy and using derivatives (approximating n being large), the marginal value of advocacy is

\frac{ q }{1+ q * n} (1-f(q,n))

and, more importantly, the marginal effect of quality on the marginal value of advocacy (the “cross-partial”) is

\frac{2 n^2 q^2}{(n q+1)^3}-\frac{3 n q}{(n q+1)^2}+\frac{1}{n q+1}

The key point is that, for reasonable range of parameters (specifically in this case, if n and q are both larger than 1), increasing the perceived quality of the best argument that can be made for Obama reduces that the marginal instrumental value of advocacy for an Obama supporter.  Note that the perceived quality of the best argument that can be made for Obama is a (weakly) increasing function of the observed quality of any pro-Obama that one is presented with.  In other words, observing a higher quality pro-Obama argument should lower an Obama support’s motivation to engage in advocacy.

Collective Action: Increasing Persuasive Strength. For the second model, let’s pull “numbers of advocates” out and, instead, let’s modify the election outcome model as follows:

f(q) \equiv \Pr[\rm{Obama\; Wins}] = \frac{ q}{1+ q},

where q>0 is the quality of the best argument that is made for Obama.  Now, add a little bit of heterogeneity.  Suppose that a(i) is the quality of the best argument that individual i “has” in favor of Obama.  This, at least initially, is private information to individual i, and suppose it is distributed according to a cumulative distribution function G.  Suppose for simplicity that the argument to which individual i is exposed is the best he or she has yet seen (this isn’t necessary, but allows us to get to the point faster), and denote this by Q.  Furthermore, suppose that individual i will find it worthwhile to advocate (i.e., spread/share his or her own pro-Obama arguments) if a(i)>Q. (This is similar to assuming that advocacy is costless, but this is not important for the conclusion.) Then what is the probability that individual i will find it strictly worthwhile to advocate after observing an argument of quality Q?  Well, it is simply

1-G(Q)

Since G is a  cumulative distribution function, it is a (weakly) increasing function of Q.  Thus, 1-G(Q) is a (weakly) decreasing function of Q.  Again, observing a higher quality pro-Obama argument should lower an Obama support’s motivation to engage in advocacy.

What’s the point?  Well, first, I think that information is a very interesting and important topic in politics—that’s “why” I wrote this. But, more specifically, it is ambiguous how to interpret the subsequent lobbying/advocacy behaviors of individuals with respect to varying qualities of information/arguments offered by others when individuals expect that the efficacy of their lobbying/advocacy efforts is itself a function of the quality of the argument.  In these examples, in other words, individuals might not be learning just about (say) Obama, but also about how effective their own advocacy efforts will be.  If this is the case, I humbly submit that the findings are not at all counterintuitive.

With that, I leave you with this.

Remuneration Of The Nerds, Or “Putting the $$ in LaTeX”

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I’ve been thinking a lot about signaling lately. The central idea of signaling is hidden (or asymmetric) information. A classic example of signaling is provided by education, or more specifically, “the degree.”

Suppose for the sake of argument that a degree is valuable in some intrinsic way: a college degree is arguably worth $1.3 million in additional lifetime earnings. (Let’s set aside for the moment the level of tuition, etc., that this estimate (if true) would justify in terms of direct costs of a college degree. I’ll come back to that below.)

Instead, let’s think about the basis of this (“market-based”) value.  A simple economic story is that the education & training acquired through obtaining the degree increase the marginal productivity of the individual by (say) $1.3M.  Well, I don’t even REMEMBER much of college (and probably thankfully…AMIRITE?), so this seems unlikely.

Another, more interesting (to me at least), explanation is that the value of the degree is through its signaling value.  There are a number of explanations consistent with this vague description, including

  1. College admissions officers are good (in admissions and the act of “allowing to graduate”) at selecting the “productive” from the “unproductive” future workers.  Maybe.  College admissions is hard, and I respect those who carry the load in this important endeavor.  But…
  2. Finishing college shows “stick-to-it-iveness” and thus filters the “hard workers” from the “lazy workers.”  Again, this is undoubtedly a little true.  But there are other ways to “work hard.”  So, finally…
  3. College does 1 & 2 and, to boot, adds a “selection cherry” on top.  In particular, the idea of the college major allows individuals to somewhat credibly demonstrate the type of work they find most appealing (controlling for market valuation, to which I return below).

Explanation 3, as you might expect, is the most interesting to me.  What am I thinking?  Well, back when I was a kid, going to law school was considered a hard, but not ULTIMATELY HARD way to score some serious dough in one’s first job.  Sure, it took some money, and some serious studying, but—HAVE YOU SEEN THOSE STARTING SALARIES?  HAVE YOU SEEN “THE FIRM”?  Oh, wait.  Wait…no, seriously…YOU CAN BE TOM CRUISE AND WIN IT ALL.

On the other hand, math (pure or applied) was considered a “very good, but…come on” kind of major.  In particular, a perception (not completely inaccurate) was that math was hard, but didn’t really “train/certify” you for any job other than, perhaps, being a math teacher.  But, this argument falls on its face after a bit of thought: you can be a math teacher without being a math major.  (I’m proof of this general concept, I am a “political science teacher” and was a math/econ double major.)  So, what gives?  Why would you be a math major?

Because you are intrinsically motivated (i.e., you “like math problems”).  In other words, you are signaling a true interest precisely because there are other, arguably easier, ways to get to the same moolah.  Which means that you’ve sent a (potentially costly) signal to potential employers that this is “what makes you tick.”  This is the information that your degree provides: you have shown them costly signals of what you actually like to “stay late” and work on.

The same argument goes for majors that are both demanding and relatively specialized, (e.g., petroleum engineering, actuarial sciences): employers can be more certain upon seeing such a degree that you really want a career in this—you like it (where “it” is the substance/drudgery of what the job entails).

In other words, to the degree (pun intended) that the value of college is just about selection (explanation 1), then admission to the “marginal school” (i.e., any school that admits every applicant) should be valueless (which I don’t think it is).  If the value of college were just about “showing you can finish something” (explanation 2), then the value of college would be no different/less than completing four years of (say) military or missionary service.  (And, maybe it is no different, but many people follow such admirable service by pursuing a college degree.)

Accordingly, the fundamental signaling value of a college degree is arguably not in its possession, but in the information contained about how it was obtained.  In other words, “the major.”  Of course, there are other, but in my mind ancillary, determinants of the value of a college degree.  As my Dad told me when I was growing up (which is kind of meta),

It isn’t all about the destination—half the fun is in “getting there.”

If that wasn’t true in terms of how one’s actions are interpreted, then one’s actions are even more easily interpretable.  Stew on that for a second.

Finally, in terms of the “math of politics” of this reasoning, note that costly signals are everywhere, and they are important far beyond college: legislative committee assignments, the development of reputations by “policy entrepreneurs” (I’m looking at you, Ron Paul, Ted Kennedy, & John McCain), the development of expertise/autonomy in bureaucracies/central banks, the emergence of “neutral independence” in judiciaries, and the credibility of “dying on the hill for a cause” necessary for policy bargaining by “fringe” political groups (see: Green Party, Pro-Choice/Life groups, PETA, Tea Party, Muslim Brotherhood, ACLU).  There are many, many applications of the notion that value is assigned by selectors (voters, employers, the unmarried) in signals that more precisely reveal hidden information about the tastes/predilections/goals of those vying for selection into potentially long-term, repeated relationships.

With that, I leave you with this.

Inside Baseball: Weather you like it or not, models are useful.

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As a theorist, I write models.  (There is a distinction between “types” of theorists in political science.  It is casually and superficially descriptive: all theorists write models, just in different languages.)

One of the biggest complaints I hear—from both (some) fellow theorists and (at least self-described) “non-theorists”—is the following equivalent complaint in different terms:

  1. Theorists: …but, is your model robust to the following [insert foil here]
  2. “Non-theorists”:  …but, your model doesn’t explain [insert phenomenon here]

It is an important point—perhaps the most (or, only) important point—of this post that these are the same objection. I have been busy for the past month or so, and in the interest of getting those phone lines lit up, I thought I would opine briefly on what a social science model “should” do.  Of course, your mileage may vary, and widely.  This is simply one person’s take on an ages-old but, to me at least, underappreciated problem.

Models necessarily establish existence results. That is, a model tells you why something might happen.  It does not even purport to tell you why something did, or will, or did not, or will not, happen.  (Though I have a different take on a related but distinct question about why equilibrium multiplicity does not doom the predictive power of game theory.)

Put it another way: a model is a (hopefully) transparent, complete (i.e., “rigorous”) story or narrative offering one—most definitively not necessarily exclusive—explanation for one or more phenomena.  I regularly (co-)write models of politics (recent examples include this piece on cabinets and other things, this piece on the design of hierarchical organizations, this piece on electoral campaigns, and this forthcoming book on legitimate political decision-making).  All of them are “simply” arguments.  None of them are dispositive.  The truth is, reality is complicated.

Politics is a lot like meteorology.  We all know and enjoy, repeatedly, jokes along the lines of “hell, if I could get a job where you only need to be right 25% of the time….,” but the joke makes a point about models in general.  Asking any model of politics to predict even half of the cases that come to you after reading the model is like asking the meteorologist to, say, correctly and exactly predict the high and low temperature every day at your house.  No model does that.  Furthermore, it is arguable that no model should be expected to, perhaps, but that’s a different question.  More importantly, no model is designed to do this…because it defeats the point of models.

Running with this, consider for a moment that a lot more is spent on meteorological models than political, social and economic ones (e.g., the National Weather Service budget is just shy of $1 billion and that of the Social and Economic Sciences at the NSF is approximately 10% of that). Models are best when they are clear and reliable.  Sometimes, reliability means—very ironically—“incomplete in most instances.”  Consider a very reliable “business model”:

“Buy low, sell high.”

This model, setting aside some signaling, tax, and other ancillary motivations (which I return to below), IS UNDOUBTEDLY THE BEST MODEL OF HOW TO GET RICH. 

However, it is incomplete.  WHAT IS LOW? And you can’t answer, “anything less than `high,'” because that merely pushes the question back to WHAT IS HIGH?

Of course, some people will rightly say that this indeterminacy is what separates theory from praxis.  The fact is, even the best good models don’t necessarily give you “the answer.”  Rather, they give you an answer.  One can reasonably argue, of course that a model is “better” the more often its basic insights apply.  But that is a different matter.

Returning to the “buy low, sell high” model, consider the following quick “thought experiment.”  Suppose that Tony Soprano approaches you and says, “please buy my 100 shares in pets.com for $10,000.”  Should you?  According to the model, the answer is clearly no: shares in pets.com are worth nothing—and never will be worth anything—on the “open market.”

But, running with this, Tony has approached you for “a favor.”  Let’s not be obtuse: he bailed you out of that, ahem, “incident” in Atlantic City back in ’09, and you actually have two choices now: pay $10,000 for worthless shares in pets.com or have both of your kneecaps broken. (Protip: buy the shares.)

The right choice, given my judicious/cherry-picking framing, is to buy shares high and “sell them low.”  Well, this proves the model wrong, right?  No.

It simply change the definition of “value when sold.”  It reveals the incompleteness of the theory/model.

This is basically my point: no model is truly “robust,” even to imaginable variations and, conversely, it is certainly the case that smart people like you can come up with examples that at least seem to suggest that the model doesn’t describe the world.

It’s kind of an analogy to a foundation of empirics and statistics: central tendency.  Models should indicate an interesting part of a phenomena of interest.  In this sense, a good model is an existence proof, sort of like the Cantor Set: it demonstrates that things can happen, not necessarily that they do.  The fact that those things don’t always happen doesn’t really say much about the model, just like you read/watch the weather every day even while making those jokes about the meteorologist.

And with that seeming non sequitur, I push forward and leave you with this.

Inside Baseball: The Off-The-Path Less Traveled

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[This is an installment in my irregular series of articles on the minutiae of what I do, “Inside Baseball.”]

Lately I have been working on a couple of models with various signaling aspects.  It has led me to think a lot more about both “testing models” and common knowledge of beliefs.  Specifically, a central question in game theoretic models is: “what should one player believe when he or she sees another player do something unexpected?” (“Something unexpected,” here, means “something that I originally believed that the other player would never do.”)

This is a well-known issue in game theory, referred to as “off-the-equilibrium-path beliefs,” or more simply as “off-the-path beliefs.” A practical example from academia is “Professor X never writes nice letters of recommendation.  But candidate/applicant Y got a really nice letter from Professor X.”

A lot of people, in my experience, infer that candidate/applicant Y is probably REALLY good. But, from a (Bayesian) game theory perspective, this otherwise sensible inference is not necessarily warranted:

\Pr[\text{ Y is Good }| \text{ Good Prof. X Letter }] = \frac{\Pr[ \text{ Y is Good \& Good Letter Prof. X Letter }]}{\Pr[ \text{ Good Prof. X Letter }]}

By supposition, Prof. X never writes good letters, so

\Pr[ \text{ Good Prof. X Letter }]=0 .

Houston, we have a problem.

From this perspective, there are two questions that have been nagging me.

  1. How do we test models that depend on this aspect of strategic interaction?
  2. Should we require that everybody have shared beliefs in such situations?

The first question is the focus of this post. (I might return to the second question in a future post, and note that both questions are related to a point I discussed earlier in this “column.”)  Note that this question is very important for social science. For example, the general idea of a principal (legislators, voters, police, auditors) monitoring one or more agents (bureaucrats, politicians, bystanders, corporate boards) generally depends on off-the-path beliefs. Without specifying such beliefs for the principal—and the agents’ beliefs about these beliefs—it is impossible to dictate/predict/prescribe what agents should do. (There are several dimensions here, but I want to try and stay focused.)

Think about it this way: an agent assigning zero-probability to an action in these situations, if the action is interesting in the sense of being potentially valuable for the agent if the principal’s beliefs after taking the action were of a certain form, is based on the agent’s beliefs about the principal’s beliefs about the agent in a situation that the principal believes will never happen. Note that this is doubly interesting because, without any ambiguity, the principal’s beliefs and the agent’s beliefs about these beliefs are causal.

Now, I think that any way of “testing” this causal mechanism—the principal’s beliefs about the agent following an action that the principal believes the agent will never take—necessarily calls into question the mechanism itself.  Put another way, the mechanism is epistemological in nature, and thus the principal’s beliefs in (say) an experimental setting where the agent’s action could be induced by the experimenter somehow should necessarily incorporate the (true) possibility that the experimenter (randomly) induced/forced the agent to take the action.

So what?  Well, two questions immediately emerge: how should the principal (in the lab) treat the “deviation” by the agent?  That’s for another post someday, perhaps.  The second question is whether the agent knows that the principal knows that the agent might be induced/forced to take the action. If so, then game theory predicts that the experimental protocol can actually induce the agent to take the action in a “second-order” sense.

Why is this? Well, consider a game in which one player, A, is asked to either keep a cookie or give the cookie to a second player, B. Following this choice, B then decides whether to reward A with a lollipop or throw the lollipop in the trash (B can not eat the lollipop).  Suppose also for simplicity that everybody likes lollipops better than cookies and everybody likes cookies better than nothing, but A might be one of two types: the type who likes cookies a little bit, but likes lollipops a lot more (t=Sharer), and the type who likes cookies just a little bit less than lollipops (t=Greedy).  Also for simplicity, suppose that each type is equally likely:

\Pr[t=\text{Sharer}]=\Pr[t=\text{Greedy}]=1/2.

Then, suppose that B likes to give lollipops to sharing types (t=Sharer) and is indifferent about giving lollipops to greedy types (t=Greedy).

From B’s perspective, the optimal equilibrium in this “pure” game involves

  1. Player B’s beliefs and strategy:
      1. B believing that player A is Greedy if A does not share, and throwing the lollipop away (at no subjective loss to A), and
      2. B believing that A is equally likely to be a Sharer or Greedy if A does share, and giving A the lollipop (because this results in a net expected gain for B).
  2. A’s strategy:
      1. Regardless of type, A gives B the cookie, because this (and only this) gets A the lollipop, which is better than the cookie (given B’s strategy, there is no way for A to get both the cookie and lollipop).

Now, suppose that the experimenter involuntarily and randomly (independently of A’s type) forces A to keep the cookie (say) 5% of the time.  At first blush, this seems (to me at least) a reasonable way to “test” this model.  But, if the experimental treatment is known to B and A knows that B knows this, and so forth, then the above strategy-belief profile is no longer an equilibrium of the new game (even when altered to allow for the 5% involuntary deviations). In particular, if the players were playing the above profile, then B should believe that any deviation is equally likely to have been forced upon a Sharer as a Greedy player A.  Thus, B will receive a positive expected payoff from giving the lollipop to any deviator.  Following this logic just about two more steps, all perfect Bayesian equilibria of this “experimentally-induced” game is

  1. Player B’s beliefs and strategy:
    1. B believes that player A is equally likely to be a Sharer or Greedy if A does not share, and thus giving A the lollipop
    2. It doesn’t matter what B’s beliefs are, or what B does if A does share. (Thus, there is technically a continuum of equilibria.)
  2. A’s strategy:
    1. Regardless of type, A keeps the cookie, because this gets A both the cookie and lollipop).

By the way, this logic has been used in theoretical models for quite some time (dating back at least to 1982).  So, anyway, maybe I’m missing something, but I am starting to wonder if there is an impossibility theorem in here.

Inside Baseball: Uncommon Knowledge

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Note: This is the first of what might be an irregular “column” of sorts, “Inside Baseball,” focusing on the minutiae of my research, as opposed to current events. 

 

The heart of game theory is “what would everyone else think if I do what I am about to do differently?”

This is slightly different than the standard “introduction to game theory” approach, where the focus is often on the related question, “what would everyone else do if I do what I am about to do differently?”  But while the difference is slight, it is fundamental.  Game theory is about beliefs, or more appropriately, about consistency of beliefs.

This point bedevils empirical applications (or, more crudely, “tests”) of game theory for at least two reasons.  First, we rarely, if ever, can measure beliefs in anything approximating a direct fashion.  There is a core concept in game theory that is amenable to this test, known as rationalizability, and—unsurprisingly to me as a game theorist—people frequently refute the claim that all actions are rationalizable.  But let’s leave that point to the side.

The second point is more important, to me at least.  At the heart of game theory is the idea that not only are beliefs consistent with one’s own actions (that’s rationalizability, in a nutshell) and consistent with others’ actions (that’s Nash equilibrium, very loosely), they are are consistent with each other.  That is, in any reasonable game theoretic notion of equilibrium, every person not only acts in accordance with his beliefs about what others will do, he or she also understands (“believes”) correctly what everyone else in the game believes, understands that the other players believe correctly about what the player in question believes, including that the player believes correctly about what the other players’ believe about what the player in question believes about their beliefs, and so forth….

This uncommon notion is an instance of what is referred to as common knowledge in game theory.

Well, this uncommon notion is simultaneously elegant and unambiguously empirically false.  For example, it flies in the face of the reality that Florida Gulf Coast University made it to the Sweet 16.

But more seriously, this point is exactly the point of game theory. Game theory is a theoretical enterprise and accordingly requires a priori constraints for the purpose of being meaningful.  And, since this constraint is theoretically elegant and epistemologically appealing, one must always keep in mind that game theory is an inherently philosophical endeavor.  While one can (and should) certainly employ the trappings of game theory for empirically-minded endeavors, the goal of equilibrium analysis is inherently normative or prescriptive.  In other words, game theory models ask “what can (in theory) be achieved in a world in which individuals are intimately involved with the interaction at hand?”

A key (and illuminating) point in this regard is the beginning point of this post: what can happen in equilibrium is, in most interesting settings (i.e., “games”), dependent on what each individual believes about what will happen—or, more fundamentally, what other involved individuals will believe—if he or she acts differently.

When you take this point seriously, you must realize that “testing” game theory models is an inherently ambiguous enterprise.  Suppose the model “works.”  Did it work for the “game theoretically correct” reasons?  Suppose the model doesn’t work.  Why did it fail?

These are important questions, and any answer to either one has no bearing on the “validity” of game theory. Rather, the fact that one could ask either of these questions, the context within which these questions is accordingly posed, is to the credit of game theory.  In a nutshell, every time equilibrium predictions fail, an empirical angel gets his or her wings thanks to game theoretic reasoning.

With that, I leave you with this.