Thursday, October 16, 2014

Inspiring Words

Leadership is, to a great extent, the gentle art of persuasion. Leaders inspire others to follow them, to work for them, sometimes even to give up their own lives for them. How do they do it? Partially by example to be sure, but even here persuasion has a role to play. When we say that Jeff Bezos lives the leadership principles articulated and promulgated at Amazon, it makes the valid point that individuals credit others for how they behave, but conveniently ignores the fact that it was Bezos who articulated and promulgated the principles in the first place.

One of the most striking examples of leadership purely by the powers of persuasion was the rise of Barack Obama. Obama, for all his subsequent faults, was matchless in using words to inspire many thousands of young people who had never even voted previously to give him money, work for his organization, and persuade others to vote for him. Even more remarkably, he duplicated the feat again four years later, by most accounts, after spending much of that period by not leading by example. This no doubt overstates the power of his oratory for he had a remarkably savvy organization helping him to vacuum up all that money and effort, but others less gifted have had equally efficient teams, yet achieved nothing like Obama's success.

What can game theory tell us about the power of leaders to persuade? The answer, if we are to be entirely honest, is surprisingly little. A large part of the problem is that communication in the world of game theory is almost entirely informational, but persuasion, while it will certainly draw upon and convey some information, taps into something much deeper and less purely transactional than what one might learn from hearing the local weather forecast. This is not to say that information-centric communication, or persuasion, is uninteresting, rather that it somewhat misses the boat if we truly wish to understand why some individuals are hailed as visionaries while others, offering the same facts and conclusions, are not.

To get the flavor for the bloodless world of communications viewed through the lens of game theory, consider the following problem. A political leader wants to convince a supporter/follower to perform a certain action. The right action depends on something called a state variable, which you might think of as a shorthand description for a set of factors, political, economic, cultural, etc., that influence what a reasonable person would conclude is the correct action. To keep things simple, suppose that one state, which we will call low, represents a low political threat environment. Some action is needed to secure victory, but not too much. The other state, which we will call high threat, requires frenzied activity such as massive calling campaigns to get out the vote, and so on.

The follower wants to do the "right thing" for the leader, but knows little about political threats, and so on.
Knowing nothing about the state, our follower will elect some intermediate range of activity, imperfect for either state but somewhat helpful in both.

Now for the rub or, as we in the profession write, the "central tension of the model." The leader too wants the follower to do the right thing, but prefers that she do more political activity in either state. The degree of difference in views about how much activity to perform in each state represents the conflict between the two. Our leader's job, then, is to inspire his followers to do more than they otherwise would, but this will prove difficult since, in game theory land, the only trump card the leader holds is his knowledge of the state.

So, to inspire his supporters, our leader comes to town and makes a speech attempting to rally them to, in the leader's eyes, the right amount of activity. How does this speech go? What should our leader say? The answer, it turns out, depends on several factors, none of which feel (to me at least) very much like leadership.

Scenario #1: Free Speech
Suppose that our leader is free to say whatever he likes. He can lie about the state, exaggerating the political threat when it is, in fact, low or do the reverse, reassuring followers that there is little to worry about. Or something in between, saying that he's not sure. Or our leader can stonewall, give his standard stump speech, shake hands and kiss babies, Purell his hands and lips afterward, and go home.

So what does he do? To answer this question, we need to make certain assumptions about what, exactly, the followers know. Suppose they know that the leader indeed knows the state and, importantly, they also know that the leader wants them to do more of the activity in each state than they themselves prefer. In the happy scenario, the leader only wants the followers to do a little more in each state, so he informs them about the state truthfully and then harangues them "exceed themselves" or to "go beyond" or something like that. He gets his applause and leaves, satisfied at a good night's work.

Game theory, however, offers the exceptionally dreary conclusion that, no matter how powerful the words of inspiration, no matter that our leader is a Shakespeare or a Churchill, the followers do precisely what they had initially planned to do in each state. They are grateful for the information, but they can hardly be said to be inspired. Ironically, this situation is, in fact, the best our leader can hope for.

Let's rerun the speech but now imagine that the leader's vaunting ambitions create a vast gulf between his preferred activity level in each state and their own. So our leader steps up to the microphone to the hushed crowd and proceeds to speak of crisis--the threat level is high, the stakes are huge, and it's all up to you, the supporters to make the difference. This address, Shakespearean in its majestic, soaring phrases, send chills down the spines of the audience. The crowd roars. They will do it. They will rise to the challenge. They will be the difference-makers. No activity is too much. Our leader, drenched in sweat from the effort, steps down from the lectern and is congratulated for his remarkably moving address. The lights in the auditorium go down, and everyone goes home.

When his supporters get up the next morning, they do...exactly what they would have done if the leader had never shown up in the first place. In game theory land, people are cynics. While the audience may have been moved in the moment, on reflection they realize that the leader makes this same speech everywhere, to all his followers, whether the state is high or low. The talk, for all its pageantry, rings hollow--full of sound and fury, but signifying nothing. Why such an uncharitable view of the leader? The answer is that his own aspirations get in the way. Since he wants a high level of action regardless of the state, the speech lacks all credibility and, since those living in game theory land are not simpletons nor dupes, it is roundly and universally disbelieved.

As a logical analysis, the above is impeccable. As a description of leadership and persuasion, it seems to mis the boat completely. But, sadly, this analysis, or something similar, quite genuinely represents the state of the art, the research frontier, if you will. Is it fixable? Yes, in a way. We can add fools who believe everything the leader says into the mix. We can add some sort of inspiration variable that magically changes tastes so that followers work harder. But none of it really gets to the heart of what makes some leaders persuasive and others not. Indeed, we learn nothing if we simply assume that leader A can change minds and leader B cannot. The whole point of using our tools is to get at the deeper, and ultimately more interesting and important question as to why some leaders are persuasive.

Scenario #2: Factual Speech
Perhaps we've accorded too much freedom to our leader. After all, exagerrations, dissembling, misrepresenting, or any of the myriad of polite words we have for lying can get a politician into terrible trouble. Claiming that the world is hanging by a thread when, in fact, every poll shows that you're 20 points ahead, catches up to most leader's eventually. So let's return to our setting, precisely as before, but with the added restriction that our leader cannot simply make up things that are not true. In academic terms, this moves us out of the world of "cheap talk" and into the world of "persuasion" proper. This nomenclature, by the way, has a lot of problems. First, talk is no less cheap in the sense of being costless to the leader when we add the no lying restriction. Second, why the heck is it "persuasion" when we restrict someone from lying outright. Lies can be an important tool in the arsenal of a persuasive individual. Indeed, criminals engaging in confidence schemes are the ultimate persuaders, but would be entirely crippled were they bound by the no lying restriction. But I digress.

So let's rewind once again and send our leader back to the lectern, but with the following restriction--the heart of his speech can be either the truth or a stonewall, where he says nothing whatever about the state. One might imagine that this changes little. After all, when conflict was low, our leader did not wish to lie even when he could, so the restriction matters not a whit. When conflict was high, our leader wanted to lie about the state, but no one believed him anyway, so the effect is identical to stonewalling. Indeed, our leader in scenario #1 would have been quite happy to make the stonewalling speech instead of what I laid out.

In the case where conflict is low, the above supposition is exactly correct. Our leader steps to the lectern and offers a fact-laden speech truthfully revealing the state. But in the second case, this is wrong. Indeed, remarkably and perhaps absurdly, game theory offers the startling prediction that, no matter how bad the conflict between leader and follower, the leader always makes the truthful speech!

Why in blazes would our leader do that? Let's start with the situation where the threat is high. Here, the leader can do no better than to report the truth. He'd like more effort from his followers to be sure, but there is simply no way to motivate them to work any harder than by revealing the high state. What about the low state? Surely our leader will stonewall here? He might, but it will do no good since, knowing that the leader would have announced high were the state indeed high, our followers treat the stonewall speech as, in effect, a report that the state is low. And they act accordingly. That being the case, the leader might as well report honestly and at least gain the credit, however small, for being straight with followers.

Now, one may suspect that this logic takes too much advantage of the fact that there are exactly two states. What if there were three, or twenty, or a thousand. It turns out that none of it matters because of something called unravelling. Here's the argument: Suppose that there are twenty states in which the leader stonewalls while revealing in the rest. Then, in the highest of these 20 states, he'd be better off revealing than stonewalling since, by stonewalling, followers assume that the average state is lower than the highest state. Repeat this argument ad nauseum to obtain the truth-telling result. In my own work on the topic, I showed how this argument could be extended to virtually any configuration of preferences between leader and follower.

The problem is that the conclusion seems completely absurd. Irrespective of the conflict between leader and follower, the leader will always tell the truth sounds very much unlike the world in which I live. Again, this problem is fixable, but the main fix is even more bizarre than the result. It turns out that the key to credible stonewalling is...drumroll please...stupidity!! Or, more precisely the possibility of stupidity. The idea here is that, if the leader might possibly not know the state then stonewalling becomes believable. But this hardly seems like a satisfying resolution.

So Where Does This Leave Us?
This post, I'm afraid, is a downer. Game theory does lots of things well, but leadership, sadly, is not one of them. This has not stopped game theorists from trying, and perhaps making some headway. There is a clever paper by Dewan and Myatt looking at leadership through communications. In their model, one of the tradeoffs is between stupidity and incomprehensibility. They ask the following question (that only a game theorist would ask) about leaders: Is it better to be smart but incomprehensible or stupid but clear? The answer seems to be that it depends on the importance of doing the right thing versus doing the same thing. But, like all work in the field, the idea that leaders, with their words, could spark passion and devotion, is entirely missing.

Sometimes I despair about my love for game theory in a place devoted to, somehow, creating innovative leaders. I can, however, take some solace that we are no better at articulating how, exactly, that transformation takes place than we are in understanding leadership through game theory.

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