Politicians and quantum "flip-flops"

One update (below)

As the campaign for the U.S. Presidential election gains momentum, we're once again subjected to the irritating spectacle of candidates responding to simple questions with paragraphs of vacuous waffle, and mouthing totally contradictory opinions to different groups. It's tempting, and maybe partially correct, to suspect they're all just slippery and mealy-mouthed weasels. But here's another idea: maybe the way they act has its origins in a deeper problem inherent in the mathematics of democracy and public opinion. There's good reason to believe that a candidate can appeal to more people by holding several contradictory views all at once.

The French philosopher, the Marquis de Condorcet, once proved a truly surprising theorem about public opinion. As individuals, people tend to be logically consistent in their opinions or preferences. If I prefer Obama over Clinton, and Clinton over Romney, then I'll also prefer Obama over Romney. If A outranks B, and B outranks C, then A should outrank C. Most of our thinking conforms to this basic rule of logic, at least most of the time.

But just because individual preferences follow such logic, this doesn't imply that groups do as well. Within a population of people, Condorcet proved, it is entirely possible for a majority to prefer A over B, a majority to prefer B over C, and a majority also to prefer C over A - making a cycle of collective preference, so that's its impossible to say which of A, B or C the people really prefer. (For example, take three voters who, respectively, rank three policy alternatives in the following orders: A > B > C, C > A > B, and B > C > A. It is easy to see that two out of three will prefer A over B, B over C, and yet also C over A.)

Nearly a decade ago, physicist David Meyer of the University of California at San Diego, and political scientist Thad Brown of the University of Missouri, suggested that this peculiar logic of popular opinion might well have something to do with the slippery views of politicians. Think of a candidate who just tries to mouth opinions that match up as closely as possible with the majority view. Quite possibly those opinions will necessarily involve some contradictions and apparently irrational cycles of preference. If so, then candidates and their advisors face a real choice between a strategy that respects ordinary logic, with the candidate promoting the kinds of consistent preferences than an individual might hold, and another in which the candidate abandons the need for consistency and uses more flexible and slippery tactics to appeal to as many voters as possible.

I'm guessing that almost all candidates follow the latter strategy, and those who don't tend to fall out of the polls very quickly. I recall being excited some years ago at the early Presidential candidacy of Governor of Arizona Bruce Babbit, who seemed to speak entirely sensibly about the importance of things like education, public health, investment in the nation's infrastructure, etc. He was so sensible and intelligent that his polling number quickly fell into the single digits and he dropped out of the race in about three weeks.

I suspect that experienced politicians may get drawn into adopting strategic contradictions more or less unconsciously, as they study polls and the results of focus groups and try to say things that put them in touch with the voters. "This," as Meyer and Brown put it, "is why it’s so hard for us as voters to discern exactly for what they stand."

The naive view of political strategy might hold that if most peoples' views fall into three sets, A, B, and C, which you might visualize in some "policy space," then the politician does best by "triangulating" -- setting out a position that falls at the center of those views. This way he or she appeals at least a little to everyone. But if cycles exist among the voting public, then a better bet may be to occupy not one point in policy space, but to spread out over a region and, roughly speaking, be as inconsistent as the voters.

Maybe there's a kind of perverse quantum logic to flip-flopping: just as quantum particles don't exist at any one point, but act as quantum waves and spread out through space, politicians defy the logic of individual thinking, and benefit by having fuzzy and ill-defined views.

Update

Just after I posted this, I remembered another interesting point relevant to this problem of Condorcet cycles in public opinion. The importance of the matter depends, of course, on the actual likelihood that public opinion really does show such cycles. Condorcet proved that it can. But in reality, does this happen very often?

Some physicists, Matteo Marsili and Giacomo Rafaelli, looked into this a few years ago. Their idea was to assume that individuals in a big population rank a series of alternatives, A, B, C, ... and so on in a random order. Each person has his or her own ranking, determined at random. Then they asked -- what is the chance, mathematically, that you'll find cycles in the group preferences when these people vote on the various alternatives in pairs? They vote on A versus B, A versus C, B versus C and so on. How likely is it that their voting shows a cycle? Their results showed that as the number of alternatives gets reasonable large, the chance of not having cycles dwindles rapidly to zero.

So if peoples' preferences were random, cycles are almost a guarantee. Of course, preferences aren't random, but treating them as such is at least crude approximation. And it suggests that the trouble presented by cycles, and the waffling strategies they make effective, may indeed be real.

On caveat, however -- Marsili and Rafaelli also showed that the tendency of people to conform with the views of others may play a powerful role in preventing Condorcet cycles and making the public's collective views more "rational" than they would otherwise be.

Coincidences... -- Mark Buchanan

A few years ago, I experienced a very strange coincidence. I emailed a physicist at the University of Chicago (I can't recall who now, maybe Tom Witten) with a couple questions on some of his work. He wrote back with some answers, and then put a P.S. in the email: "Say hello to Haim Diamant."

Now I'd never heard of Haim Diamant, so I wrote back saying, "Thanks for your response, but who is Haim Diamant?"

In a few hours I got another email: "Is it really possible," he wrote, "that there could be two Mark Buchanan's, both physicists and both living in France?"

As it turns out, there were, me, and Mark Buchanan, a physicist who had formerly worked in Chicago (now at the University of Oslo), and who emailed me the following day. It's a very odd experience getting an email from someone with your exact name. Anyway, I've followed Mark's work over the past few years; curiously, we not only share the name but a deep interest in the same kind of physics, the physics of liquids and solids, pattern formation, the spontaneous emergence of collective organization, and so on. Strange.

I mention this because I just had another weird coincidence today, getting an email from one Mark Earls who has written a book quite similar to my The Social Atom. His book is called Herd, and, while I have't read it yet, it looks very interesting. I just visited his blog, and noticed one very interesting comment on a cognitive bias that most of us have...

"we find it really much easier to respond to individual others than to the confusion of the group. It's easier to think of the face in the crowd than the crowd. Now there's a psychology insight that might be useful... "

Indeed, Nicolas Kristof wrote a very powerful essay in the New York Times on just this issue in May. He cited some experiments that show people respond with more generosity to a photo of one starving child, with a face and name, that to a verbal plea for aid for starving millions. A brief excerpt:

"In one experiment, psychologists asked ordinary citizens to contribute $5 to alleviate hunger abroad. In one version, the money would go to a particular girl, Rokia, a 7-year-old in Mali; in another, to 21 million hungry Africans; in a third, to Rokia -- but she was presented as a victim of a larger tapestry of global hunger.

Not surprisingly, people were less likely to give to anonymous millions than to Rokia. But they were also less willing to give in the third scenario, in which Rokia's suffering was presented as part of a broader pattern."

I'm not sure what evolutionary psychologists would say, but it seems reasonable to speculate that we're just not evolved to think properly of hundreds or millions of people. Our ancestors spent their lives overwhelmingly in groups of at most 25 to 30 people, and usually in sub-groups of far fewer, and they evolved to make good decisions in those contexts. Nothing in evolution has prepared us for the massive collectivity we experience today.

Winning by repeating -- Mark Buchanan

I'm going to have some more to say on the issue of the polarization of opinions, which I wrote about a little last week. Cass Sunstein emailed me with some insightful comments I'd like to share, but I first have to read and digest a couple papers he sent me.

Meanwhile, check out some new work that brings out in a disturbing way how the apparent consensus of a group can be strongly influenced by the loudest members. Suppose you go around and talk to the students in some class, listen to their opinions, and then later try to give an impression of the distribution of opinions within the group. Clearly you do better in terms of accuracy if you hear from lots of people, and so sample the group in a reasonably fair way.

But psychologist Kimberlee Weaver of Virginia Tech and colleagues found that real people don't form their views this way. Rather, if we encounter one person, repeatedly, who voices the same opinion many times, we tend to weight that opinion more strongly, even though it is obviously just one person's opinion. They found that if one person voiced an opinion, say, three times, it ended up being counted almost as much as if the opinion were voiced separately by three different people. The reason our minds do this, the researchers suspect, is that "the more often an opinion has been encountered in the past, the more accessible it is in memory and the more familiar it seems when it is encountered again." You can read the full paper here.

The conclusion is worrying: "repetition of the same opinion gives rise to the impression that the opinion is widely shared, even if all the repetitions come from the same single communicator."

This psychological propensity clearly feeds into the problem of "pluralistic ignorance," which I touched on in one of my New York Times essays. Unfortunately, our instincts for assessing what "most people think" can easily be led astray, especially by a powerful (and often less than responsible) media.

Damaging deliberations

Ideas from a meeting on Complex Networks, 2-6 July, Sardinia, Italy

In one of my recent New York Times columns, I explored the worrying polarization evident between the conservative and liberal bloggers in the US. I argued that it might well be the almost mechanical outcome of an amplifying feedback driven by simple psychological factors that influence how people form opinions and attitudes. First, the psychological phenomenon of “cognitive dissonance” tends to make us more comfortable with view that confirm rather than contradict our own. Second, people also have a strong tendency to adopt, even unconsciously, the attitudes of those with whom they interact. So the more conservative or liberal bloggers read the views in their own sphere, the more they're drawn into that sphere, express similar views, and end of living in an intellectual world of views that merely confirm their own.

That was speculation. But there's some exciting recent work that I think supports it -- some from network theorists here in Sardinia who are looking, rather abstractly, at the mathematics of opinion change within groups, and some from lawyers trying to address, in practical terms, how we might heal our polarization with greater deliberation. The lesson, I think, is that we had better be quite careful in what we do, or we could make the matter even worse.

Yesterday, physicist Renaud Lambiotte of the University of Liege in Belgium talked about his recent work (with physicists Marcel Ausloos and Janus Hoylst) in modeling the evolution of opinions. Their modeling suggests that two groups holding opposing views may quickly become reconciled, or remain at odds, and that what happens --and this is the important point -- can be very strongly influenced by the presence or absence of only a few social links between the groups. Here's the basic idea.

They supposed that individuals hold one of two opinions (it's not hard to think of some relevant issue), assigned randomly at the start. People in the model would then change their views, step by step, by a “majority rule” – each person would adopt (in the next time step) the opinion held by a majority of those with whom they were linked in the social network. The interesting thing to explore is how the structure of the network influences what ultimately happens.

Lambiotte and colleagues started by imagining two groups that were isolated from one another, or nearly isolated. Not surprisingly, perhaps, they found that people within each group quickly came to share one opinion. The groups came to a consensus, although the two groups were as likely to agree as disagree with each other. But the researchers then began adding social links between the groups, to see how this might change the outcome.

They found no change, at first, as the two groups continued to form opinions independently. But rather than a gradual increase in the way opinions “leak” from one group to the other as more connections are added, the researchers found a surprise when the number of links between the groups reached a precise threshold. Abruptly, the final opinions of the two groups were now always identical. Even a few extra links between groups were enough to “tip” their final opinions from a state of full polarization to full agreement.

This finding represents the social equivalent (in this simple model) of what physicists call a "phase transition", closely akin to the abrupt transformation of liquid water to ice. The interesting thing is that the change from one outcome to the other isn't gradual, but very rapid, and happens at some critical threshold of links between the groups. Near this boundary, a tiny alteration of the network structure can lead to drastic consequences.

Now this is quite abstract, but it may still be highly relevant to the real world. A number of studies have noted increasing polarization in recent years, not only in the web, but in geographical zones as well, with some parts of the US, for example, becoming more homogeneously conservative or liberal. Legal academics have been concerned with the consequences of this trend for our democratic discourse, and ability to come to collective decisions. What can we do?

Some legal theorists have suggested that one way to counter this trend would be to have special "deliberation days", during which people would come together in "town hall" meetings to discuss key issues. But some experiments carried out by Cass Sunstein and colleagues at the University of Chicago suggest that he outcome of such meetings can be counterproductive.

They had both liberals and conservatives from different cities in Colorado come together to discuss contemporary issues (gay marriage, the Iraq war, and so on) for a day, using surveys to gauge their views both before and after the deliberations. The liberals discussed issues among themselves, in one group, as did the conservatives, in another. What they found is that both groups became more extreme in their views during the discussions, and that the distance between the two groups became larger as a result. The conservatives became more conservative, and the liberals more liberal.

The lesson of these experiments is that those intermediary links between groups are absolutely essential to building overall consensus, and that, in their absence, we should expect an evolution toward greater extremism. But the more encouraging lesson from the network theory of Labiotte and colleagues is that only a few links between such groups can be remarkably successful in breaking down such polarization. Even if the situation seems bleak, and unchangeable, it may take only a few more contacts to seed a tremendous change.

How do extremists prevail?

I once tried to read Salman Rushdie's The Satanic Verses, and frankly, I couldn't do it. It just bored me. So I stopped. But that book, and Rushdie's writing in general, even his mere existence, is anything but boring to lots of people out there who would very much like to slit his throat. Over at The Agonist, Ali Eteraz in an interesting and spirited post offers his view as a Pakastini on the reasons for the seemingly infinite energy available in the Islamic world for hating Rushie, but more importantly, on the origins of this energy and how it is directed by political and religious leaders for their own ends.

Eteraz also notes that the resulting images -- apparently insane multitudes rioting and burning anything they can find -- play into the fearful imaginations of right-wing demoagogues here in the West, who take these images as the depiction of EVERYONE in the Islamic world. The outcome is a grim feedback cycle in which the extremists on one side succeed in stirring up the extremists on the other, with the ordinary folks in the middle dragged alone for the scary ride.

In a recent post I mentioned the classic work of Robert Axelrod on the famous Prisoner's Dilemma, in which he showed how the TIT-FOR-TAT strategy -- I'll be nice to you to begin with, and then mimic your behavior in the future, meeting either cooperation or cheating with same -- can arise naturally as self-interested people (or other kinds of organisms or agents of any kind) come to learn that conflict is expensive and that cooperation pays. TIT-FOR-TAT is open to cooperation, and willing to stick its neck out to start it off, but clearly prepared for vigorous self-defense. But I wonder this: what happens in such a scenario if the players aren't single individuals able to act in a consistent way, but a population of individuals with views and aims across the board? Would some elements in a population find it easy to sabatoge the cooperation toward which others are working?

I've often wondered if some of the more long-run inter-ethnic struggles -- Israel-Palestine, and Northern Ireland, until recently, for example -- don't somehow reflect the ability of the more extreme components of populations to undermine the natural cooperation that would tend to emerge between self-interested but competing parties. Without the extremists, perhaps these kinds of conflict would settle down quite quickly. Does anyone know of such work? I haven't seen any myself.