Calver-Travis et al. "Bayesian Confidence in Optimal Decisions"

Let's talk about this new preprint by Calder-Travis et al. It’s an interesting piece because it deals with the difficult question of the relation between confidence and response time. They do a very nice job explaining all the different options, and I have to say, the article is a model of clarity. It’d be great if all scientific articles were written as clearly as this one.

If you’re not interested in this question, I understand. It doesn’t seem so exciting at first. But it turns out the relation between confidence and response time is far from being straightforward. So, let me try to spark your interest.

Imagine that you have to determine whether a briefly flashed stimulus is a square or a diamond, and then provide a confidence judgment. You don’t always take the exact same time to answer. Sometimes you answer a bit more quickly, sometimes a bit more slowly. That’s just how things are.

Now let me ask you a question. When will you be more confident: when you take a lot of time to respond, or when you answer immediately after the stimulus is presented?

The first option seems right. If I don’t have enough time to decide, I won’t be confident in my decision. Confidence should increase as decision time increases.

But the other option could be true as well. After all, if I’m confident in my decision, there’s no need for me to wait before answering. So, we should expect confidence to decrease as response time increases.

See? Not so straightforward! Does confidence increase with response time? Or does it decrease with response time?

The sad truth is... it depends. It depends on whether the experimenter sets the response time, or whether you're free to set your own response time. Under time pressure set by the experimenter, confidence tends to increase as response time increases. But when subjects can set their own response time, confidence decreases as response time increases.

This phenomenon can be (approximately) explained by drift diffusion models, or, more precisely, by a variant developed by Pleskac & Busemeyer (2010): the 2-stage signal detection model (2DSD).

Drift diffusion models postulate that perceptual systems sequentially accumulate evidence favoring one alternative over the other, until a threshold is reached and a perceptual decision is triggered. The quality of the evidence determines how fast evidence is accumulated – also called the drift rate of the evidence. In turn, confidence judgments are based on the evidence accumulated in favor of the choice.

The 2DSD model can explain why confidence increases as decision time increases when subjects aren’t free to set their own response time. They do so in part by postulating that evidence continues to accumulate after the decision is reached to inform confidence judgments. More time means more accumulated evidence, which leads to higher confidence. So, as decision time increases, confidence increases.

To some extent, the 2DSD model can also explain why confidence decreases as decision time increases when participants are free to set their own response time. In their model, Pleskac & Busemeyer postulate that, all other things being equal, the quality of the evidence accumulated (i.e. the drift rate) can vary randomly from trial to trial. A high drift rate leads to fast decision times and high levels of confidence. A low drift rate leads to slow decision times and low levels of confidence. As a result, as drift rate decreases, decision time increases and confidence decreases.

That’s a convincing story, but it’s still somewhat incomplete. As Pleskac & Busemeyer recognize, “The model does, however, underestimate the relationship between observed decision time and confidence” (p.881).

Here come Calder-Travis et al. now. In a nutshell, their model keeps the basic features of the 2DSD model but also postulates that the system generating confidence judgments takes as input an estimate of the rate of accumulation of evidence.

That’s not an ad hoc hypothesis to explain a weird feature of confidence judgments. It really makes intuitive sense. If I accumulate evidence in favor of one decision (and not the other) at a crazy rate, it’s probably because this trial is really easy, so I should be more confident. On the other hand, if I struggle to accumulate evidence, it’s probably a difficult trial, and then I shouldn’t be confident in my response.

In sum, under time pressure, confidence increases as response time increases, because more evidence accumulates if you take more time to answer, and this should make you more confident. Without time pressure, confidence decreases as response time increases, because a long response time indicates a difficult trial, and if the trial is difficult you shouldn’t be confident. So, overall, the model nicely explains what we currently know about confidence and response time.

Still, it seems to me that Calder-Travis et al.’s model doesn’t account for the intuition that I answer faster because I’m more confident. There seems to be a causal relation between the fact that I’m more confident and the fact that I answer more quickly. Maybe it’s just an illusion, or a “strange inversion” as Dennett would say. But before saying that, we could search for models that do account for this.

In fact, several research groups have recently suggested that confidence could modulate the accumulation of evidence online, even before a perceptual decision is reached (See here, here, and here for some evidence that, in my opinion, goes in that direction). I really like this idea. Maybe confidence influences evidence accumulation, or can modulate the decision boundary. If that’s right, then we can make sense of the intuition that we take some perceptual decisions faster because we’re more confident.

But again, things aren’t so easy… One question is: where does confidence come from, if not from the accumulation of evidence that leads to the perceptual decision itself? If confidence is computed at least partly based on the evidence accumulated for the perceptual decision, it can’t, at the same time, modulate the accumulation of evidence for that very same perceptual decision.

As a result, these models have to postulate two accumulators: one for the perceptual decision, and one for confidence (as done here). This can be accomodated with some kind of dual channel model. However, as Calder-Travis et al. remark, it’s unclear why Mother Nature would have duplicated evidence accumulation in this way. In this respect, models like Calder-Travis et al.’s are much simpler for now.

In addition, these models have to explain exactly how the system that computes confidence influences the accumulation of evidence online. That’s a tough problem too! So, even if I like the idea that confidence modulates perceptual decisions online, I have to admit that it’s not so clear how things work at this point.

Who knows, maybe Mother Nature did partly duplicate evidence accumulation, and maybe things aren’t so simple. The relation between response time and confidence is still mysterious. But Calder-Travis et al.’s piece, among others, shows that we can make a lot of progress on this question.

This line of work also illustrates something about the field. People often seem puzzled by the place that the study of confidence has taken in recent years. Sure, studying confidence is interesting in itself. But there’s also a higher purpose to all this. Ultimately, analyzing the mechanisms of perceptual confidence can reveal a lot on the mechanisms of perceptual decision making.

I thank Joshua Calder-Travis for his comments on a previous version of this blogpost.

MM

"Is Iconic Memory Iconic?" by Quilty-Dunn

Here's my first blog post. I recently read Quilty-Dunn’s article “Is Iconic Memory Iconic?” Quilty-Dunn recently received the William James prize, from ASSC, for this excellent piece. The end of the article, in particular, contains an argument that I find interesting, so I wanted to take some time to discuss it here.

Representations in iconic memory have an iconic (image-like) format. Representations in visual working memory have a discursive (language-like) format. Quilty-Dunn shows this convincingly, in my opinion. If you disagree, please take this for granted in what follows anyway.

Now, some mental phenomena are cognitive. Others are perceptual. What’s the difference between the two? Well, some have suggested that it’s a difference in representational formats. Visual perception, for instance, depends on representations that have an iconic format. Cognition depends on symbolic, language-like representations. If you hold that the difference between perception and cognition is a difference in representational format, then only iconic memory representations are truly perceptual (in the visual domain). Representations stored in working memory, on the other hand, are not perceptual representations.

In the consciousness literature, some – notably, global workspace theorists – hold that the contents of conscious experiences correspond to working memory (or global workspace) representations. Given that working memory representations aren’t perceptual, it means that, if global workspace theory is true, properly perceptual contents are never conscious. Perceptual contents are never conscious... What?! How did we get there? That doesn’t seem right.

What should we do? Quilty-Dunn suggests several possibilities.

The obvious option is to reject the view that conscious contents are the representational contents stored in working memory. Proponents of local theories of consciousness, like Victor Lamme or Ned Block, for instance, would probably go this way.

The second option is to accept higher-order theories. According to at least some versions of higher-order theory, the content of your visual experience (what you visually experience) depends on iconic representations, but those representations don’t become conscious on their own. Instead, you become conscious of their content through higher-order mechanisms (whatever they are). So, no problem here.

I'm not a big fan of the first option. I like the second option (an advantage of the higher-order theory is that it gives you some flexibility on this issue). But if you’re a global workspace theorist – and after all, why not, it’s a good theory – you don’t want that. And, obviously, you don’t want to go with the first option either.

So, this article makes quite clear that you can’t hold both that the difference between cognition and perception is a difference in representational format, and that our (perceptual) experiences depend only on the contents of working memory – or global workspace.

The third option is to reject the view according to which the difference between cognition and perception is a difference in representational format. Instead, you should turn to more “architectural” accounts of the border between perception and cognition, and hold that perception can involve both iconic as well as language-like representations.

As it happens, Quilty-Dunn wrote another paper defending precisely that view. His view is that perception involves "object files" that can incorporate index-like representations of individual objects, as well as abstract, amodal features. If visual perception depends on those object files, then visual perception can’t be defined as involving only iconic representations.

At first, I wasn’t convinced by this view. After all, those object files don’t seem genuinely perceptual. Indeed, object files are used as inputs in inferences, and they don’t reduce to “perceptual or sensor-motor primitives”, as Susan Carey would have it. If so, a simple way to answer Quilty-Dunn’s argument is just to deny that object files are genuinely perceptual. And if object files are not perceptual in nature, why are they relevant to the debate, and why should we care?

Of course, Quilty-Dunn addresses this worry. I'm still not entirely sure where I stand on this, but here's one point I found convincing: it does seem like object files are crucially involved in perceptual phenomena, like transsaccadic memory. The fact that the same objects can be re-identified easily across saccades despite changes in the input is because of this memory. And you wouldn’t hold that transsaccadic memory is not a perceptual phenomenon, would you? Then… there you have it, it seems like you have to hold that object files can be properly perceptual, since they are at the center of crucial perceptual functions. If so, you can’t define the difference between perception and cognition as a difference in representational format, since object files aren’t (purely) iconic representations.

To sum up, if you like the global workspace theory, or if you think that conscious contents are the contents stored in working memory, you’re committed to an “architectural” view of the difference between perception and cognition. But that’s all good, Quilty-Dunn says, because you can accept a kind of “perceptual pluralism”, according to which working memory representations can be considered genuinely perceptual, even if they don’t have an iconic format.

Unfortunately, those "architectural accounts" are under-developed at the moment. When you reject the "representational format" account of the difference between perception and cognition, you know what you lose, but it's unclear what you get. So, I guess we'll have to wait for additional research in this domain.


I thank Jake Quilty-Dunn for reading this before I posted it. Again, congratulations to him for the William James prize!


MM

Why create yet another blog on consciousness?

Hi all, I'm starting a blog. There are already several good blogs on consciousness, like Richard Brown's blog, or Hakwan Lau's. So, why add yet another blog on consciousness? Two main reasons.

First, the literature on consciousness is starting to be pretty big now, especially if we include the literature on metacognition in there as well. It's difficult to keep up with the current empirical and philosophical literatures on this topic. So, I thought maybe some of you would be interested in having short summaries of articles that I, for one, find important. By writing about the articles that I find good and interesting, maybe this can spark your interest so you can read those as well – or at least my blogposts should give you just enough material so you can pretend you've read those articles.

The second reason is a bit more selfish. I find that I understand things better when I write about them, and hopefully having this blog will be helpful for me. As I usually try to write a few thoughts about the articles I read, I thought maybe some of you would find that interesting. It'd be even better if we can discuss those articles together in the comments.

So, that's basically why I created yet another blog on consciousness. Nothing too fancy.

As my blogposts will often include summaries of scientific or philosophical articles, I'll try to contact the authors to make sure I've correctly understood their points before posting anything. By doing so hopefully I won't spread misinformation. Don't hesitate to comment if you think I'm wrong about something, or I'm missing the point. I'll gladly edit the blogpost if I'm making a mistake. I want this blog to be a reliable source of information for people interested in the cognitive neuroscience of consciousness.

I'll try to keep things simple. Hopefully people who aren't too familiar with the field can understand what I'm saying. As much as possible, I'll try to refer to what I regard as the relevant literature when things get a bit complicated.

In any case, I hope you'll enjoy reading this blog.

Matthias Michel