Is the common rule for decision making in animal collectives also applicable to human collectives?

 After studying Arganda et al.’s paper which claims  to present a common rule for decision making in animal collectives, we wondered whether their model is applicable to human collectives, particularly in case of two people; one as the focal individual and the other as the social peer. Before anything else, I was curious to see the general model prediction of the focal individual choosing ‘x’ when the social peer has already chosen option ‘x’ (n_x=1 so n_y=0) or ‘y’ (n_x=0 so n_y=1). I plotted the probability of choosing x as a function of ‘a’ and ‘s’ for three values of k (0, 0.5, 1) in each of these two cases.

As we can see, when the peer has chosen x, the dominant red colour in Fig.1 shows that the focal individual is more likely to choose ‘x’ as well, unless ‘s’ is low. If we go back to definition of ‘s’, it indicates social information, i.e. very low ‘s’ means that the individual doesn’t consider the peer’s behaviour. An interesting point to me was the independency of ‘a’ value (subjective confidence that ‘x’ is not good as we discussed) predicted by the model in this case.

The opposite behavior is predicted when the peer goes to ‘y’ site, i.e. the focal individual is not likely to choose ‘x’ unless ‘s’ is very low

Green areas, indicating no difference between two choices are narrow bars parallel to ‘a’ axis in low ‘s’ (at most s = 2) or narrow bars parallel to ‘s’ axis in low ‘a’s. These trend decreases as ‘k’ increases.

I think with this simple insertion of numbers of people, we can find an appropriate a,s and k which can explain the social decision-making behavior of an individual.

In Further steps, I’m thinking of manipulating the model to obtain a better fit. In the case of any special result, I will let you know.

Does the “signed-max” model prediction for emergence of high-confidence errors in visual clutter justify the results of Graziano & Sigman study?

In the ‘visual clutter paper’, Stefano Baldassi is trying to verify his “signed-max” model by testing the model’s prediction about the distribution of confidence reports in near-threshold multiple-interval discrimination tasks. In a task where the observer is supposed to monitor multiple stimuli and make a decision about a signal that is embedded in one [undetermined] stimuli, in addition to the noisy representation of signal itself, all stimuli contribute to the noise in the evidence-representation axis. The mechanism by which the observer accumulates these noisy evidences is controversial. The Baldassi’s “signed-max” model beat the simplistic “sum” model in simulation analyses (check this paper). The “signed-max” model assumes that all stimuli are treated equally and each produce a piece of evidence (=signal) and visual system chooses the most extreme of noisy signals as the target. This model predicts a binominal probability density function for evidence representations. And as the number of intervals increases the probability that a distractor would generate larger representation than the signal increases, hence performance decreases.

Unlike the Gaussian distribution of noise in the familiar one-interval 2AFC task, the binominal noise of “signed-max” model predicts that in higher set-sizes most errors are due to evidence representations far away from the 0[= neutral] on evidence axis. Hence in multiple interval tasks more errors would be high-confidence errors (also there will be more high confidence corrects). This is just what they confirmed behaviorally in the “clutter” paper.

In the “construction of confidence” paper Graziano & Sigman report the confidence ratings in a ‘partial reporting’ experiment. What they find is that a large portion of errors were high-confidence errors. They investigate the rationale behind these high-confidence errors and discuss that it is due to location-misattribution of correctly identified targets (a process reminiscent of ‘Binding problem’ studies where in short presentation times separate perceptual attributes of stimuli [e.g. shape, color, location] are perceived but does not integrate to form a unified percept of each object).

Assessment of current results based on “signed-max” model is impeded by several challenges:

1. The evidence in ‘partial report’ task is two-dimensional (letter identity and location) while the “signed-max” is based on one evidence axis (the direction of tilt).
2. Performance in ‘partial report’ is believe to rely on working memory while orientation discrimination is [hypothetically] based on primordial physiologic processes (V1 cells). The memory mechanisms is located down-stream to sensory perception circuits and are amenable to much more confounding factors.
3. The signature pattern of binominal evidence in “signed-max” is defined for the near-threshold signal strength (P(c) = 75%) where the signal is just noticeable and noise perturbations largely shape the accumulative pattern of decision-maker’s behavior. While the performance in ‘partial report’ is much lower (P(c) = 30%).
4. And a big contradiction: “signed-max” assumes that all stimuli are monitored independently, while “partial report” results clearly show that observers monitor some spatial locations at the sake of others.

All these obstacles make it unreasonably hard to do a mathematically plausible generalization of model. However, by subjective inspection an uncanny resemblance is seen between the bimodal distribution of confidence ratings in Graziano & Sigman paper and the bimodal distribution of evidence probability that “signed-max” model proposes for large set sizes.

But, and this is a big but, these graph have different x-axes, and we know that the confidence distribution is a derivative of the evidence distribution. Monte Carlo simulations (see above) show that error and correct representations peak at somewhat similar distances from 0, and this suggests that the confidence distribution from this evidence set would be a unimodal one. Moreover “signed-max” model predict that the ratio of high-confidence corrects and high-confidence errors both increase at larger set-sizes. In fact the increase in set size induces a bias in confidence reports rather than affecting the metacognition in any substantial way. This interpretation is also evident in this excerpt from the paper itself:

If the decision-maker has to monitor many events […] there will be a high probability that the decision, whether right or wrong, will be made with high confidence. […] as American presidential candidate John Kerry mentioned in the first 2004 debate: ‘‘It’s one thing to be certain, but you can be certain, and you can be wrong. Certainty sometimes can get you into trouble.’’

At the end let me state that I believe that the two-dimensional nature of the ‘partial report’ task underlies the formation of high-confidence errors. Low ‘feature-binding’ efficiency at short time-scales in combination with ‘retinotopic spatial bias’ can lead to many high-confidence errors but not as much high-confidence corrects. I’m not confident though!

why does social influence lead to consensus? What is the benefit of consensus if the consensus opinion is different from the Wisdom of the Crowd opinion (and hence, sub-optimal)?

Accepting “majority” as “correct” has been so powerful that Galileo did not dare to reveal the fact about rotation of the earth around the sun. This is because it has been though that if something is true, it is seen by most of the people. But it is not always the case as we saw in the two papers of How Social Influence Can Undermine the Wisdom of crowd effect and Effects of Social Influence on the Wisdom of Crowds; more does not imply better

Now, our first question is why social influence leads to consensus. It seems obvious that one of the main reasons is uncertainty about the answer of the question and also lack of absolute confidence. I doubt if an individual who is completely sure about the answer or at least thinks so is willing to change his opinion just because others say something else.

Our second question is that: What is the benefit of consensus if the consensus opinion is different from the Wisdom of the Crowd opinion?

According to above two papers, necessary conditions for consensus to be optimal are diversity, independence of opinions, specialization in expert knowledge and a mechanism for aggregating individual opinions. How far the initial individuals’ estimation is from the true answer is also important. According to Mavrodiev et al. if the average initial estimations is close to the truth, only a short and mild interaction would be enough to get closer to reality but keeping it on would divert the aggregate opinion from truth. However if the initial estimation is relatively, interaction would make it better.

In addition to these I want to add some more which I believe have serious effects on “collective intelligence” which in turn modulate the effect of social influence on consensus:

1-      What kind of information is shared; only the final output result or the reasons behind that. In the case of revealing only the output answer, the density of a particular answer would be much important than the time members also give their reasons for their opinions. Because in the latter case, even if the related opinion is not very common, those mentioned reasons can motivate others to be in agreement with them.

2-      Also knowing WHO says what is vital especially if the background and career of the group members are known.

Are they overconfident in their study of overconfidence?

A “Nature” paper is treated like a solid fact in most undergraduate communities. But here we are challenging the Dominic Johnstone’s paper, “The evolution of overconfidence”. In this study they show that relative to the amount of uncertainty regarding the opponent’s capabilities, it is evolutionary plausible that individuals be overconfident and overestimate their own capabilities. In simple words they say that if you are not sure that the other one will win, it is better to get up and enter the fight [BTW: does this qualify as a 3-minute version?].

Claire El Mouden has criticized this study in her blog post, going as far as pitying that it even passed the peer-review process. What amused me as much as El Mouden was how olden are the computational studies of animal conflict. A cursory search brought up studies with similar methodology and results dating back to 60s and 70s. However El Mouden’s main argument in criticizing the current study was that the authors’ novel bias term, “K”, is not equal to confidence and they have over-interpreted it. Bahador exemplified the argument by asking that if we applied the model to increasingly simpler organisms (cows, insects, Amebae) would it still be appropriate to regard the “K” as a measure of confidence? At first I felt tricked by the authors. I thought they managed to sell me a colored-Gonjeshk as Ghanari! But I’ve got some justification that their interpretation can still be defended.

Before projecting the scenario to simple organisms’ ecology, it is important to pay attention to the model’s assumptions. To quote the paper:

“Individuals choose whether or not to claim a resource on the basis of their perceived capability relative to the capability of other claimants.”

So the individual that we are modeling is capable of perceiving his own capabilities, and perceiving his opponent’s capability, and is capable of making informed decisions as to whether claim the resource or not. The Amebae might be able to calculate a signifier of his own capability and retreat from approaching the resource if obstacles turn out to surpass his capacity. But I highly doubt that Amebae be able to calculate another Ameba’s capabilities and then decide accordingly! So I’m saying that an organism that fits those assumed criteria, can also be credited to be perceptually biased in one way or another (i.e. over or underestimating capabilities; hence being over or under-confident). I do not find anything wrong with calling the “K” overconfidence, as long as you take the model’s presumptions into account. We also shall remember that this study is a modeling of conflict between two individuals. It is not a model of approaching resources in environment. The model does not consider any cost for approaching resources per se (if you claim and no one else does, you will gain and pay no cost). So this is not an exact replica of early studies that show when cost of claiming a resource decreases, more individuals would approach it (a ripe fruit at a 10cm distance is more frequently claimed compared by a fruit on the other side of a wide dangerous valley). At least we can say this study is applying similar calculations to the issue of inter-individual conflicts, but is not the same.

Next comes the argument that the study’s findings are dated. Despite the huge literature of animal conflict, they does not discuss the biased perception of capabilities per se. Take the 1976 study of John Maynard Smith for instance. Therein they discuss several scenarios of asymmetric conflicts and yet none is about a biased self-deception. They actually conclude that in an asymmetric conflict it is best to obey the cue features and settle the conflict without even entering a fight, thereby precluding costs altogether. To my interest the same paradigm of thought lives on in widespread recent scientific works. The other day I was reading a chapter from Jared Diamond’s book, “why is sex fun?”. In a chapter on physical body signals, he proclaims that in a conflict accurate exchange of knowledge about each one’s capabilities would benefit either individuals:

“It would be advantageous to both individuals to exchange signals that accurately indicate their relative strength, and hence the likely outcome of a fight. By avoiding a fight, the weaker individual is spared the likelihood of injury or death, while the stronger individual saves energy and risk”

The argument sound intuitive and the author expect us to take it for granted. But the current study demonstrates that this framework of thought is not necessarily true. In situations that claiming is not relatively costly it is more rewarding to be biased and over confident and enter conflicts against the odds; even though that the cost might be larger than benefit in a single confrontation, as the calculations showed that benefit to cost ratio critical point for over-confidence is r/c > 0.7.

All in all, I do not find the terminology of equalizing a positive “K” and overconfidence, wrong, but it is true that the results are not that novel theoretically. Someone familiar with the literature on animal conflict would not be that much astonished by this study. But Johnson and Fowler were (over-)confident enough to claim this and apparently no one in Nature’s editorial board stepped in for a conflict. The odds were on their side and they published this not so much phenomenal finding in Nature. As it turns out “Fortune favours the bold”.

Importance of liking distributions in decision-induced cognitive dissonance studies

There were two main critical points about the paper “The neural basis of rationalization: cognitive dissonance reduction during decision-making”:

1-      In order to choose similarly rated pairs used in the 2^nd phase of the experiment, a constant absolute difference between two ratings (mentioned as 10 points) could not be a well-defined suitable criteria for all the subjects to account for a difficult trial.

Consider two subjects; an easy-going or indifferent person who gives OK to nearly everything and one with a picky attitude who even makes distinctions between two very similar choices. The first one rates all the items in a short interval, e.g. 40-70 whereas the second one does the rating task using a much wider range. Therefore a 10-point difference is a big difference for the first person but a slight difference for the second one. It is obvious that the cognitive dissonance experienced by these two are not the same. So, it would be better to take into account the distribution of subjects’ liking in specifying the criteria for creating difficult decision-making situations.

2-      The authors associated the reduction of cognitive dissonance to a pleasant feeling of relief. However there is no scientific evidence of this relief. They could have measured some relief-related parameters like breathing rate or skin conductance in order to prove their claim.

Besides the critical issues, this paper created some research questions in our mind:

1.       Is there any biological differences between people with and without experiencing cognitive dissonance?

2.       Can we categorize people based on the degree of dissonance they experience?

3.       Is an individual inserted in the same category when confronted with different dissonance-making contexts (I mean the four famous cognitive dissonance-producing paradigms)

I’m to do a literature survey about these questions. I would share my results in the blog.

Accuracy vs influence contribution as utility functions of interactive decision making

According to this paper (Optimal Reporting of Predictions), in the notion of group decision making, besides “accuracy” of the output decision, personal “influence” on the decision might be another goal function which is interested to be maximized in experts’ reports. It seems that fully depending on the case of decision making, either one of these two, regardless of the other, or a combination of the two could contribute. Now the question is that when and how they can be dissected? Maybe in the case that there is no exact “correct” answer, each expert tries to take or keep his influence to the maximum level, so that he can achieve his own preference as a satisfying reward, e.g. as Bahador mentioned in the meeting, selecting the best movie in a festival. However in the case of existing one “correct” answer, when the ultimate reward for all is in finding a solution which best leads to the correct answer, the goal function might change to “accuracy”. In long term and iterative cases which mostly happen in a group of experts of a company, as mentioned in this particular study, both of these utility functions are to be taken in to account; rationally thinking, an expert can keep being influential as long as he decides well enough leading to a profitable outcome or a reliable but not in the eyes of the boss expert can increase his reliability in front of the boss by increasing his influence.
For researchers of social decision making, this concept is very important in designing their paradigms and modeling the behavior of the group.

As we can see in the article, properties 3.3 and 3.4 are given to suggest the optimal report for different ALPHAs, but now my question is that, how can an expert be known of his prior weight given to him by boss?! Is there any necessary relationship between self-confidence and the expert’s prior weight in the boss’s opinion? If not, is the expert necessarily get informed by boss before starting giving reports?

interactive agents and the problem of social influence or social accuracy

The paper by Bayarri and Degroot contributed to two mail prediction:

1-as an expert’s decision weight approaches zero (very small) his/her optimal prediction is to report a large number for one option.

2-as an expert’s decision weight approaches 1, one should never report probability zero to any option.

In both cases, the experts try to maximize their posterior decision weight. This suggests that, in an interactive environment, a participant with low reliability should be overconfident about his decision in order to maximize his/her influence. In this point of view, overconfidence is an optimal behavior.

Here the question is that do people try to maximize their influence? If this is the case, then we would expect that people get reward when their opinion is accepted as group’s opinion regardless of the outcome of the decision. It is also could be true that they try to maximize a synthesis of accuracy and influence. For example in reinforcement learning paradigm, the cumulative reward an agent receive is a linear combination of being correct (accuracy) and being selected (influence). It is there a task we could separate these two kinds of rewards?

   

Utility of Social Influence

Previous works on social influence have investigated two main questions: How can we maximise our target population's compliance when we influence them? What are the psychological and brain mechanisms of compliance (i.e. being influenced)? Here by compliance I refer to ANY form of change (in behaviour, preference, taste, valuation etc) taking place in the target of influence. Our readings of the literature of social influence tells us that a different viewpoint is also possible. We can ask the question: What are the cognitive components involved in exerting influence? This question can be broken down to the following: 

1) What is the utility function that the influencer tries to maximise? It is possible that being influential may be inherently rewarding irrespective of (a) influence outcome for the influencer and (b) accuracy of the influence?

An example of case (a) would be when a salesman persuades a buyer to spend money on his product. Social influence has paid off for the salesman. An example of case (b) would be an investment advisor persuades an investor to buy some share and the share price subsequently goes up. In these two cases, the utility of influence is obvious and traceable to external, if you may, objective factors. We suggest that people may strive to be influential in the absence of any such external reinforcements. If this suggestion is correct, then the utility of exerting influence may at least have three components: compliance-related rewards (direct gain), accuracy-related rewards (e.g. reputation) and the inherent value of influence (e.g. vanity).    

2) What is the transformation from subjective opinion to shared advice that maximises the above-described utility function?  

A special case of this question is addressed by Bayarri and Degroot (1989): assuming no conflict of interest and perfect honesty, they show formally that there are strategic recommendations for how to give the same advice (ie the transformation from the same subjective opinion to numerous forms of shared advice) such as to maximise compliance from the decision making body (ie target of influence). Their prescription is to be radical when you expect little compliance and conservative when you expect high compliance. Is this a general formulation? Do the assumptions of Bayarri & Degroot fit with our prior knowledge from psychology? For example, B&D solve the case for repeated iterations of unlimited number. What is the best strategy when the number of interaction rounds are limited? 

3) Empirically,  do advisers modify their stated advice  to maximise their expected influence (ie compliance rate by influence target)? If so, can a negotiation process be decomposed into separate components of what is shared to maximise influence and what is shared to maximise collective accuracy? 

   

Session 7 | Direct injection of noise to the visual cortex decreases accuracy but increases decision confidence

On our 7th session Morteza presented : Rahnev, Dobromir A., et al. "Direct injection of noise to the visual cortex decreases accuracy but increases decision confidence." Journal of neurophysiology 107.6 (2012): 1556-1563.

At first Morteza talked about previous investigations on association/dissociation between accuracy and confidence. Then he talked about different effects of using Transcranial Magnetic Stimulation (TMS) to the visual cortex and indicated the use of TMS in this research.

With a brief introduction to Signal Detection Theory (SDT) concepts, we started reviewing paper's data acquisition. Morteza explained us what is phosphene and we talked about the procedure of finding phosphene location, we finally reviewed the experimental task of the paper.

Later Morteza explained paper's data analysis and computational modeling assumptions, then we reviewed the specification of each computational model used in the paper, we talked about parameters and the characteristic of each one.

we understand the procedure of model comparison and verification used in the paper.

As in the last part, we talked about results created from the computational models and the comparison to empirical data. Morteza briefly explained us the discussion section.
A discussion on different aspects of this research may be started in future posts.

Session 6 | Dissociable Effects of Dopamine and Serotonin on Reversal Learning

On our 6th session Mona presented : den Ouden, Hanneke EM, et al. "Dissociable Effects of Dopamine and Serotonin on Reversal Learning." Neuron 80.4 (2013): 1090-1100.

At first we had a discussion on Dopamine and Serotonin's role in behavioral control. Mona described us the previous researches and experimental findings in electrophysiological, pharmacological and fMRI studies.
We understand that these neurotransmitters are involved in learning from reinforcement and dopamine enhances relative learning from reward, while serotonin has been associated with learning from negative events.
We talked about the experimental paradigm and had a long debate on behavioral measurements used for the task, there is a significant difference between correct/incorrect and rewarding/punishing choice in their task.
Mona described us that polymorphism of serotonin and dopamine transporter genes can be used to investigate effects of the dopamine and serotonin systems.
We spent a good time on understanding results in figure 2 and computational models proposed for investigating the mechanisms that underlie genotype results.
A discussion on different aspects of this research may be started in future posts.