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?