Who’s going next? - Homework Discussion
2005 Graduate Workshop in Computational Social Science Modeling and Complexity
Santa Fe Institute, July 10-23
Andreas Pape Sheila Conway
University of Michigan, MI Old Dominion University, VA
The Problem:
A group of, say, ten students each need to give a five minute talk, one after the other. The order of presentations is not specified. What happens?
Model development:
This task is composed of two sub-tasks: the basic scheme or social norm used to order the talks, and a model of how the students participate under these norms, influencing their position.
Group ordering mechanism: Any volunteers?
There are two general approaches to the problem of ordering: One could define the order of all the talks using various strategies before any were given. The other approach affords an emergent order. Each student in turn is selected after the previous speaker has finished, leaving the complete order undefined until the second-to-last speaker.
We interpreted the homework problem as prediction not of any general ordering task, but rather one specific to students in a particular scenario (our own). Without a strongly centralized figure implied in the problem statement (and the workshop is about, amongst other things, emergence after all), the emergent approach was selected.
That said, then how was each student to be chosen? We identified four possible mechanisms, loosely ordered in decreasing constraint:
· Consensus
· Vote
· Pick someone to delegate who’s next
· Volunteer
Consensus in this scheme would require all students to agree on who should go next, each round. We felt that this was a very unlikely mechanism for many reasons: To make informed choices, students would need substantial a priori knowledge of their colleague’s talks. Convergence or consensus would be time and effort intensive. There is also little precedence for using such a mechanism.
One step back is the process of majority
vote: Students would be asked to say who’s next, but the decision would come
from a of majority votes rather than full agreement. Though a voting mechanism
is reasonable, it still seemed to be a lot of overhead for the task at hand,
and outside the experience of either of the investigators in similar
applications.
Next to be considered is election of a single entity who then would have the responsibility to choose the speakers in order. While this could be an excellent mechanism to order a conference session, it did not seem to fit the nature of the workshop.
Finally, a volunteer mechanism was
explored. One of our key assumptions was that other students’ actions early in
the presentations should be able to influence later ordering and
presentations. Given this feature, the nature of the homework problem, the
context of the workshop, and the lack of knowledge the participants had of each
other, volunteerism stood out as a feasible mechanism for further consideration.
We assumed that a moderator could also participate.
From these notions a basic model of voluntary speaker selection was developed:
· If only one volunteers, they go
· If more than one (“at bat” in simulation below)
o Moderator chooses randomly amongst them
o Continues until all volunteers get their turn
Students’ influence the order: To choose when to volunteer
Thus the actual selection mechanism was modeled quite simply, but there was still the more complex issue of determining if each of the students would volunteer in that turn. Their decision could be influenced by many considerations: a priori knowledge of speakers and/or their topics, their interest in the quality and coherence of the whole session, a desire to make their point understood, and simple intrinsic preferences to presenting in a particular position (e.g. first, last, in the middle). These were captured in four dimensions:
· Topic closeness: were the previous speakers’ topics closely related to mine? Can I expect the remaining talks to me more or less relevant to mine?
· Presentation Quality: Were the previous presentations much better than what I can do? Will I look “good” or “bad”? On the other hand, were they so bad that the audience is exasperated, and I may want to wait until the general quality improves (which I expect it to).
· Slot: Is this opportunity near to where I want to be in the order?
· Aversion to the “Pregnant Pause”: Has the amount of time since the last volunteer exceeded my tolerance?
For the purpose of this initial simulation, student were randomly assigned values representing personality traits.
The Simulation
Students were modeled as agents, each with a randomly assigned personality. Each agent had their own image of the personality traits of the other students. These were either assumed to b random, as if they had no a priori knowledge of the other students, or assigned the actual average of the group, assuming some general knowledge of their peers. As the simulation progressed, each agent was able to establish the “true” personality of previous speakers, and could infer their own standing among the remaining participants. Once agents determined (based on their own personality criteria and inferred traits of the other students) that the next opportunity would be most advantageous compared to remaining turns, they volunteer.
Gone At
Bat Not Gone
Simulation GUI
Simulation Results
The graph shows data from the two different a priori data made accessible to the agents. Across ten runs, the mean for meanpop was 3.9 with a variance of 1.4. When the agents were assigned a random guess of everyone else’s personality, the mean was 4.6 with a variance of 3.2.
The difference in variance is likely explained by the random-guessers either over estimating the topic-closeness or underestimating the quality of the remaining students.
Future Directions
• Other strategies to cope with the multi-volunteer case
• Sensitivity analysis
– A likely family of results rather than a single prediction
– Which personality traits are most influential?
• Estimating “personality” matrix of each student
– Personality distribution through the population
– Other personality variables?
– Select rather than random weights, representing distinct personalities – see below
• Each student’s inference of other students’ personalities
– Dynamic adjustment or learning – see below
To reduce the dimensionality of the agent population, and to better represent qualities often encountered in presenters, personality traits could be purposefully weighted, creating distinct “personalities.” For example, some students may just want to “get it over with”. They may only be concerned with slot, and would volunteer first regardless of all other considerations. Other students may be more focused on influencing the audience and therefore being understood. They would be more inclined to be concerned with the grouping of like papers and the appropriate order, e.g. I should follow Ms. X because that work is fundamental to my own.
Finally, this study investigated two different estimates of other student’s personalities. An extension of the concept of using a priori knowledge would be a learning mechanism, exploiting past and present knowledge via learning algorithms that could provide better estimates of the remaining student pool.