The Standing Ovation Problem By Miller and Page 2004

PLEASE HOLD YOUR APPLAUSE UNTIL THE END!!!

Will You clap after the presentation?Will the clapping develop into a Standing Ovation?Why are you clapping?•You want to signal to me this presentation have been informative/ interesting. Enjoyable?•Did I meet / exceed your expectations?•Because everyone else is?•Because you don’t want to hurt my feeling by not clapping?

The decisions is based on a Complex Adaptive Social system that can be modeled in a computational setting

Why is this questions important?•It can explain key themes in social systems such as learning, heterogeneity, incentives, and networks•It is easily explained and can be models•Similar dynamics can be extended to model many binary choice questions: i.e. Crime (Gakeser 1996), riot (Granovetter, 1978), to search for jobs (Menczer and Tassier, 2001), to retire (Axtell and Epstein, 1999)• An example of a decentralized dynamical systems consisting of spatially distributed agents who respond to local information.

What is the unifying theme of these examples:people are socially influenced, they have varying degrees of sophistication, and information flows over a network

Agent Based Models• Agents interact and rely on preset algorithms to determine

behavior (although learning is possible) • Agents interact in both SPACE AND TIME• This creates dynamic patterns (evolution over time)• Agents can be heterogeneous and posses different

preferences and may even be irrational. (the distribution of such criteria can also be pre-set)

• Expectations and strategy differentiate the social science realm from similar physics based models.

• Information transition can follow a pre-set structure or be determined in the models (e.g. the audience in the back has the most information they see the largest portion of the audience)

Why Do SOP Occur?

• Diffusion• Information Aggregation• Conformity• Information Cascades • Growth

Information Cascades • The model:

– Two signals: Stand or Sit. – Agents receive a signal and also receive information from observing the

decisions of other agents– Agents that make the correct choice receive some utility others do not– Rational agents do not simply follow their signals since the choices of previous

agents contain information

• Because prefaces must fall into one of these two buckets herding may occur

• An information cascade occurs when at some point all agents ignore their signal and simply choose according to the actions of the previous agents

• If the first few agents all make the same choice the others follow

In a Cascade

Set-up • Sequential Decisions by rowRound 1:

Round 2:

Assume:Agents in the front row can look to their left and rightAgents in rows two and three can see all agents in front of them, but cannot look to their left or right.

Stand Sit Stand

?

? ?

Stand Stand Stand

?

? ?

In a Cascade cntd.Round 3:

2nd row surmises that with equal probability either two or three agents were standing initially; therefore, their optimal decision is to stand

Round 3:

Everyone is standing regardless of their signal because initial 2/3 in the first row received a + signal

How the SOP Differs

• Decisions need not be made sequentially • Agents can change their decisions• Agents get an initial signal of the reaction of

others within their sight lines. This can prevent cascades.

In a SOP

• In a standing ovation, agents neither make decisions or receive information in a predefined sequence.

• Agents 4 and 5 have information that two of four signals were HIGH.

• If they randomize in this environment. One quarter of the time, they would both stand.

• Even if both agents 4 and 5 stand, agent 6 will not. Her information, which in this example is complete, is that four of the six signals were LOW

Why Do SOP Occur?

• Democratic Ovations- agents care about outcomes and not their individual votes. This concern with outcomes prevents inefficient cascades in noiseless environments- omission of communication and information networks

• Pure Conformity-people modify their behavior to match their neighbors. then either all standing or all sitting are efficient outcomes.

Why Do SOP Occur?• Growth and Coordination- The actions of others determine

an aggregate variable that in turn influences the costs and benefits of the two actions. So, instead of choosing A because her neighbors chose A, an agent chooses A because her neighbors' actions make A less costly than B

• Diffusion Models- – The decision to stand must be irreversible. – Agents are more likely to stand as more other agents stand.

Similar to conformity as the benefits of standing increase with the number of people who stand.

– Diffusion models assume random mixing. The spatial structure (initial setting ) an important determinant of the dynamics in the SOP is ignored.

Another Approach

• Central tenet: Deciding whether to stand at the end of a performance, audience members should balance their desire to provide an honest signal of their enjoyment level of the performance against the pressure to conform to others.

• Level of interdependence of the agents is an important dynamic

Key Variables• Information, expectations, and actions- What

assumptions should be made• Rational or Rule of thumb agents (all agents have the

same behavior rules)• How is information spread in the crowd (do people in

the front get less information than audience members in the rear?)

• How realistic should the model be? Is the added level of complication justified (do audience members look behind them before making a decision, are audience member in the front more likely to be critical because they paid more for their ticket)

Model Description

• Agents are seated in a rectangular auditorium with R rows and C seats per row

• At the conclusion of a performance each agent makes an evaluation of the performance's quality (1=row, J=seat, Q is the evaluation)

• Each agent possesses an exogenous threshold level in addition to his or her quality evaluation

• total number of audience members standing at time t

• equals the number of agents standing

s

Model Description cntd.• Agents who remain seated must decide whether to

stand, and vice versa• They rely on local information (the number of

neighbors standing or the percentage of audience members within sight who are standing)as well as the initial quality appraisal of the individual

• Behavior can be represented by a heuristic that maps information and quality appraisal into an action.

• Periods are considered as discrete units• Behavioral rules may depend on the time period-

members may require different motivation in subsequent time periods

A Computational Model of Standing Ovations

• A square auditorium with 400 seats is modeled• Initially, audience members make their decisions based solely on perceived quality• Each individual has an identical standing threshold of 0:5, and thus will stand

initially if and only their perceived quality exceeds 0:5. • Each audience member uses a majority rule heuristic. If a majority of the people

the sees are standing they conform in the next period• Focus on: timing of updating and the information structure• Three possible procedures for updating:

– Synchronous- all agents update simultaneously– Asynchronous- random- agents update one at a time based on a

random order– Asynchronous-incentive-based- the order is not random but depends

upon incentives. Assume that those agents surrounded by agents taking the opposite action are the first to update (an explicit ordering rule that has agents who are least like the people that surround them move first)

Evaluation Criteria

• Number of Iterations (NI) - The number of periods until a steady state is achieved.

• Stick in the Mud (SM)- The percentage of people that do the opposite of the majority in the steady state

• Informational Efficiency (IE) - The percentage of the time that the majority of agents in the steady state takes the same action as the majority did initially

Information Structure

– Five Neighbors: Agents look at the two neighbors on either side and the three agents directly ahead of their current location.

• Cones: the three agents in the row directly ahead, the five agents two rows ahead, and so on

Outcomes Under Different Scenarios

•Asynchronous-Random updating leads to a higher IE and more SM than either of the other two updating rules. Suggesting aggregating information efficiently requires some SM activity•Synchronous updating takes a very long time to settle down into a steady state. This is because members of the crowd can stand and sit many times while trying to coordinate.

Outcomes Under Different Scenarios

•Even though the agents see more agents with cone neighborhoods, and have better information, the IE is lower. •Agents in the front have enormous influence almost everyone cues off of the behavior of the front row agents, and we have a phenomenon that is similar to an information cascade.

Models Conclusion

• The system often converges to the wrong equilibrium (1- IE)

• Greater pressures to conform, captured by the cones, leads to a less efficient aggregation of information

• A plot of the number of people standing over time tends to be roughly S-shaped as predicted by diffusion models

• People in the front can have a large impact.• Mathematical models (with some added noise) imply

that all agents eventually take the same action. This rarely happens in the computations

Takeaways

• Good form is to include several types of agent behaviors and show the model results are robust to such choices

• A simple setting can yield rich results that apply to many other situations

• SOP offers a platform for considering worlds with social learning, diffusion, networks, and heterogeneity

Criticisms

• Computational setup is vague– Distribution of quality perception– Evolution over time- S Diffusion plot not provided– Why were cones and rectangles chosen and why

those sizes? What about different bigger shapes that seem more realistic.

– How the dynamics change within the audience. Front vs. Rear and likelihood of sticking with initial perception

– Test for the validity of other assumptions. (larger sample, sitting next to friends, ect.)

TIME FOR THE STADING OVATION

Questions?