Patrick Girard, Valery Pavlov, Mark C. Wilsonwww.cs.auckland.ac.nz/˜mcw/

University of Auckland

CMSS seminar, Auckland, 2014-05-20

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of diseaseI adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physics

I spread of diseaseI adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of disease

I adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of diseaseI adoption of new products, technologies, behaviours

I spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of diseaseI adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of diseaseI adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Diffusion in (social) networks

I Diffusion models on connected graphs have been widelystudied. Main applications:

I percolation in statistical physicsI spread of diseaseI adoption of new products, technologies, behavioursI spread of beliefs, preferences, information

I Abstractly, each node has a certain state (colour), and eachnode updates its colour based on some local rule. Updatescan be simultaneous, sequential (fixed order of agents), orasynchronous (anyone can move).

I Can be thought of as a form of dynamic voting.

Research programme

Belief diffusion models

I We focus on belief diffusion in social networks.

I Key ingredients:

I Micro properties: how nodes influence their neighbours(transition rules).

I Topology: how nodes are connected in a network.I Macro properties: distribution of colours among nodes.

Research programme

Belief diffusion models

I We focus on belief diffusion in social networks.I Key ingredients:

I Micro properties: how nodes influence their neighbours(transition rules).

I Topology: how nodes are connected in a network.I Macro properties: distribution of colours among nodes.

Research programme

Belief diffusion models

I We focus on belief diffusion in social networks.I Key ingredients:

I Micro properties: how nodes influence their neighbours(transition rules).

I Topology: how nodes are connected in a network.I Macro properties: distribution of colours among nodes.

Research programme

Belief diffusion models

I We focus on belief diffusion in social networks.I Key ingredients:

I Micro properties: how nodes influence their neighbours(transition rules).

I Topology: how nodes are connected in a network.

I Macro properties: distribution of colours among nodes.

Research programme

Belief diffusion models

I We focus on belief diffusion in social networks.I Key ingredients:

I Micro properties: how nodes influence their neighbours(transition rules).

I Topology: how nodes are connected in a network.I Macro properties: distribution of colours among nodes.

Research programme

Micro: transition rules

I There are many models! The best one for a given situationmay depend on exogenous factors (such as degree of commonknowledge).

I We focus on threshold models, where a node deterministicallychanges state depending on the number or fraction of itsneighbours of various colours.

I This is opposed to epidemic-type models of a probabilisticnature.

Research programme

Micro: transition rules

I There are many models! The best one for a given situationmay depend on exogenous factors (such as degree of commonknowledge).

I We focus on threshold models, where a node deterministicallychanges state depending on the number or fraction of itsneighbours of various colours.

I This is opposed to epidemic-type models of a probabilisticnature.

Research programme

Micro: transition rules

I There are many models! The best one for a given situationmay depend on exogenous factors (such as degree of commonknowledge).

I We focus on threshold models, where a node deterministicallychanges state depending on the number or fraction of itsneighbours of various colours.

I This is opposed to epidemic-type models of a probabilisticnature.

Research programme

Fundamental macro questions

I (equilibrium) Do beliefs converge in finite time?

I (unanimity) Do beliefs converge to a common belief?

I (wisdom of crowds) Do beliefs converge to the correct belief?if not, does the “correct” belief win a plurality vote?

Research programme

Fundamental macro questions

I (equilibrium) Do beliefs converge in finite time?

I (unanimity) Do beliefs converge to a common belief?

I (wisdom of crowds) Do beliefs converge to the correct belief?if not, does the “correct” belief win a plurality vote?

Research programme

Fundamental macro questions

I (equilibrium) Do beliefs converge in finite time?

I (unanimity) Do beliefs converge to a common belief?

I (wisdom of crowds) Do beliefs converge to the correct belief?if not, does the “correct” belief win a plurality vote?

Research programme

Progress so far

I Exploration of simulations (with Alex Raichev, as shown forexample in CMSS Summer Workshop 2012-13).

I Analysis of a specific 3-colour model (Girard, Seligman, Liu).

I Laboratory experiment (today’s talk).

I We aim to generate hypotheses about beliefs that can beexperimentally validated, and conjectures about the modelthat can be proved.

Research programme

Progress so far

I Exploration of simulations (with Alex Raichev, as shown forexample in CMSS Summer Workshop 2012-13).

I Analysis of a specific 3-colour model (Girard, Seligman, Liu).

I Laboratory experiment (today’s talk).

I We aim to generate hypotheses about beliefs that can beexperimentally validated, and conjectures about the modelthat can be proved.

Research programme

Progress so far

I Exploration of simulations (with Alex Raichev, as shown forexample in CMSS Summer Workshop 2012-13).

I Analysis of a specific 3-colour model (Girard, Seligman, Liu).

I Laboratory experiment (today’s talk).

I We aim to generate hypotheses about beliefs that can beexperimentally validated, and conjectures about the modelthat can be proved.

Research programme

Progress so far

I Exploration of simulations (with Alex Raichev, as shown forexample in CMSS Summer Workshop 2012-13).

I Analysis of a specific 3-colour model (Girard, Seligman, Liu).

I Laboratory experiment (today’s talk).

I We aim to generate hypotheses about beliefs that can beexperimentally validated, and conjectures about the modelthat can be proved.

Experimental setup

DECIDE lab

I A dedicated space for computer experiments by volunteerparticipants.

I 32 machines on a local area network.

I Located in OGGB Level 0.

I Directors F. Beltran, A. Chaudhuri, V. Pavlov.

Experimental setup

DECIDE lab

I A dedicated space for computer experiments by volunteerparticipants.

I 32 machines on a local area network.

I Located in OGGB Level 0.

I Directors F. Beltran, A. Chaudhuri, V. Pavlov.

Experimental setup

DECIDE lab

I A dedicated space for computer experiments by volunteerparticipants.

I 32 machines on a local area network.

I Located in OGGB Level 0.

I Directors F. Beltran, A. Chaudhuri, V. Pavlov.

Experimental setup

DECIDE lab

I A dedicated space for computer experiments by volunteerparticipants.

I 32 machines on a local area network.

I Located in OGGB Level 0.

I Directors F. Beltran, A. Chaudhuri, V. Pavlov.

Experimental setup

Our pilot experiment - motivation

I We aim to get a sense of how things work at micro level.

I We also wanted to look at the role of information on themacro behaviour.

I We chose an extreme topology intended to bring out largeeffects. This necessitated a directed network which makes iteven less realistic.

I We need to look for large effects, given the small number ofparticipants.

Experimental setup

Our pilot experiment - motivation

I We aim to get a sense of how things work at micro level.

I We also wanted to look at the role of information on themacro behaviour.

I We chose an extreme topology intended to bring out largeeffects. This necessitated a directed network which makes iteven less realistic.

I We need to look for large effects, given the small number ofparticipants.

Experimental setup

Our pilot experiment - motivation

I We aim to get a sense of how things work at micro level.

I We also wanted to look at the role of information on themacro behaviour.

I We chose an extreme topology intended to bring out largeeffects. This necessitated a directed network which makes iteven less realistic.

I We need to look for large effects, given the small number ofparticipants.

Experimental setup

Our pilot experiment - motivation

I We aim to get a sense of how things work at micro level.

I We also wanted to look at the role of information on themacro behaviour.

I We chose an extreme topology intended to bring out largeeffects. This necessitated a directed network which makes iteven less realistic.

I We need to look for large effects, given the small number ofparticipants.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Our pilot experiment - details

I 30 subjects.

I Computers linked according to a fixed directed graph chosenby us.

I There are 5 questions.

I Subjects are given a question with an objectively correctanswer, and choose one of 3 options.

I There are 3 answers given: the correct one, an incorrect one,and “I don’t know”.

I At each iteration, each node receives information on thefraction of its feeds choosing each option. They can changetheir answer if desired.

Experimental setup

Difficulties with experimental work

I Ethics approval.

I Payments to subjects.

I Subjects not following instructions, or treating the experimentseriously.

I Equipment failures.

I Unanticipated problems occurring in real time.

Experimental setup

Difficulties with experimental work

I Ethics approval.

I Payments to subjects.

I Subjects not following instructions, or treating the experimentseriously.

I Equipment failures.

I Unanticipated problems occurring in real time.

Experimental setup

Difficulties with experimental work

I Ethics approval.

I Payments to subjects.

I Subjects not following instructions, or treating the experimentseriously.

I Equipment failures.

I Unanticipated problems occurring in real time.

Experimental setup

Difficulties with experimental work

I Ethics approval.

I Payments to subjects.

I Subjects not following instructions, or treating the experimentseriously.

I Equipment failures.

I Unanticipated problems occurring in real time.

Experimental setup

Difficulties with experimental work

I Ethics approval.

I Payments to subjects.

I Subjects not following instructions, or treating the experimentseriously.

I Equipment failures.

I Unanticipated problems occurring in real time.

Experimental setup

Incentives to participate

I We offered cash incentives for obtaining the correct answer.

I Payments: 10 units for correct, 0 for incorrect/no answer, 6for “I don’t know”.

I We hope this will induce sincere behaviour. How to check thisafter the fact?

Experimental setup

Incentives to participate

I We offered cash incentives for obtaining the correct answer.

I Payments: 10 units for correct, 0 for incorrect/no answer, 6for “I don’t know”.

I We hope this will induce sincere behaviour. How to check thisafter the fact?

Experimental setup

Incentives to participate

I We offered cash incentives for obtaining the correct answer.

I Payments: 10 units for correct, 0 for incorrect/no answer, 6for “I don’t know”.

I We hope this will induce sincere behaviour. How to check thisafter the fact?

Experimental setup

The questions (which we rephrased as multiple choice)

I (Cognitive reflection test, Frederick 2005): If it takes 5machines 5 minutes to make 5 widgets, how long would ittake 100 machines to make 100 widgets?

I (Wason test, Wason 1966)http://en.wikipedia.org/wiki/Wason_selection_task

I What is the first name of the character played by Paul Walkerin the Fast and Furious movies?

I Note that some are experience-based and othersreasoning-based. Also we expect the beliefs about theknowledge of others to vary between questions.

Experimental setup

The questions (which we rephrased as multiple choice)

I (Cognitive reflection test, Frederick 2005): If it takes 5machines 5 minutes to make 5 widgets, how long would ittake 100 machines to make 100 widgets?

I (Wason test, Wason 1966)http://en.wikipedia.org/wiki/Wason_selection_task

I What is the first name of the character played by Paul Walkerin the Fast and Furious movies?

I Note that some are experience-based and othersreasoning-based. Also we expect the beliefs about theknowledge of others to vary between questions.

Experimental setup

The questions (which we rephrased as multiple choice)

I (Cognitive reflection test, Frederick 2005): If it takes 5machines 5 minutes to make 5 widgets, how long would ittake 100 machines to make 100 widgets?

I (Wason test, Wason 1966)http://en.wikipedia.org/wiki/Wason_selection_task

I What is the first name of the character played by Paul Walkerin the Fast and Furious movies?

I Note that some are experience-based and othersreasoning-based. Also we expect the beliefs about theknowledge of others to vary between questions.

Experimental setup

The questions (which we rephrased as multiple choice)

I (Cognitive reflection test, Frederick 2005): If it takes 5machines 5 minutes to make 5 widgets, how long would ittake 100 machines to make 100 widgets?

I (Wason test, Wason 1966)http://en.wikipedia.org/wiki/Wason_selection_task

I What is the first name of the character played by Paul Walkerin the Fast and Furious movies?

I Note that some are experience-based and othersreasoning-based. Also we expect the beliefs about theknowledge of others to vary between questions.

Experimental setup

The topology we used

Preliminary results

Convergence to truth

Preliminary results

Convergence to falsehood

Preliminary results

Degrees do not matter much

Preliminary results

Unclear what this means

Preliminary results

Possible followup work

I Concentrate on effects of topology.

I Allow participants to construct their own network.

I Your ideas?

Preliminary results

Possible followup work

I Concentrate on effects of topology.

I Allow participants to construct their own network.

I Your ideas?

Preliminary results

Possible followup work

I Concentrate on effects of topology.

I Allow participants to construct their own network.

I Your ideas?