Collective Decision Making Systems:

From the Ideal State to Human Eudaimonia

Marko A. RodriguezT-5, Center for Nonlinear StudiesLos Alamos National Laboratory

http://markorodriguez.com

February 13, 2009

Collaborators

• Jennifer H. Watkins

? International and Applied Technology

? Los Alamos National Laboratory

? http://public.lanl.gov/jhw

• Alberto Pepe

? Center for Embedded Networked

Sensing

? University of California at Los Angeles

? http://albertopepe.com

Collective Decision Making SystemsLos Alamos National Laboratory

http://cdms.lanl.gov

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Why do we do the things we do?

• Few scholastic disciplines have within them an explicit ideal beyond theproduction of knowledge.

• With computer science and engineering, the implicit ideal is to ensurebetter living through circuitry.

• Personally, my motivation is driven by the sense that social algorithmswill lead to a greater human experience.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

The Eighteenth Century’s Age of Enlightenment

• Citizen’s began to question the traditional forms of aristocratic and monarchic

governance and began to envision an ideal state.

• The United States was the social experiment to achieve this ideal state.

• Unfortunately, the ideals of these thinkers could not reach their purest forms due to the

limitations of the technology at the time. Moreover, as a people we should value the

ideals, not the implementation of government.1

Marquis de Condorcet Thomas Paine Adam Smith

1Marko A. Rodriguez and Jennifer H. Watkins, “Revisiting the Age of Enlightenment from a Collective Decision Making

Systems Perspective”, LA-UR-09-00324, February 2009.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Marquis de Condorcet (French: 1743 – 1794)Social Choice Theory

0 10 20 30 40 50 60 70 80 90 100

0.0

0.2

0.4

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0.8

1.0

p

n

• Suppose a group of n decision makers under a two option, majority rule vote, where each decisionmaker has probability p of choosing the optimal option.

• If p > 0.5 and as n→∞, then the probability of yielding the optimal decision approaches 1.0.

• if p < 0.5 and as n→∞, then the probability of yielding the optimal decision approaches 0.0.

• Condorcet’s Jury Theorem is considered the first non-ethical justification for democratic governance2.2

Marquis de Condorcet, “Essai sur l’Application de l’Analyse aux Probabilites des Decisions prises a la Pluralite des Voix”,

1785.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Thomas Paine (English: 1737 – 1809)Representation – Ensuring a Large Population

• Ardent supporter of the American Revolution. His passion was drivenprimarily by his ideal of self-governance.3

• When a population is small, “some convenient tree will afford them aState house.”

• As the population increases in size, representatives must “act in thesame manner as the whole body would act were they present.”

3Thomas Paine, “Common Sense”, 1776.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Dynamically Distributed Democracy

• Imagine a government architecture where there is no a priori establishedpower structure: no president, no representatives, no senators.

• Imagine an Internet-based, fraud-proof, direct democratic, decisionmaking system.

• Problem: there are too many decisions and not enough time in acitizen’s day to participate in all decision making processes.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Dynamically Distributed Democracy

xi = 1.0

xj = 0.5

xk = 0.0

• x ∈ [0, 1]: voter tendency.

• A ∈ Rn×n+ : the social network.

• a ∈ {0, 1}n: k-percent participation.

• y ∈ Rn+: received vote power.

• π ∈ Rn+: propagated vote power.

4

Dynamically distributed democracy is a social representa-tion algorithm that provides a means by which any subset ofthe population can accurately simulate the decision makingresults of the whole population [4]. As such, the algorithm re-flects the primary tenet of representation as originally outlinedby Thomas Paine. The argument for the use of the algorithm asa mechanism for representation goes as follows. Not everyonein a population needs to vote as others in that same populationmore than likely have a nearly identical political tendency andthus, identical vote. What does need to be recorded is thefrequency of that sentiment in the population. If an active,voting citizen is similar in tendency to 10 non-active citizens,then the active citizen’s ballot can be weighted by 10 to reflectthe tendencies of the non-participating citizens. Dynamicallydistributed democracy accomplishes this weighting througha similarity- or trust-based social network that is used topropagate voting “power” to active voters so as to mitigatethe error incurred by waning citizen participation.

As previously stated, let x ! [0, 1]n denote the politicaltendency of each citizen in this population, where xi is thetendency of citizen i and, for the purpose of simulation, isdetermined from a uniform distribution. Assume that everycitizen in a population of n citizens uses some social network-based system to create links to those individuals that theybelieve reflect their tendency the best. In practice, these linksmay point to a close friend, a relative, or some public figurewhose political tendencies resonate with the individual. Inother words, representatives are any citizens, not politicalcandidates that serve in public office. Let A ! [0, 1]n!n denotethe link matrix representing the network, where the weight ofan edge, for the purpose of simulation, is denoted

Ai,j =

!1" |xi " xj | if link exists0 otherwise.

In words, if two linked citizens are identical in their politicaltendency, then the strength of the link is 1.0. If their tendenciesare completely opposing, then their trust (and the strength ofthe link) is 0.0. Note that a preferential attachment networkgrowth algorithm is used to generate a degree distribution thatis reflective of typical social networks “in the wild” (i.e. scale-free properties). Moreover, an assortativity parameter is usedto bias the connections in the network towards citizens withsimilar tendencies. The assumption here is that given a systemof this nature, it is more likely for citizens to create links tosimilar-minded individuals than to those whose opinions arequite different. The resultant link matrix A is then normalizedto be row stochastic in order to generate a probability distribu-tion over the weights of the outgoing edges of a citizen. Figure6 presents an example of an n = 100 artificially generatedtrust-based social network, where red denotes a tendency of0.0, purple a tendency of 0.5, and blue a tendency of 1.0.

Given this social network infrastructure, it is possible to bet-ter ensure that the collective tendency and vote is appropriatelyrepresented through a weighting of the active, participatingpopulation. Every citizen, active or not, is initially provide with1n “vote power” and this is represented in the vector ! ! Rn

+,such that the total amount of vote power in the population is

Fig. 6. A visualization of a network of trust links between citizens. Eachcitizen’s color denotes their “political tendency”, where full red is 0, full blueis 1, and purple is 0.5. The layout algorithm chosen is the Fruchterman-Reingold layout.

1. Let y ! Rn+ denote the total amount of vote power that has

flowed to each citizen over the course of the algorithm. Finally,a ! {0, 1}n denotes whether citizen i is participating (ai = 1)in the current decision making process or not (ai = 0). Thevalues of a are biased by an unfair coin that has probability kof making the citizen an active participant and 1"k of makingthe citizen inactive. The iterative algorithm is presented below,where # denotes entry-wise multiplication and " $ 1.

! % 0while

"i"ni=1 yi < " do

y % y + (! # a)! % ! # (1" a)! % A!

end

In words, active citizens serve as vote power “sinks” inthat once they receive vote power, from themselves or froma neighbor in the network, they do not pass it on. Inactivecitizens serve as vote power “sources” in that they propagatetheir vote power over the network links to their neighborsiteratively until all (or ") vote power has reached activecitizens. At this point, the tendency in the active populationis defined as #tend = x · y. Figure 4 plots the error incurredusing dynamically distributed democracy (black line), wherethe error is defined as

etendk = |dtend

100 " #tendk |.

Next, the collective vote #votek is determined by a weighted

majority as dictated by the vote power accumulated by activeparticipants. Figure 5 plots the proportion of votes that aredifferent from what a fully participating population wouldhave rendered (black line). In essence, if a citizen, for anyreason, is unable to participate in a decision making process,

• Collective tendency: y · x• The round of y · x is the collective vote.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Dynamically Distributed Democracy

percentage of active citizens

error

100 90 80 70 60 50 40 30 20 10 0

0.00

0.05

0.10

0.15

0.20

(n)

error =

!!!!!"

1n

i!n#i=1

xi

$! (x · y)

!!!!!

dynamically distributed democracy

direct democracy

percentage of active citizens

pro

port

ion o

f corr

ect decis

ions

100 90 80 70 60 50 40 30 20 10 0

0.500.600.700.800.901.00

(n)

dynamically distributed democracy

direct democracy

• A parameter k ∈ [0, 1] denotes the percentage of citizens that are actively

participating.

• Any subset of the whole can be made to behave as the whole. In other words, “act in

the same manner as the whole body would act were they present.”

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Adam Smith (Scottish: 1723 – 1790)Self Interested Actors - Ensuring an Enlightened Majority

• When a citizen pursues “his own interest he frequently promotesthat of the society more effectually than when he really intends topromote it”.4

• Market mechanisms are not only useful for determining commodity pricesas they can be generally applied to information aggregation.

4Adam Smith, “An Inquiry in the Nature and Causes of the Wealth of Nations”, 1776.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Decision Markets

• A decision market functions because it guarantees a return oninvestment for quality information.

• A decision market is a tool for attracting a population ofknowledgeable citizens much like a commodity market is a tool forattracting knowledgeable speculators.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Decision Markets

[1,1,1]

[0,0,0] [0.7,0,0]

[0,0,0.4]

[0.7,0.6,0]

[0.5,0,0.4]

[0.7,0.6,0.7]

[0.5,0.5,0.4]

e

m

• e ∈ {1}d: the environment.

• m ∈ [0, 1]d: the market.

• red path: incentive-free market.

• blue path: incentive market.

• Market accuracy: 1√d

qPi≤di=1(mi − ei)2.

• Rounding each dimension of m yields the

collective decision.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Decision Markets

average citizen knowledge

error

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(p)

error =1!d

!""#i!d$i=1

(mi " ei)2

incentive market

incentive-free market

average citizen knowledge

pro

port

ion o

f corr

ect decis

ions

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(p)

incentive market

incentive-free market

• Incentives in decision making ensure a thoughtful contribution ofknowledge.

• Moreover, it ensures participation from those who have knowledge of thedomain.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Artistotle (Greek: 384 – 322 B.C.)Eudaimonia – Ensuring a Virtuous Citizenry

• Being virtuous is repeatedly choosing correctly.

• Habitual correct behavior leads to the ultimate, objective goal of life: eudaimonia –

complete engagement in the world, doing what you do because nothing else matters.5,6

• Can systems aid citizens in choosing correctly – in all aspects of life?

Aristotle

5Aristotle, “Nicomachean Ethics”, 350 B.C.

6Mihaly Csikszentmihalyi, “Flow: The Psychology of Optimal Experience”, Harper Perennial, 1990.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Recommendation Systems

But if the development of character is a the moral objective, it is obvious that[...] the choices of vocation and avocations to pursue, of friends to cultivate, ofbooks to read are moral for they clearly influence such development.7

• Web services are continuing to build richer models of humans, resources,and the relationships between them.

• There exists an increasing reliance on such services to aid in decisionmaking: correct books (Amazon.com), correct movies (NetFlix.com),correct music (Pandora), correct occupation (Monster.com), correctfriends (PointsCommuns.com), correct life partner (Match.com), etc.

7David L. Norton, “Democracy and Moral Development: A Politics of Virtue”, University of California Press, 1991.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Grammar-Based Random Walkers

• Algorithms can search multi-relational data structures in a way thatbiases towards the requirements of the problem domain?8

? What venue should I submit this article to?? Who is the best person to peer-review this article?? Who should I talk to at this conference and what should I talk to them about?

Person

Document Document

read

cites

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authored

Conference

attending attending

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editorOf

Journal

containedIn

? ?Institution

affiliation

sponsors

8Marko A. Rodriguez, “Grammar-Based Random Walkers”, Knowledge-Based Systems, 21(7), pp. 727-739, 2008.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009

Conclusion

• Thomas Jefferson stated that the purpose of a government is to ensure“life, liberty, and the pursuit of happiness.”

• Are we as a society still too myopic to take on the bigger task of ensuringlife, liberty, and the guarantee of eudaimonia?

• This is the only reason why we should do the things we do.9

• Collective decision making systems offer solutions to this age oldproblem.10

9Marko A. Rodriguez and Alberto Pepe, “Faith in the Algorithm, Part 1: Beyond the Turing Test”, 2008.

10Jennifer H. Watkins and Marko A. Rodriguez, “A Survey of Collective Decision Making Systems”, in Studies in

Computational Intelligence: Evolution of the Web in Artificial Intelligence Environments, Springer-Verlag, pp. 245–279, 2008.

External Advisory Committee Presentation – Los Alamos, New Mexico – February 13, 2009