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Home , Age of Enlightenment, Marquis de Condorcet, Thomas Paine

1 Revisiting the from a Collective Decision Making Systems Perspective Marko A. Rodriguez and Jennifer H. Watkins Los Alamos National Laboratory Los Alamos, New Mexico 87545

Abstract—The ideals of the eighteenth century’s Age of En- systems that maintain and support these merit no such lightenment are the foundation of modern . The permanence. While modern democratic strive to era was characterized by thinkers who promoted progressive achieve the ideals of the Enlightenment, it is put forth that social reforms that opposed the long-established aristocracies and of the time. Prominent examples of such reforms governments can better serve them by making greater use of include the establishment of inalienable , self- the technological advances of the present day . governing , and market . Twenty-first cen- The technological infrastructure that now supports modern tury democratic nations can benefit from revisiting the systems nations removes the physical restrictions that dictated many developed during the Enlightenment and reframing them within of the design choices of these early architects. As the techno-social context of the Information Age. This article explores the application of social algorithms that make use such, many of today’s government structures are remnants of of ’s (English: 1737–1809) representatives, Adam the technological constraints of the eighteenth century. Modern Smith’s (Scottish: 1723–1790) self-interested actors, and Marquis nations have an obligation to improve their systems so as to de Condorcet’s (French: 1743–1794) optimal decision making better ensure the fulfillment of the . Inscribed at groups. It is posited that -enabled social algorithms can the is this statement by better realize the ideals articulated during the Enlightenment. (American: 1743–1826), another thinker of the Enlightenment: Index Terms—collective decision making, computational gover- “[...] institutions must go hand in hand with the nance, e-participation, e-, computational social choice of the human mind. As that becomes more developed, more theory. enlightened [...] institutions must advance also to keep pace with the times.” To move in this direction, the principle of I.INTRODUCTION citizen representation as articulated by Thomas Paine (En- Eighteenth century is referred to as The Age of glish: 1737–1809) and the principle of competitive actors for Enlightenment, a period when prominent thinkers began to the common good as articulated by (Scottish: question traditional forms of authority and power and the 1723–1790) are considered from a techno-social, collective moral standards that supported these forms. One of the most decision making systems perspective. Moreover, the rationale significant and enduring contributions of the time was the for these principles can be understood within the mathematical notion that a government’s existence should be predicated on formulations of ’s (French: 1743–1794) protecting and supporting the natural, immutable rights of its requirements for optimal decision making. citizens. Among these rights are the right to self-governance, of thought, and equality. The inherent virtue of II.THE CONDORCET JURY THEOREM:ENSURING these ideas forced many European nations to relinquish time- OPTIMAL DECISION MAKING arXiv:0901.3929v2 [cs.CY] 31 Jul 2009 honored aristocratic and monarchic systems. Moreover, it was the of the Enlightenment that inspired the Marquis de Condorcet (portrayed in Figure 1) ardently formalization of a governing structure that would define a new supported equal rights and free and universal public . nation: the of America. These ideals were driven as much by his as they were Natural rights exposed during the Enlightenment are im- by his mathematical investigations into the requirements for mutable. That is, they are rights not granted by the govern- optimal decision making. One of his most famous results is ment, but instead are rights inherent to man. However, the the Condorcet statement and its associated theorem. In his 1785 Essai sur l’Application de l’Analyse aux Probabilites´ des M.A. Rodriguez is with T-5/Center for Nonlinear Studies, Los Alamos Decisions prises a` la Pluralite´ des Voix (english : National Laboratory, Los Alamos, NM 87545 USA e-mail: [email protected]. Jennifer H. Watkins is with the International and Applied Technology on the Application of Analysis to the Probability of Group, Los Alamos National Laboratory, Los Alamos, NM 87545 USA e- Majority Decisions), Condorcet states that when a group of mail: [email protected]. “enlightened” decision makers chooses between two options This research was conducted by the Collective Decision Making Systems (CDMS) project at the Los Alamos National Laboratory under a majority rule, then as the size of the decision making (http://cdms.lanl.gov). population tends toward infinity, it becomes a certainty that Rodriguez, M.A., Watkins, J.H., “Revisiting the Age of Enlightenment from the best choice is rendered [1]. The first statistical proof a Collective Decision Making Systems Perspective,” First Monday, volume 14, number 8, ISSN:1396-0466, LA-UR-09-00324, University of Illinois at of this statement is the Condorcet jury theorem. The model Chicago Library, August 2009. is expressed as follows. Imagine there exists n independent 2

Unfortunately, the theorem does not suggest a means to achieve these conditions, though in practice many mechanisms do exist that strive to meet them. For instance, democracies do not rely on a single decision maker, but instead use senates, parliaments, and referendums to increase the size of their voting population. Moreover, for general elections, equal voting rights facilitate large citizen participation. Furthermore, democratic nations tend to promote universal public education so as to ensure that competent leaders are chosen from and by an enlightened populace. It is noted that the practices employed by democratic nations to ensure competent decision making are implementation choices, and a must not the implementation of its government. must be forgone if another implementation would serve better. Im- Fig. 1. A portrait of Marquis de Condorcet. This is a public domain photograph courtesy of Wikimedia Commons. plementations of government should be altered and amended so as to better realize the ideals of . Technology-enabled social algorithms may provide a means by which to reliably achieve the conditions of the “light” side decision makers and each decision maker has a probability of the Condorcet jury theorem, thus ensuring optimal decision p [0, 1] of choosing the best of two options in a decision. making. Furthermore, modern algorithms have the potential to ∈ If p > 0.5, meaning that each individual decision maker is do so in a manner that better honors the right of each citizen to enlightened, and as n , the probability of a majority vote participate in government decision making as such algorithms → ∞ outcome rendering the best decision approaches certainty at are not constrained by eighteenth century technology. Present 1.0. This is known as the “light side” of the Condorcet jury day social algorithms, in the form of information retrieval theorem. The “dark side” of the theorem states that if p < 0.5 and recommendation services, already contribute significantly and as n , the probability of a majority vote outcome to the augmentation of human and social intelligence [2]. In → ∞ rendering the best decision approaches 0.0. Figure 2 plots the line with these developments, this article presents two social relationship between p and n, where the gray scale values algorithms that show promise as mechanisms for governance- denote a range from 100% probability of the group rendering based collective decision making. One algorithm exaggerates the best decision (white) to a 0% probability (). Thomas Paine’s citizen representation in order to accurately simulate the behavior of a large decision making population

1.0 (n ), and the other employs Adam Smith’s market → ∞ philosophy to induce participation by the enlightened within that population (p 1). Both algorithms utilize the Condorcet 0.8 → jury theorem to the society’s advantage.

0.6 III.DYNAMICALLY DISTRIBUTED DEMOCRACY: p SIMULATING A LARGE DECISION MAKING POPULATION 0.4 0.2 0.0 0 10 20 30 40 50 60 70 80 90 100 n

Fig. 2. The relationship between p ∈ [0, 1] and n ∈ (1, 2,..., 100) according to the Condorcet jury theorem model. Darker values represent a lower probability of a majority vote rendering the best decision and the lighter values represent a higher probability of a majority vote rendering the best decision.

The Condorcet jury theorem is one of the original formal justifications for the application of democratic principles to government. While the theorem does not reveal any startling Fig. 3. An oil portrait of Thomas Paine painted by Auguste Milliere` in 1880. This is a public domain photograph courtesy of Wikimedia Commons. conditions for a successful democracy, it does distill the neces- sary conditions to two variables (under simple assumptions). If a decision making group has a large n and a p > 0.5, then the Thomas Paine (portrayed in Figure 3) was born in , group is increasing its chances of optimal decision making. but in his middle years, he relocated to America on the 3 recommendation of . It was in America, dtend [0, 1] and dvote 0, 1 denote the collective tendency 100 ∈ 100 ∈ { } in the time leading up to the American , that his and vote given by 100% participation. Let dtend [0, 1] and k ∈ enlightened ideals were well received. In 1776, the year in dvote 0, 1 denote the collective tendency and vote if k ∈ { } which the Declaration of Independence was written, Thomas only k-percent of the population participates. The error in the Paine wrote a widely distributed pamphlet entitled Common collective tendency for k-percent participation is calculated as Sense which outlined the values of a democratic society etend = dtend dtend . [3]. This pamphlet discussed the equality of man and the k | 100 − k | necessity for all those at stake to partake in the decision The further away the active voters’ collective tendency is from making processes of the group. As a formal justification of the full population’s collective tendency, the higher the error. this value, the Condorcet jury theorem would hold that a The gray line in Figure 4 plots the relationship between k direct democracy would be the most likely democracy to yield and etend. As citizen participation wanes, the ability for the optimal decisions as the voting population is the largest it can k remaining, active participants to reflect the tendency of the possibly be for a nation. In practice, the desire for a direct whole becomes more difficult. Next, the error in the collective democracy is tempered by the tremendous burden that constant vote is calculated as the proportion of voting outcomes that voting would impinge on citizens (not to mention the logistical are different than what a fully participating population would problems such a model would incur within present day voting have voted and is denoted evote. The gray line in Figure 5 plots infrastructures). For this , representation is required. k the relationship between k and evote. As participation wanes, Thomas Paine states that when populations are small “some k the proportion of decisions that differ from what would have convenient tree will afford them a State house”, but as the pop- occurred given full participation decreases. As with collective ulation increases it becomes a necessity for representatives to tendency, a small active voter population is unable to replicate act on behalf of their constituents. Moreover, the central tenet the voting behavior of the whole. 4 of political representation is that representatives “act in the same manner as the whole body would act were they present.” The remainder of this section presents a social algorithm that direct democracy 0.20 dynamically distributed democracy simulates the manner in which the whole population would act 0.95 without requiring pre-elected, long-standing representatives.

Assuming a two-option majority rule, an individual citizen’s 0.15 judgement can be placed along a continuum between the 0.80 two options such that the “political tendency” of citizen i error is denoted x [0, 1]. For example, given United States 0.10 i ∈ , a political tendency of 0 represents a fully Republican 0.65 perspective, a tendency of 1 represents a fully Democratic 0.05 dynamically distributed democracy perspective, and a tendency of 0.5 denotes a moderate. Given direct democracy this definition, there are two ways to quantify the population proportion of correct decisions 0.50 0.00 as a whole. One way is to calculate the average tendency of 100100 9090 8080 7070 6060 5050 4040 3030 2020 1010 00 1 i n all citizens. That is dtend = ≤ x , where dtend [0, 1] is n i=1 i ∈ percentagepercentage of of active active citizenscitizens (n) the collective tendency of the population. Given a uniform P distribution of political tendency within x, the collective tendvote Fig.Fig. 4. 5. The relationship between kk andand eekk forfor direct direct democracy democracy (gray (gray tendency approaches 0.5 as the size of the population increases line)line) and and dynamically dynamically distributed distributed democracy democracy (black (black line). line). The The plot plot provides provides the toward infinity. The other way to quantify the group is to averagethe proportion error over of identical, a simulation correct that decisions was run with over 1000 a simulation artificially that generated was run networkswith 1000 composed artificially of generated 100 citizens networks each. composed of 100 citizens each. require that the citizen’s tendency be reduced to a binary Fig. 6. A visualization of a network of trust links between citizens. Each option (i.e. a two option vote). If a citizen has a political citizen’s color denotes their “political tendency”, where full red is 0, full blue tendency that is less than 0.5, then they will vote 0. For a Dynamically distributed democracy is a social representa- is 1, and purple is 0.5. The layout algorithm chosen is the Fruchterman- tendency greater than 0.5, they will vote 1. If they have a tionAs algorithm previously that stated, provides let ax means[0, 1] byn whichdenote any the subset political of Reingold layout. ∈ tendency equal to 0.5 then a fair coin toss will determine their thetendency population of each can citizen accurately in this simulate population, the decision where x makingi is the vote. This majority wins vote is denoted dvote 0, 1 . resultstendency of the of wholecitizen populationi and, for [4]. the As purpose such, the ofsimulation, algorithm re- is ∈ { } Imagine a direct democracy in the purest sense, where a flectsdetermined the primary from tenet a uniform of representation distribution. as Assume originally that outlined every 1 “vote power” and this is represented in the vector π Rn , n ∈ + raise of hands or a shout of voices is replaced by an Internet bycitizen Thomas in a Paine. population The argument of n citizens for the uses use some of the social algorithm network- as such that the total amount of vote power in the population is architecture and a sophisticated error- and fraud-proof ballot abased system for to representation create linksto goes those as follows. individuals Not everyone that they 1. Let y Rn denote the total amount of vote power that has ∈ + system. All citizens have the potential to vote on any decisions inbelieve a population reflect theirneeds tendency to vote as the others best. in In that practice, same population these links flowed to each citizen over the course of the algorithm. Finally, they wish; if they cannot vote on a particular decision for moremay pointthan likely to a close have afriend, nearly a identical relative, political or some tendency public figure and a 0, 1 n denotes whether citizen i is participating (a =1) ∈ { } i whatever reason, they abstain from participating. In practice, thus,whose identical political vote. tendencies What does resonate need with to be the recorded individual. is the In in the current decision making process or not (ai =0). The not every decision will be voted on by all n citizens. Citizens frequencyother words, of that representatives sentiment in are the any population. citizens, If not an political active, values of a are biased by an unfair coin that has probability k n n will be constrained by time pressures to only participate votingcandidates citizen that is serve similar in public in tendency office. to Let10Anon-active[0, 1] × citizens,denote of making the citizen an active participant and 1 k of making ∈ − in those votes in which they are most informed or most thenthe link the active matrix citizen’s representing ballot the can network, be weighted where by the10 weightto reflect of the citizen inactive. The iterative algorithm is presented below, passionate. If we assume that all citizens have a tendency, theanedge, tendencies for the of purpose the non-participating of simulation, citizens. is denoted Dynamically where denotes entry-wise multiplication and " 1. ◦ ≈ whether they vote or not, how would the collective tendency distributed democracy accomplishes this weighting through and collective vote change as citizen participation waned? Let a similarity- or trust-based1 xi socialxj networkif link exists that is used to Ai,j = − | − | π 0 !0 otherwise. ← i n while i=1≤ yi < " do y y +(π a) In words, if two linked citizens are identical in their political π ←"π (1 ◦a) tendency, then the strength of the link is 1.0. If their tendencies π ← A◦π − are completely opposing, then their trust (and the strength of end ← the link) is 0.0. Note that a preferential attachment network growth algorithm is used to generate a degree distribution that is reflective of typical social networks “in the wild” (i.e. scale- In words, active citizens serve as vote power “sinks” in free ). Moreover, an assortativity parameter is used that once they receive vote power, from themselves or from to bias the connections in the network towards citizens with a neighbor in the network, they do not pass it on. Inactive similar tendencies. The assumption here is that given a system citizens serve as vote power “sources” in that they propagate of this nature, it is more likely for citizens to create links to their vote power over the network links to their neighbors similar-minded individuals than to those whose opinions are iteratively until all (or ") vote power has reached active quite different. The resultant link matrix A is then normalized citizens. At this point, the tendency in the active population to be row stochastic in order to generate a probability distribu- is defined as δtend = x y. Figure 4 plots the error incurred · tion over the weights of the outgoing edges of a citizen. Figure using dynamically distributed democracy (black line), where 6 presents an example of an n = 100 artificially generated the error is defined as trust-based social network, where red denotes a tendency of etend = dtend δtend . 0.0, purple a tendency of 0.5, and blue a tendency of 1.0. k | 100 − k | vote Given this social network infrastructure, it is possible to bet- Next, the collective vote δk is determined by a weighted ter ensure that the collective tendency and vote is appropriately majority as dictated by the vote power accumulated by active represented through a weighting of the active, participating participants. Figure 5 plots the proportion of votes that are population. Every citizen, active or not, is initially provide with different from what a fully participating population would 44 0.95 0.95 0.80 0.80 0.65 0.65

dynamicallydynamically distributed distributed democracy democracy directdirect democracy democracy proportion of correct decisions proportion of correct decisions 0.50 0.50 100100 9090 8080 7070 6060 5050 4040 3030 2020 1010 00 percentagepercentage of of active active citizenscitizens (n)

votevote Fig.Fig. 5. 5. The relationship between between kk andand eekk forfor direct direct democracy democracy (gray (gray line)line) and and dynamically dynamically distributed distributed democracy democracy (black (black line). line). The The plot plot provides provides thethe proportion proportion of of identical, identical, correct correct decisions decisions over over a a simulation simulation that that was was run run withwith 1000 1000 artificially artificially generated generated networks networks composed composed of of 100 100 citizens citizens each. each. Fig.Fig. 6. 6. A visualization of a network of trust links links between between citizens. citizens. Each Each citizen’scitizen’s color color denotes denotes their their “political “political tendency”, tendency”, where where full full red red is is00,, full full blue blue isis 11,, and and purple purple is is 00..55.. The The layout layout algorithm algorithm chosen chosen is is the the Fruchterman- Fruchterman- propagateAs previously voting “power” stated, let tox active[0, voters1]n denote so as the to mitigate political ReingoldReingold layout. layout. ∈ thetendency error incurred of each by citizen waning in this citizen population, participation. where xi is the tendencyAs previously of citizen stated,i and, let forx the[0, purpose1]n denote of simulation, the political is ∈ 1 n tendencydetermined of fromeach citizen a uniform in this distribution. population, Assume where thatxi is every the represented“vote power” through and athis weighting is represented of the in active, the vector participatingπ R , n ∈ + tendencycitizen in of a population citizen i and, of n forcitizens the purpose uses some of social simulation, network- is population.such that the Every total citizen, amount active of vote or not, power is initially in the populationprovide with is 1 n n determinedbased system from to a create uniform links distribution. to those individuals Assume that that every they 1.“vote Let y power”R+ denote and this the is total represented amount inof thevote vector powerπ thatR has, n ∈ ∈ + citizenbelieve in reflect a population their tendency of n citizens the best. uses In some practice, social these network- links suchflowed that to the each total citizen amount over ofthe vote course power of the in algorithm. the population Finally, is n n basedmay point system to a to close create friend, links a to relative, those orindividuals some public that figure they 1a. Let0y, 1 Rdenotesdenote whether the total citizen amounti is of participating vote power ( thatai =1 has) ∈ { ∈} + believewhose reflect political their tendencies tendency resonate the best. with In practice, the individual. these links In flowedin the tocurrent each citizen decision over making the course process of the or algorithm. not (ai =0 Finally,). The n mayother point words, to a representatives close friend, a arerelative, any or citizens, some public not political figure avalues0, of1 a aredenotes biased whether by an citizenunfair coini is participating that has probability (ai = 1k) n n ∈ { } whosecandidates political that serve tendencies in public resonate office. Let withA the[0 individual., 1] × denote In inof the making current the decisioncitizen an making active participant process or and not1 (ak=of 0 making). The ∈ −i otherthe link words, matrix representatives representing the are network, any citizens, where thenot weight political of valuesthe citizen of a inactive.are biased The by iterative an unfair algorithm coin that is has presented probability below,k n n candidatesan edge, for that the serve purpose in public of simulation, office. Let A is denoted[0, 1] × denote ofwhere makingdenotes the citizen entry-wise an active multiplication participant and and1 " k of1. making ∈ ◦ −≈ the link matrix representing the network, where the weight of the citizen inactive. The iterative algorithm is presented below, an edge, for the purpose1 ofx simulation,i xj if islink denoted exists where denotes entry-wise multiplication and  1. Ai,j = − | − | ◦ π 0 ≈ !0 otherwise. ← i n while i=1≤ yi < " do 1 xi xj if link exists Ai,j = − | − | π y0 y +(π a) In words, if two linked citizens are identical in their political ← ←"i n ◦ (0 otherwise. π π≤ y(1 this is accomplished through frequent elections [3]. The utilization of an Internet- based social network system affords repeated “elections” in the form of citizens creating outgoing links to other citizens as they please, when they please, and to whom them please. That is, citizens can dynamically choose representatives who need not be picked from only a handful of candidates. Moreover, if a selected representative falters in their ability to represent Fig. 7. An etching of Adam Smith originally created by Cadell and Davies a citizen, incoming links can be immediately retracted from (1811), John Horsburgh (1828), or R.C. Bell (1872). This is a public domain photograph courtesy of Wikimedia Commons. them. Such an architecture turns the representative’s status from that of elected public official to that of a self-intentioned citizen. While many countries have political institutions that are requirements of a society as a whole is difficult to know. Adam set up according to a left, right, and moderate agenda, the Smith appreciated markets for their ability to expose these individual perspectives of a citizen may be more complex. requirements through the “natural price” of goods. Moreover, In many cases, a citizen’s political tendency may only be he understood that within the market was a nec- amenable to a multi-dimensional representation. In a multi- essary driving force guaranteeing an accurate representation relational social network, the links are augmented with labels of commodity prices. Adam Smith states that when a citizen in order to denote the type of trust one citizen has for another. pursues “his own interest he frequently promotes that of In this way, voting power propagates over the links in a manner the society more effectually than when he really intends to that is biased to the domain of the decision. For example, promote it” [7]. citizen i may trust citizen j in the domain of “education” Market mechanisms are not only useful for determining but not in the domain of “health care”. This design has been commodity prices as they can be generally applied to informa- articulated in [5]. Supporting systems, including the means tion aggregation and ultimately, to collective decision making. by which ballots are proposed and issues are discussed, is Such markets are called decision markets [8]. Similar to a presented in [6]. division of labor, the knowledge required to make optimal With the Internet, supporting Web , and dy- decisions for a society is dispersed throughout the population. namically distributed democracy, it is possible to dynamically For difficult problems, it is na¨ıve to think that a single determine a representative-layer of government that accurately individual has the requisite knowledge to yield an optimal reflects a full direct democracy. In this respect, the larger decision, much like it is na¨ıve to think a single merchant will population helps to ensure, according to the Condorcet jury offer the optimal price. A decision market functions because theorem, that the decisions are either definitely right or def- it guarantees a return on investment for quality information. initely wrong. Other technologies can be utilized to induce In this respect, a decision market is a tool for attracting a participation by only those that are more likely than not to population of knowledgeable citizens much like a commodity choose the optimal decision. market is a tool for attracting knowledgeable speculators. In short, a decision market is a self-selection mechanism that incentivizes participation from those who have knowledge IV. DECISION MARKETS:INCENTIVIZINGAN regarding the problem and are confident in their knowledge ENLIGHTENED MAJORITY and discourages participation from others without forbidding Adam Smith (portrayed in Figure 7) was a Scottish moral it. and economic who is best known for his two most Decision markets reward individuals for buying low and famous works entitled The Theory of Moral Sentiments (1759) selling high, thus encouraging those who believe they know and An Inquiry into the Nature and Causes of the Wealth which way the market will move to contribute their infor- of Nations (1776). In the latter work, Adam Smith outlines mation in the form of the price at which they purchase the economic benefits of a division of labor within a society. and sell shares. A decision market differs from commodity Each citizen in the population serves a particular specialized markets (such as the New York Stock Exchange) in that stocks function, and only in the dependency relationships amongst represent objective states about the world that can ultimately these specialists does an efficient, decentralized economy be determined, but are presently unknown. For example, given emerge. With many suppliers and consumers, the production the market question “Will decisions markets be used in U.S. 6 government by the year 2013?”, shares of stocks in a “yes” space with both markets (bottom left purple point) and an outcome and in a “no” outcome are purchased and sold on environment (top right green point). The behavior of the the market. A high market price for a stock indicates that citizens denotes the market paths (red and blue arrows). Also, the collective believes this outcome to be true with a high there exists a p = 0.5 population of 3 citizens, where citizen likelihood. The purpose of the market is to incentivize knowl- c1 = [0.7, 0.5, 0.4], citizen c2 = [0.5, 0.6, 0.3], and citizen edgeable citizens to contribute to the decision by rewarding c3 = [0.3, 0.5, 0.7]. At time step t = 0, both the incentive- them for useful contributions and conversely to inflict a penalty free and incentive markets are at [0, 0, 0]. At t = 1, citizen for contributing poor information. c1 participates in both markets. In the incentive-, In order to demonstrate the benefits of incentives in decision citizen c1 has no incentive to contribute his best knowledge making, a simulation is provided. Suppose there exists n and thus, randomly chooses a dimension in which to move citizens and a d-dimensional “knowledge space”. Each citizen the market. According to the diagram, the citizen’s random is represented as a point in this space. That is, citizens have choice moves the market in the 3rd dimension by 0.4. In different degrees of knowledge in the various dimensions the incentivized market, citizen c1 chooses the dimension in (i.e. domains) of the space. A citizen’s point in this space is which he has the most knowledge (i.e. the dimension with generated by a normal distribution with a mean of p [0, 1] the maximum value). Moreover, a biased coin toss determines ∈ and a variance of (p(1 p))2. Next, there exists an objective whether he participates or not, where c1 has a 70% chance − in this spaced called the environment. For the purpose of participating in the incentive market. Assuming the coin of simulation, the environment e is the largest valued point in toss permits it, c1 moves the incentivized market in the 1st the knowledge space (i.e. e = 1 : 1 i d). There also dimension to 0.7. This process continues in sequence for i ≤ ≤ exists a market m which denotes the collective’s subjective citizens c2 and c3. Assuming that all citizens participate understanding of the objective environment. For the purpose in both markets, at the end, the incentive-free market is of simulation, the market starts as the smallest valued point in located at point [0.5, 0.5, 0.4], while the incentive market is the knowledge space (i.e. m = 0 : 1 i d). Each citizen located at point [0.7, 0.6, 0.7]. The market error is calculated i ≤ ≤ participates in the market, moving the market closer or further as the normalized Euclidean distance between the final market away from the environment. The closer the market is to the position and the environment for a given p, environment, the more accurate the collective decision. There i d are two markets in the simulation: an incentive-free market 1 ≤ edist = (e m )2. and an incentive market. The results of these two markets p √ v i − i dui=1 are compared in order to demonstrate the benefits of using uX t incentives. The incentive-free market has an error of 0.287 and the incentive market has an error of 0.113. Thus, the incentive [1,1,1] market is closest to the environment. There are two distinctions between the markets. In the incentive-free market, there is no benefit to producing an enlightened solution, so the cit-

[0.7,0.6,0.7] izen makes a contribution without comparing his knowledge against the environment. In the incentive market, there are two incentive structures. The first incentive is to participate along the dimension in which the citizen is most knowledgeable. [0.5,0.5,0.4] [0.7,0.6,0] The second incentive is to participate only if the citizen has a satisfactory degree of knowledge. This means that poor information is excluded from the market and that the most valuable knowledge of the citizen is included. To demonstrate the effects of an incentive-free and incentive market on a larger population, over various values of p, and in a 50-dimensional knowledge space simulation results are [0,0,0.4] [0.5,0,0.4] provided. Figure 9 depicts the normalized Euclidean distance error of the incentive-free market (gray line) and the incentive [0,0,0] [0.7,0,0] market (black line) for varying p. Next, Figure 10 provides the proportion of correct collective decisions. A decision is Fig. 8. The states of the incentive-free and incentive markets (purple) and the objective state of the environment (green) are diagrammed in a 3-dimensional either correct or incorrect. While the market yields a point in d knowledge space. There exists two paths: the incentive-free market path (red) [0, 1] , rounding the dimension values of the point to either and the incentive market path (blue). The dotted cubes denote the range of 1 or 0 provides the final decision made by the citizens. For an incentive-free market (red - 0.5) and incentive market (blue - 0.75) for a p p = 0.5. Refer to the text for a description of the diagrammed market paths. a given , the proportion of times that the market rounds to the environment is the proportion of correct decisions and is denoted edeci [0, 1]. p ∈ Before presenting the results of a larger simulation, a small It is the principle of self-selection, and therefore citizen diagrammed example is provided to better elucidate the sim- choice, that provides the mechanism by which knowledge ulation rules. Figure 8 diagrams a 3-dimensional knowledge is aggregated. Choice is manifested in a number of ways. 7

7

1.0 probability parameter of the Condorcet jury theorem model is misleading. It is not through probability that one achieves

1.0 the requisite knowledge in all dimensions to make informed incentive-free market 0.8 incentive market decisions.an optimal The ability decision, to reach but an optimal through decision the careful is de- application of

0.8 pendentknowledge on the many to the dimensions decision. such The that use ignorance of a of market is not a

0.6 one dimensionguarantee may that lead decision to a suboptimal makers conclusion. have p> The0.5. The market probability parameter of the Condorcet jury theorem model 0.6

error is a guarantee that citizen knowledge has been thoughtfully is misleading. It is not through probability that one achieves 0.4 error an optimalapplied decision, to the but decision. through the careful application of 0.4 knowledge to the decision. The use of a market is not a

0.2 guarantee that decision makers have p > 0.5. The market 0.2 V. CONCLUSION is a guarantee that citizen knowledge has been thoughtfully The purpose of a democratic government is to preserve and 0.0 applied to the decision. 0.0 1.0 0.91.0 0.90.8 0.80.7 0.70.60.6 0.50.5 0.40.4 0.30.3 0.20.20.10.10.0 0.0 support the ideals of its population. The ideals established V. CONCLUSION averageaverage citizen citizen knowledge knowledge (p) during the Enlightenment are general in nature: life, , Theand purpose the ofpursuit a democratic of happiness. government In is articulating to preserve and these values, the dist Fig. 9. The relationship between p distand ep for an incentive-free market support the ideals of its population. The ideals established Fig. 9. The relationship between p and ep for an incentive-free market (gray founders of modern democracies provided a moral heritage (gray line) and an incentive market (black line). The plot provides the average during the Enlightenment are general in nature: life, liberty, line) anderror an incentive over 1000 marketsimulations (black with line).d = 50 Theand plotn = 1000provides. the average error that remains highly regarded in today. However, it over 1000 simulations with d = 50 and n = 1000. and the pursuit of happiness. In articulating these values, the 7 foundersshould of modern be remembered democracies that provided it is a the moral ideals heritage that are valuable, that remainsnot the highly specific regarded implementation in societies today. of However, the systems it that protect 1.0 1.0 shouldprobabilityand be remembered support parameter them. that of it the isIf the Condorcet there ideals is that jury another are theorem valuable, implementation model of notis the misleading. specific implementation It is not through of probabilitythe systems that that one protect achieves

0.8 government that better realizes these ideals, then, by the rights 0.8 andan support optimal them. decision, If there but through is another the implementation careful application of of governmentknowledgeof man, that to it better the must realizesdecision. be enacted. these The ideals, use It then,of was a by marketthe the great rights is not thinkers a of the 0.6 0.6 ofguarantee man,eighteenth it must that be decision century enacted. makers It Enlightenment was the have greatp> thinkers who0.5. The ofprovided the market the initial

error eighteenthis agovernance guarantee century that Enlightenmentsystems. citizen knowledgeIt is who the provided challenge has been the thoughtfully andinitial the mandate of 0.4 0.4 governanceappliedthe Information to systems. the decision. It is Age thechallenge to redesign and these the mandate governance of systems in the Information Age to redesign these governance systems in

0.2 light of present day technologies. 0.2 light of present day technologies.V. CONCLUSION incentive-free market proportion of correct decisions incentive market

0.0 The purpose of a democratic government is to preserve and 0.0 REFERENCESREFERENCES 1.01.0 0.90.9 0.80.8 0.7 0.60.6 0.50.5 0.40.4 0.30.3 0.20.2 0.10.10.00.0 support the ideals of its population. The ideals established [1] M.[1] de Condorcet,M. de Condorcet, “Essai sur l’application “Essai sur de l’application l’analyse a´ la de probabilit l’analysee´ a´ la probabilite´ averageaverage citizen citizen knowledgeknowledge (p) during the Enlightenment are general in nature: life, liberty, des decisions´ des d renduesecisions´ a´ la rendues pluralite´a´ des la voix,” pluralit ,e´ des , voix,” 1785. Paris, France, 1785. [2] andJ. H. the Watkins pursuit and M. of A. happiness. Rodriguez, InEvolution articulating of the Web these in Artificial values, the dist deci [2] J. H. Watkins and M. A. Rodriguez, Evolution of the Web in Artificial Fig.Fig. 9. 10. The relationship The relationship between betweenp and ep andfor anep incentive-freefor an incentive-free market (gray foundersIntelligence of Environments modern, democracies ser. Studies in providedComputational amoral Intelligence. heritage p Intelligence Environments, ser. Studies in Computational Intelligence. line)market and (gray an incentive line) and market an incentive (black line).market The (black plotline). provides The the plot average provides error thatBerlin, remains DE: Springer-Verlag, highly regarded 2008, in ch. societies A Survey today. of Web-Based However, it overthe proportion1000 simulations of correct with decisionsd = 50 overand1000n =simulations 1000. with d = 50 and CollectiveBerlin, Decision DE: Making Springer-Verlag, Systems, pp. 245–279. 2008, [Online]. ch. A Available: Survey of Web-Based n = 1000. shouldhttp://repositories.cdlib.org/hcs/WorkingPapers2/JHW2007-1/Collective be remembered Decision that Making it is theSystems, ideals pp. that 245–279. are valuable, [Online]. Available: deci [3] T. Paine, “,” American colonies, 1776. Fig. 10. The relationship between p and ep for an incentive-free market not thehttp://repositories.cdlib.org/hcs/WorkingPapers2/JHW2007-1/ specific implementation of the systems that protect [4] M. A. Rodriguez and D. J. Steinbock, “A social network for (gray line) and an incentive market (black line). The plot provides the and[3] supportT. Paine, them. “Common If there sense,” is American another implementationcolonies, 1776. of proportion of correct decisions over 1000 simulations with d = 50 and societal-scale decision-making systems,” in Proceedingss of the North governmentAmerican[4] M. Association A. that Rodriguez better for Computational realizes and these D. Social J. ideals, Steinbock, and then, Organizational by “A the social rights network for n = 1000First,. citizens choose whether or not to participate in the ofScience man,societal-scale Conference it must, be Pittsburgh, decision-making enacted. PA, It 2004. was [Online].systems,” the great Available: in thinkersProceedingss http: of the of the North market at all. This reduces the amount of poor information //arxiv.org/abs/cs.CY/0412047American Association for Computational Social and Organizational that enters the market. Second, citizens choose how often to [5] eighteenthM. A. Rodriguez, century “Social Conference Enlightenment decision, makingPittsburgh, with who multi-relational PA, provided 2004. networks [Online]. the initial Available: http: governanceand grammar-based systems. particle It swarms,” is the challenge in Proceedings and of the the mandate Hawaii of participate. The market, therefore, induces citizens to become International//arxiv.org/abs/cs.CY/0412047 Conference on Systems Science. Waikoloa, Hawaii: the Information Age to redesign these governance systems in that entersmore the knowledgeable market. Second, so as to gain citizens from choose the market. how Finally, often to IEEE[5] ComputerM. A. Rodriguez, Society, January “Social 2007, decision pp. 39–49. making [Online]. with Available: multi-relational networks citizens choose the extent of their participation. If a citizen has lighthttp://arxiv.org/abs/cs.CY/0609034 ofand present grammar-based day technologies. particle swarms,” in Proceedings of the Hawaii participate. The market, therefore, induces citizens to become[6] M. Turrof, S. R. Hiltz, H.-K. Cho, Z. Li, and Y. Wang, “Social decision knowledge that is not well reflected in the market, suggesting International Conference on Systems Science. Waikoloa, Hawaii: supportIEEE system Computer (SDSS),” in Society,Proceedings January of the 2007, Hawaii pp. International 39–49. [Online]. Available: more knowledgeablethat their knowledge so as is uniqueto gain and from therefore the market. valuable, Finally, the Conference on Systems ScienceREFERENCES Hawaii International Conference on http://arxiv.org/abs/cs.CY/0609034 citizenscitizen choose is incentivized the extent to of participate their participation. more so than ifIf the a citizen market has Systems Science. Waikoloa, Hawaii: IEEE Computer Society, January [1]2002,[6]M. pp. deM. 81–90. Condorcet, Turrof, S. “Essai R. Hiltz, sur l’application H.-K. Cho, de Z. l’analyse Li, anda´ Y. la Wang, probabilit “Sociale´ decision knowledgeclosely that mimics is not their well knowledge. reflected In decisionin the market, markets, suggestingit is the [7] A. Smith,des dsupportecisions´An Inquiry renduessystem into thea´ (SDSS),” laNature pluralit ande´ inCauses desProceedings voix,” of the Paris, Wealth France, of of Nationsthe 1785. Hawaii. International that theirpricing knowledge mechanism isof the unique market and that servestherefore the incentivizing valuable, the [2]London,J. H.Conference England: Watkins W. and Strahan on M. SystemsA. and Rodriguez, T. Cadell, ScienceEvolution Londres, Hawaiiof 1776. the International Web in Artificial Conference on role. However, the asset traded in the market need not be [8] R. Hanson,IntelligenceSystems “Decision Environments Science markets,”., Waikoloa,IEEE ser. Studies Intelligent Hawaii: in Systems Computational IEEE, vol. Computer 14, Intelligence.no. 3, Society, January citizen is incentivized to participate more so than if the market pp., 16–19, May DE: 1999. Springer-Verlag, 2008, ch. A Survey of Web-Based . 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Londres, 1776. proportion of correct decisions over 1000 simulations with d = 50 and [4] [8]M.R. A. Hanson, Rodriguez “Decision and D. markets,” J. Steinbock,IEEE “A Intelligent social network Systems for, vol. 14, no. 3, role. However,nbeen= 1000 demonstrated. the asset that traded virtual money in the is ablemarket to preserve need notthe be societal-scale decision-making systems,” in Proceedingss of the North accuracy of decision markets [9]. pp. 16–19, May 1999. money. To maintain the egalitarian nature of self-selection, [9]AmericanE. Servan-Schrieber, Association for Computational J. Wolfers, SocialD. M. and Pennock, Organizational and B. Galebach, Science Conference, Pittsburgh, PA, 2004. [Online]. Available: http: the marketAs presented can be in based the simulation in virtual the decisions money ofwith a society rewards, “Prediction markets: Does money matter?” Electronic Markets, vol. 14, are multi-dimensional. It is likely that no single citizen has //arxiv.org/abs/cs.CY/0412047 reputation, or other social inducements as the backing. It has [5] M. A.no. Rodriguez, 3, pp. 243–251, “Social decision September making 2004. with multi-relational networks that enters the market. Second, citizens choose how often to and grammar-based particle swarms,” in Proceedings of the Hawaii been demonstratedparticipate. The that market, virtual therefore, money induces is able citizens to preserve to become the International Conference on Systems Science. Waikoloa, Hawaii: accuracymore of knowledgeable decision markets so as [9]. to gain from the market. Finally, IEEE Computer Society, January 2007, pp. 39–49. [Online]. Available: citizens choose the extent of their participation. If a citizen has http://arxiv.org/abs/cs.CY/0609034 As presented in the simulation the decisions of a society [6] M. Turrof, S. R. Hiltz, H.-K. Cho, Z. Li, and Y. Wang, “Social decision knowledge that is not well reflected in the market, suggesting support system (SDSS),” in Proceedings of the Hawaii International are multi-dimensional.that their knowledge It is is unique likely and that therefore no single valuable, citizen the has Conference on Systems Science Hawaii International Conference on the requisite knowledge in all dimensions to make informed Systems Science. Waikoloa, Hawaii: IEEE Computer Society, January citizen is incentivized to participate more so than if the market 2002, pp. 81–90. decisions.closely The mimics ability their to knowledge. reach an In optimaldecision markets, decision it is is the de- [7] A. Smith, An Inquiry into the Nature and Causes of . pendentpricing on mechanism the many of dimensions the market that such serves that the ignoranceincentivizing of London, England: W. Strahan and T. Cadell, Londres, 1776. [8] R. Hanson, “Decision markets,” IEEE Intelligent Systems, vol. 14, no. 3, one dimensionrole. However, may the lead asset to traded a suboptimal in the market conclusion. need not be The pp. 16–19, May 1999. money. To maintain the egalitarian nature of self-selection, [9] E. Servan-Schrieber, J. Wolfers, D. M. Pennock, and B. Galebach, the market can be based in virtual money with rewards, “Prediction markets: Does money matter?” Electronic Markets, vol. 14, reputation, or other social inducements as the backing. It has no. 3, pp. 243–251, September 2004. been demonstrated that virtual money is able to preserve the accuracy of decision markets [9]. As presented in the simulation the decisions of a society are multi-dimensional. It is likely that no single citizen has the requisite knowledge in all dimensions to make informed decisions. The ability to reach an optimal decision is de- pendent on the many dimensions such that ignorance of one dimension may lead to a suboptimal conclusion. The