Can Partisan Voting Lead to Truth?

We study an extension of the voter model in which each agent is endowed with an innate preference for one of two states that we term as “truth” or “falsehood”. Due to interactions with neighbors, an agent that innately prefers truth can be persuaded to adopt a false opinion (and thus be discordant with its innate preference) or the agent can possess an internally concordant “true” opinion. Parallel states exist for agents that inherently prefer falsehood. We determine the conditions under which a population of such agents can ultimately reach a consensus for the truth, a consensus for falsehood, or reach an impasse where an agent tends to adopt the opinion that is in internal concordance with its innate preference so that consensus is never achieved. PACS numbers: 02.50.-r, 05.40.-a, 89.75.Fb Can Partisan Voting Lead to Truth? 2 There has been considerable recent public attention in the US on the following question: “Is President Obama a Muslim?” A Pew Research Center public opinion poll in the US found that 19% of respondents answered this question affirmatively in August 2010 [1]. Independent of one’s personal views, there are two incontrovertible facts on this matter: (i) the question “Is President Obama a Muslim?” has a definite answer, and (ii) there is a lack of consensus on the answer to what seems to be a clear-cut question. What is the source of this lack of consensus? Does conflicting evidence exist? Do people interpret the same evidence differently? What are the roles of the mass media and fellow peers in influencing the beliefs of individuals? In this work, we focus on peer influence by formulating a voter-like model in which we account for the possibility that each agent’s opinion may be in concordance or discordance with an internal and fixed set of beliefs. Our model incorporates two distinct mechanisms for an agent to change its opinion: one is the desire for an individual to be in concordance with this inviolate belief set, while the second is the tendency to agree with neighbors to minimize conflict. Our goal is to shed light on whether global truth can ultimately emerge in a socially-interacting population where the desire for internal concordance may conflict with global truth. Our approach is in the spirit of work by physicists in applying minimalist modeling to real social phenomena (see, e.g., [2, 3, 4, 5]). The dichotomy between one’s private beliefs and publicly-expressed opinions can take many forms [6]. One such example is H. C. Andersen’s fairy tale “The Emperor’s New Clothes” [7], in which the Emperor’s absence of clothes is finally exposed by the innocent remark of young child. The phenomenon of the spread of false norms has recently been elucidated by a simple computational model [8]. In a related vein, Asch [9] found that respondents to an uncomfortable question would conform to a clearly false consensus judgment rather than risk the stigma of being viewed as deviant. Similarly, white Americans overestimated the degree of support for forced racial segregation during the 1960’s and 70’s [10]. While 18% of whites indicated that they favored segregation, 47% of these respondents believed that most whites favored segregation. Another relevant example is the maddening feature that the general public has strong divergences of opinion on issues for which there is agreement within the scientific community [11]. Motivated in part by these examples, we construct a simple generalization of the voter model — the “partisan” voter model — to account for the competing influences of social consensus and personal concordance. The classic voter model accounts for the evolution to consensus in a population of binary and spineless agents that repeatedly evolve by adopting the opinion state of a randomly-selected neighbor [12]. In our model, we posit that each individual has an internal ethos — namely, a fixed beliefs on a set of fundamental issues, and that each agent is more likely to alter its opinion to be in concordance with this internal ethos [13]. We also ascribe a value to the opinion states that we label as “truth” (T ) and “falsehood” (F ). Individuals evolve by voter model dynamics but the rate of an update step depends on the direction of the opinion change. An opinion change that makes an agent concordant with its internal ethos occurs Can Partisan Voting Lead to Truth? 3 preferentially to a change that causes discordance. As a result of interactions among neighboring agents by voter model dynamics, an agent that intrinsically prefers the truth can thus actually have a false opinion. The resulting model bears some resemblance to a multi-state voter model of Page et al. [14], in which an agent can self-adjust its vector set of opinions to be internally consistent in addition to regular voting dynamics. In general, there are four possibilities for the opinion state of each agent (figure 1): • An agent intrinsically prefers truth and is in the true state. Such an agent is concordant. • An agent intrinsically prefers falsehood and is in the false state. Such an agent is also concordant. • An agent intrinsically prefers truth but is in the false state. Such an agent is discordant. • An agent intrinsically prefers falsehood but is in the true state. Such an agent is also discordant. We define the densities of agents in these four states as T+, F+, T−, and F−, respectively, each of which evolves with time t. The subscripts + and − indicate concordance and discordance, respectively. The total density of agents that intrinsically believe the truth (independent of their instantaneous state) is the time-independent quantity T = T++T− (figure 1), and similarly the density of agents that intrinsically believe falsehood is F = F+ + F−. However, the density of agents that happen to be in the true state at a particular time is time-dependent quantity T++F−; this includes concordant agents that prefer truth and discordant agents that prefer falsehood but happen to be in the true state. Similarly, the density of agents that happen to be in the false state is F+ + T−. The total density of agents of any type, i.e., T +F , is fixed and may be set to 1 without loss of generality. Our goal is to understand if global truth can emerge by this voting dynamics.