Phase transition and information cascade in a voting model

In this paper, we discuss a voting model by considering three different kinds of networks: a random graph, the Barabási-Albert(BA) model, and a fitness model. A voting model represents the way in which public perceptions are conveyed to voters. Our voting model is constructed by using two types of voters-herders and independents-and two candidates. Independents conduct voting based on their fundamental values; on the other hand, herders base their voting on the number of previous votes. Hence, herders vote for the majority candidates and obtain information relating to previous votes from their networks. We discuss the difference between the phases on which the networks depend. Two kinds of phase transitions, an information cascade transition and a super-normal transition, were identified. The first of these is a transition between a state in which most voters make the correct choices and a state in which most of them are wrong. The second is a * [1] masato.hisakado@fsa.go.jp † [2] mori@sci.kitasato-u.ac.jp 1 transition of convergence speed. The information cascade transition prevails when herder effects are stronger than the super-normal transition. In the BA and fitness models, the critical point of the information cascade transition is the same as that of the random network model. However, the critical point of the super-normal transition disappears when these two models are used.In conclusion, the influence of networks is shown to only affect the convergence speed and not the information cascade transition. We are therefore able to conclude that the influence of hubs on voters' perceptions is limited.2

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“…We refer to these herders as a kind of analog herders [21]. We are interested in the behavior at the limit τ → ∞.…”

Section: Random Graphmentioning

confidence: 99%

“…This type of transition has been studied for analog herders [21]. We expand X τ around the solutionvτ + (1 − p)(2q − 1)τ.…”

Section: Random Graphmentioning

confidence: 99%

Information cascade on networks

Hisakado

Mori

2016

Physica A: Statistical Mechanics and its Applications

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“…Let X t and Y t be the number of independent voters and that of imitators at time t. We also have their 1 Our notion of imitators is the same as that of copycat voters in the model of [17]. Moreover, our assumption that independent voters and imitators appear randomly is similar to that of [17]. However, as defined in the first paragraph of Sect.…”

Section: Modelmentioning

confidence: 99%

“…However, as defined in the first paragraph of Sect. 2, our Model 1 allows undecided voters to exist, whereas [17] does not. Owing to the existence of undecided voters, an imitator who samples an undecided voter gives up the imitation, and potentially becomes an independent voter next time.…”

Section: Modelmentioning

confidence: 99%

Effective group size of majority vote accuracy in sequential decision-making

Sekiguchi

Ohtsuki

2015

Japan J. Indust. Appl. Math.

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We investigate a sequential decision-making situation wherein, with a certain probability, each voter imitates the decision of another voter who has already made a decision; otherwise, she makes a decision independently. After all individuals reach decisions, the group decision is determined using the simple majority rule. To evaluate the collective performance in this situation, we introduce the concept of effective group size, which measures how many independent voters are needed to obtain the same majority vote accuracy realized by non-independent sequential votes. We have found the deterioration of majority vote accuracy by imitation behavior of voters, and quantified it by a decrease in the effective group size. We argue that this decline in the majority vote accuracy is caused by the two factors: a decrease in the number of independent voters and an increase in the disparity of influences of voters on succeeding voters' decisions.

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“…Two types of phase transitions have been predicted in a twochoice voting model depending on the strength of conformity of the people [19,20]. We set two types of individuals: herders and independents.…”

Section: Introductionmentioning

confidence: 99%

Phase transition to a two-peak phase in an information-cascade voting experiment

Mori

Hisakado²,

Takahashi

2012

Phys. Rev. E

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Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a suboptimal option. When this occurs and whether it is a phase transition remain unanswered. To address these questions we perform a voting experiment in which subjects answer a two-choice quiz sequentially with and without information about the prior subjects' choices. The subjects who could copy others are called herders. We obtain a microscopic rule regarding how herders copy others. Varying the ratio of herders leads to qualitative changes in the macroscopic behavior of about 50 subjects in the experiment. If the ratio is small, the sequence of choices rapidly converges to the correct one. As the ratio approaches 100%, convergence becomes extremely slow and information aggregation almost terminates. A simulation study of a stochastic model for 10(6) subjects based on the herder's microscopic rule shows a phase transition to the two-peak phase, where the convergence completely terminates as the ratio exceeds some critical value.

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Phase transition and information cascade in a voting model

Cited by 28 publications

References 15 publications

Information cascade on networks

Information cascade on networks

Effective group size of majority vote accuracy in sequential decision-making

Phase transition to a two-peak phase in an information-cascade voting experiment

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