arXiv subjects

Masato Hisakado

Publications and source records attributed to Masato Hisakado.

At least 37 records · Page 2Linked to original sources

arXiv2017

The Pitman-Yor process and an empirical study of choice behavior

This study discusses choice behavior using a voting model in which voters can obtain information from a finite number of previous $r$ voters. Voters vote for a candidate with a probability proportional to the previous vote ratio, which is visible to the voters. We obtain the Pitman sampling formula as the equilibrium distribution of $r$ votes. We present the model as a process of posting on a bulletin board system, 2ch.net, where users can choose one of many threads to create a post. We explore how this choice depends on the last $r$ posts and the distribution of these last $r$ posts across threads. We conclude that the posting process is described by our voting model with analog herders for a small $r$, which might correspond to the time horizon of users' responses.

physics.soc-ph↗

arXiv2017

Mean Field Voter Model of Election to the House of Representatives in Japan

In this study, we propose a mechanical model of a plurality election based on a mean field voter model. We assume that there are three candidates in each electoral district, i.e., one from the ruling party, one from the main opposition party, and one from other political parties. The voters are classified as fixed supporters and herding (floating) voters with ratios of $1-p$ and $p$, respectively. Fixed supporters make decisions based on their information and herding voters make the same choice as another randomly selected voter. The equilibrium vote-share probability density of herding voters follows a Dirichlet distribution. We estimate the composition of fixed supporters in each electoral district and $p$ using data from elections to the House of Representatives in Japan (43rd to 47th). The spatial inhomogeneity of fixed supporters explains the long-range spatial and temporal correlations. The estimated values of $p$ are close to the estimates obtained from a survey.

physics.soc-ph↗

arXiv2016

Phase transition of social learning collectives and "Echo chamber"

An "Echo chamber" is the state of social learning agents whose performances are deteriorated by excessive observation of others. We understand this to be the collective behavior of agents in a restless multi-armed bandit. The bandit has $M$ good levers and bad levers. A good lever changes to a bad one randomly with probability $q_{C}$ and a new good lever appears. $N$ agents exploit ones' lever if they know that it is a good one. Otherwise, they search for a good one by (i) random search (success probability $q_{I}$) and (ii) observe a good lever that is known by other agents (success probability $q_{O}$) with probability $1-p$ and $p$, respectively. The distribution of agents in good levers obeys the Yule distribution with power law exponent $1+γ$ in the limit $N,M\to \infty$ and $γ=1+\frac{(1-p)q_{I}}{pq_{O}}$. The expected value of the number of the agents with a good lever $N_{1}$ increases with $p$. The system shows a phase transition at $p_{c}=\frac{q_{I}}{q_{I}+q_{o}}$. For $p p_{c})$, the variance of $N_{1}$ per agent $\mbox{Var}(N_{1})/N$ is finite (diverges as $\propto N^{2-γ}$ with $N$). There is a threshold value $N_{s}$ for the system size that scales as $\ln N_{s} \propto 1/(γ-1)$. For $p>p_{c}$ and $N<N_{s}$, all agents tend to share only one good lever. $\mbox{E}(N_{1})$ decreases to zero as $p\to 1$, which is referred to as the "Echo chamber".

physics.soc-ph↗

arXiv2015

Information cascade on networks

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 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.

physics.soc-ph↗

arXiv2015

Detection of phase transition in generalized Pólya urn in information cascade experiment

We propose a method of detecting a phase transition in a generalized Pólya urn in an information cascade experiment. The method is based on the asymptotic behavior of the correlation $C(t)$ between the first subject's choice and the $t+1$-th subject's choice, the limit value of which, $c\equiv \lim_{t\to \infty}C(t)$, is the order parameter of the phase transition. To verify the method, we perform a voting experiment using two-choice questions. An urn X is chosen at random from two urns A and B, which contain red and blue balls in different configurations. Subjects sequentially guess whether X is A or B using information about the prior subjects' choices and the color of a ball randomly drawn from X. The color tells the subject which is X with probability $q$. We set $q\in \{5/9,6/9,7/9,8/9\}$ by controlling the configurations of red and blue balls in A and B. The (average) lengths of the sequence of the subjects are 63, 63, 54.0, and 60.5 for $q\in \{5/9,6/9,7/9,8/9\}$, respectively. We describe the sequential voting process by a nonlinear Pólya urn model. The model suggests the possibility of a phase transition when $q$ changes. We show that $c>0\,\,\,(=0)$ for $q=5/9,6/9\,\,\,(7/9,8/9 )$ and detect the phase transition using the proposed method.

physics.data-an↗

arXiv2015

Correlation function for generalized Pólya urns: Finite-size scaling analysis

We describe a universality class of the transitions of a generalized Pólya urn by studying the asymptotic behavior of the normalized correlation function $C(t)$ using finite-size scaling analysis. $X(1),X(2),\cdots$ are the successive additions of a red (blue) ball [$X(t)=1\,(0)$] at stage $t$ and $C(t)\equiv \mbox{Cov}(X(1),X(t+1))/\mbox{Var}(X(1))$. Furthermore, $z(t)=\sum_{s=1}^{t}X(s)/t$ represents the successive proportions of red balls in an urn to which, at the $t+1$-th stage, a red ball is added, [$X(t+1)=1$], with probability $q(z(t))=(\tanh [J(2z(t)-1)+h]+1)/2,J\ge 0$, and a blue ball is added, [$X(t)=0$], with probability $1-q(z(t))$. A boundary $(J_{c}(h),h)$ exists in the $(J,h)$ plane between a region with one fixed point and another region with two stable fixed points for $q(z)$. $C(t) \sim c+a\cdot t^{l-1}$ with $c=0\,(>0)$ for $J J_{c})$, and $l$ is the (larger) value of the slope(s) of $q(z)$ at the stable fixed point(s). On the boundary $J=J_{c}(h)$, $C(t)\simeq c+a\cdot \log(t)^{-α'}$ and $c=0\,(c>0), α'=0.5\,(1.0)$ for $h=0\,(h\neq 0)$. The system shows a continuous phase transition for $h=0$ and $C(t)$ behaves as $C(t)\simeq t^{-α'}g((1-l)\log t)$ with an universal function $g(x)$ and a length scale $1/(1-l)$ with respect to $\log t$. $β=ν_{||}\cdot α'$ holds with critical exponent $β=1/2$ and $ν_{||}=1$.

cond-mat.stat-mech↗

arXiv2015

Detection of non-self-correcting nature of information cascade

We propose a method of detecting non-self-correcting information cascades in experiments in which subjects choose an option sequentially by observing the choices of previous subjects. The method uses the correlation function $C(t)$ between the first and the $t+1$-th subject's choices. $C(t)$ measures the strength of the domino effect, and the limit value $c\equiv \lim_{t\to \infty}C(t)$ determines whether the domino effect lasts forever $(c>0)$ or not $(c=0)$. The condition $c>0$ is an adequate condition for a non-self-correcting system, and the probability that the majority's choice remains wrong in the limit $t\to \infty$ is positive. We apply the method to data from two experiments in which $T$ subjects answered two-choice questions: (i) general knowledge questions ($T_{avg}=60$) and (ii) urn-choice questions ($T=63$). We find $c>0$ for difficult questions in (i) and all cases in (ii), and the systems are not self-correcting.

physics.data-an↗

arXiv2015

Finite-size scaling analysis of binary stochastic processes and universality classes of information cascade phase transition

We propose a finite-size scaling analysis of binary stochastic processes $X(t)\in \{0,1\}$ based on the second moment correlation length $ξ$ for the autocorrelation function $C(t)$. The purpose is to clarify the critical properties and provide a new data analysis method for information cascades. As a simple model to represent the different behaviors of subjects in information cascade experiments, we assume that $X(t)$ is a mixture of an independent random variable that takes 1 with probability $q$ and a random variable that depends on the ratio $z$ of the variables taking 1 among recent $r$ variables. We consider two types of the probability $f(z)$ that the latter takes 1: (i) analog [$f(z)=z$] and (ii) digital [$f(z)=θ(z-1/2)$]. We study the universal functions of scaling for $ξ$ and the integrated correlation time $τ$. For finite $r$, $C(t)$ decays exponentially as a function of $t$, and there is only one stable renormalization group (RG) fixed point. In the limit $r\to \infty$, where $X(t)$ depends on all the previous variables, $C(t)$ in model (i) obeys a power law, and the system becomes scale invariant. In model (ii) with $q\neq 1/2$, there are two stable RG fixed points, which correspond to the ordered and disordered phases of the information cascade phase transition with critical exponents $β=1$ and $ν_{||}=2$.

cond-mat.stat-mech↗

arXiv2015

Interactive Restless Multi-armed Bandit Game and Swarm Intelligence Effect

We obtain the conditions for the emergence of the swarm intelligence effect in an interactive game of restless multi-armed bandit (rMAB). A player competes with multiple agents. Each bandit has a payoff that changes with a probability $p_{c}$ per round. The agents and player choose one of three options: (1) Exploit (a good bandit), (2) Innovate (asocial learning for a good bandit among $n_{I}$ randomly chosen bandits), and (3) Observe (social learning for a good bandit). Each agent has two parameters $(c,p_{obs})$ to specify the decision: (i) $c$, the threshold value for Exploit, and (ii) $p_{obs}$, the probability for Observe in learning. The parameters $(c,p_{obs})$ are uniformly distributed. We determine the optimal strategies for the player using complete knowledge about the rMAB. We show whether or not social or asocial learning is more optimal in the $(p_{c},n_{I})$ space and define the swarm intelligence effect. We conduct a laboratory experiment (67 subjects) and observe the swarm intelligence effect only if $(p_{c},n_{I})$ are chosen so that social learning is far more optimal than asocial learning.

cs.AI↗

arXiv2014

Information cascade, Kirman's ant colony model, and kinetic Ising model

In this paper, we discuss a voting model in which voters can obtain information from a finite number of previous voters. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) $\tanh$-type herders. In our previous paper [1], we used the mean field approximation for case (i). In that study, if the reference number $r$ is above three, phase transition occurs and the solution converges to one of the equilibria. However, the conclusion is different from mean field approximation. In this paper, we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of $r$ select the correct (wrong) candidate. In this paper, we show that there is no phase transition when $r$ is finite. If the annealing schedule is adequately slow from finite $r$ to infinite $r$, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman's ant colony model, and it follows beta binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model.As case (i) is the limit of case (iii) when $\tanh$ function becomes a step function, the phase transition can be observed in infinite size limit. We can confirm that there is no phase transition when the reference number $r$ is finite.

physics.soc-ph↗

arXiv2013

Collective Adoption of Max-Min Strategy in an Information Cascade Voting Experiment

We consider a situation where one has to choose an option with multiplier m. The multiplier is inversely proportional to the number of people who have chosen the option and is proportional to the return if it is correct. If one does not know the correct option, we call him a herder, and then there is a zero-sum game between the herder and other people who have set the multiplier. The max-min strategy where one divides one's choice inversely proportional to m is optimal from the viewpoint of the maximization of expected return. We call the optimal herder an analog herder. The system of analog herders takes the probability of correct choice to one for any value of the ratio of herders, p<1, in the thermodynamic limit if the accuracy of the choice of informed person q is one. We study how herders choose by a voting experiment in which 50 to 60 subjects sequentially answer a two-choice quiz. We show that the probability of selecting a choice by the herders is inversely proportional to m for 4/3 < m < 4 and they collectively adopt the max-min strategy in that range.

physics.soc-ph↗

arXiv2012

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

Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a sub-optimal option. When it occurs and whether it is a phase transition remain unanswered. To address these questions, we performed a voting experiment in which subjects answered a two-choice quiz sequentially with and without information about the prior subjects' choices. The subjects who could copy others are called herders. We obtained a microscopic rule regarding how herders copy others. Varying the ratio of herders led to qualitative changes in the macroscopic behavior in the experiment of about 50 subjects. If the ratio is small, the sequence of choices rapidly converges to the true 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 showed a phase transition to the two-peaks phase, where the convergence completely terminates, as the ratio exceeds some critical value.

physics.soc-ph↗

arXiv2012

Two kinds of Phase transitions in a Voting model

In this paper, we discuss a voting model with two candidates, C_0 and C_1. We consider two types of voters--herders and independents. The voting of independents is based on their fundamental values; on the other hand, the voting of herders is based on the number of previous votes. We can identify two kinds of phase transitions. One is an information cascade transition similar to a phase transition seen in Ising model. The other is a transition of super and normal diffusions. These phase transitions coexist. We compared our results to the conclusions of experiments and identified the phase transitions in the upper limit of the time t by using analysis of human behavior obtained from experiments.

physics.soc-ph↗

arXiv2011

Digital herders and phase transition in a voting model

In this paper, we discuss a voting model with two candidates, C_1 and C_2. We set two types of voters--herders and independents. The voting of independent voters is based on their fundamental values; on the other hand, the voting of herders is based on the number of votes. Herders always select the majority of the previous $r$ votes, which is visible to them. We call them digital herders. We can accurately calculate the distribution of votes for special cases. When r>=3, we find that a phase transition occurs at the upper limit of t, where t is the discrete time (or number of votes). As the fraction of herders increases, the model features a phase transition beyond which a state where most voters make the correct choice coexists with one where most of them are wrong. On the other hand, when r<3, there is no phase transition. In this case, the herders' performance is the same as that of the independent voters. Finally, we recognize the behavior of human beings by conducting simple experiments.

physics.soc-ph↗

arXiv2010

Component Ratios of Independent and Herding Betters in a Racetrack Betting Market

We study the time series data of the racetrack betting market in the Japan Racing Association (JRA). As the number of votes t increases, the win bet fraction x(t) converges to the final win bet fraction x_{f}. We observe the power law $(x(t)-x_{f})^{2} \propto t^{-β}$ with $β\simeq 0.488$. We measure the degree of the completeness of the ordering of the horses using an index AR, the horses are ranked according to the size of the win bet fraction. AR(t) also obeys the power law and behaves as $\mbox{AR}_{f}-\mbox{AR}(t)\propto t^{-γ}$ with $γ\simeq 0.589$, where AR_{f} is the final value of AR. We introduce a simple voting model with two types of voters-independent and herding. Independent voters provide information about the winning probability of the horses and herding voters decide their votes based on the popularities of the horses.This model can explain two power laws of the betting process. The component ratio of the independent voter to the herding voter is 1:3.

physics.data-an↗

arXiv2010

Phase transition and information cascade in a voting model

We introduce a voting model that is similar to a Keynesian beauty contest and analyze it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial distribution (independent voters) doped in a beta binomial distribution (copycat voters). We find that the phase transition in this system is at the upper limit of $t$, where $t$ is the time (or the number of the votes). Our model contains three phases. If copycats constitute a majority or even half of the total voters, the voting rate converges more slowly than it would in a binomial distribution. If independents constitute the majority of voters, the voting rate converges at the same rate as it would in a binomial distribution. We also study why it is difficult to estimate the conclusion of a Keynesian beauty contest when there is an information cascade.

physics.data-an↗

arXiv2010

Exact Scale Invariance in Mixing of Binary Candidates in Voting Model

We introduce a voting model and discuss the scale invariance in the mixing of candidates. The Candidates are classified into two categories $μ\in \{0,1\}$ and are called as `binary' candidates. There are in total $N=N_{0}+N_{1}$ candidates, and voters vote for them one by one. The probability that a candidate gets a vote is proportional to the number of votes. The initial number of votes (`seed') of a candidate $μ$ is set to be $s_μ$. After infinite counts of voting, the probability function of the share of votes of the candidate $μ$ obeys gamma distributions with the shape exponent $s_μ$ in the thermodynamic limit $Z_{0}=N_{1}s_{1}+N_{0}s_{0}\to \infty$. Between the cumulative functions $\{x_μ\}$ of binary candidates, the power-law relation $1-x_{1} \sim (1-x_{0})^α$ with the critical exponent $α=s_{1}/s_{0}$ holds in the region $1-x_{0},1-x_{1}<<1$. In the double scaling limit $(s_{1},s_{0})\to (0,0)$ and $Z_{0} \to \infty$ with $s_{1}/s_{0}=α$ fixed, the relation $1-x_{1}=(1-x_{0})^α$ holds exactly over the entire range $0\le x_{0},x_{1} \le 1$. We study the data on horse races obtained from the Japan Racing Association for the period 1986 to 2006 and confirm scale invariance.

physics.soc-ph↗

arXiv2009

Emergence of scale invariance and efficiency in a racetrack betting market

We study the time change of the relation between the rank of a racehorse in the Japan Racing Association and the result of victory or defeat. Horses are ranked according to the win bet fractions. As the vote progresses, the racehorses are mixed on the win bet fraction axis. We see the emergence of a scale invariant relation between the cumulative distribution function of the winning horse $x_{1}$ and that of the losing horse $x_{0}$. $x_{1}\propto x_{0}^α$ holds in the small win bet fraction region. We also see the efficiency of the market as the vote proceeds. However, the convergence to the efficient state is not monotonic. The time change of the distribution of a vote is complicated. Votes resume concentration on popular horses, after the distribution spreads to a certain extent. In order to explain scale invariance, we introduce a simple voting model. In a `double' scaling limit, we show that the exact scale invariance relation $x_{1}=x_{0}^α$ holds over the entire range $0\le x_{0},x_{1}\le 1$.

physics.soc-ph↗