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We have studied a random walk model based on majority rule. At a giveninstant, the moving direction of a cargo is determined by motor coordinationmediated by a tug-of-war mechanism between two kinds of competing motorproteins. We have demonstrated that the probability distribution $P(t)$ forunidirectional run time $t$ of a cargo can be remarkably described by Levy walkfor $t<\gamma_u^{-1}$ as $P(t)\propto t^{-3/2} e^{-\gamma_u t}$ with $\gamma_u$being the unbinding rate of a motor protein from microtubule. The mean squareddisplacement of a cargo changes from super-diffusive behavior $\langleX^2\rangle\propto t^2$ for $t<\gamma_u^{-1}$ to normal diffusion $\langleX^2\rangle\propto t$ for $t>\gamma_u^{-1}$. By considering the correlationeffect in binding of a motor protein to microtubule, we have shown that Levywalk behavior of $P(t)\propto t^{-{3/2}}$ persists robustly againstcorrelations only adding an effective cutoff time $\gamma_b/\gamma_c^2$ with$\gamma_c$ representing the amount of correlations.

Random Walk by Majority Rule and L\'evy walk