Abstract
Parrondo’s paradox is the phenomenon whereby combining two individually losing choices results in a winning outcome. Parrondo’s paradox is the convergent of concepts from convex linear combination, complexity theory, stochastic theory, Markov theory, discrete theory, nonlinear theory, dynamical systems, and fractals, all in a compact model. While much is still unexplored in Parrondo’s paradox, this thesis provides a springboard for pathways into two fields: quantum and social physics. This thesis first demonstrates a new form of quantum Parrondo’s paradox - the quantum coin-toss protocol. In particular, the 2-sided fair quantum coin-toss protocol does not have a classical Parrondo’s paradox counterpart. We will show that by stochastically or periodically switching between tossing two fair 2-sided quantum coins, we can achieve weak Parrondo’s paradox. By increasing the dimension to the 4-sided fair quantum coin-toss protocol, we can improve the performance of Parrondo’s paradox to achieve a strong Parrondo effect. Subsequently, by employing chaotic switching, we will show that it is possible to achieve strong Parrondo’s paradox even for the 2-sided fair quantum coin-toss protocol. Developing on the dynamics of chaotic switching for 2-sided fair quantum coins, we then demonstrate a working example of semiclassical secret key exchange encryption using the classical chaotic switching protocol. Next, we explore Parrondo’s paradox in three aspects of sociodynamical Parrondo’s paradox under a unified framework of preference aggregation. Firstly, we introduce the preference aggregation framework and provide insights into how preference aggregation Parrondo’s paradox played in a network of interacting agents can lead to critical phenomena observed in statistical physics akin to a phase transition. Next, we consider agents in a network with preferences modelled as a mean-field synchronization. We show that synchronization and the population’s average fitness have a sublinear relationship. Under a decision-making model, we also demonstrate that we can predict Dunbar’s number for band sizes, a guide often followed for organizations to size their decision-making group. Lastly, we explored the outcome of single-prioritization voting between three losing options, where several theoretic phenomena, such as the volunteer’s dilemma, emerge.