The Inequality Process As An Evolutionary Process

The Inequality Process (IP) is a competition process that models the dynamics of personal income and wealth at the micro (individual person) and macro (distribution) levels. At the micro level, it is a particle system. It has a macro model in terms of the parameters of the micro model, a gamma pdf that approximates the stationary distribution of the micro model. Randomly paired particles compete for each other’s wealth with an equal chance to win. The loser gives up a fraction of its wealth to the winner. That fraction is its parameter. By hypothesis and empirical analogue, that fraction scales inversely with the particle’s productivity of wealth. Long term, wealth flows to particles that lose less when they lose, robust losers, nourishing their further production of wealth. Given a survival function that is an increasing function of wealth, the more robust loser is more losses away from death (Gambler’s Ruin) at any given amount of wealth than others. As the level of productivity rises among particles, holding the global mean of wealth constant, expected particle wealth in each productivity equivalence class decreases relative to global mean wealth and the variance of wealth in each equivalence class decreases, i.e., the transfer of wealth from the less to the more productive occurs more efficiently making wealth a better indicator of productivity. The IP operates with no information about how wealth is produced and consequently adapts fluidly to higher productivity, change in constraints on wealth production and over time variation in global mean wealth. The IP is a dynamic attractor for a population, maximizing wealth production, minimizing extinction risk. It is an evolutionary process in an interdependent population, a colony of organisms, in which each organism depends on the product of the whole population. As an evolutionary process it focuses on selection rather than search. The IP might be adapted as a method to allocate computing resources to a population of parallel processors. In nature, the IP operates in parallel without central direction.