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The redistribution game is a Communist argument in favor of redistribution.
Without redistributive efforts, the "natural" distribution of a desired finite good is an arrangement that few would consider just: one or a few individual(s) owns most of the resource, and the vast majority own very little, if anything at all. This is not based upon merit, but often factors which, while not technically random, can only be attributed to luck.
For a model of why this occurs, consider the following game. A hundred individuals are given 1000 tokens, each player having between 1 and 19 tokens, and the number of tokens each player has is public knowledge. They are free to move about and challenge other players. When this happens, both players flip all their tokens and the player flipping more heads is the winner. He or she receives the loser's tokens, and the losing player is eliminated from the game. Each player's objective is not specifically to own all the tokens, but to avoid elimination while attaining as many tokens as "safely" possible.
Several outcomes are possible from this scenario. It is possible that one player will end up with all the tokens (monarchy). An alternative ending scenario is that multiple players, in roughly equitable distributions, will remain at the end of the game (oligarchy). For example, a distribution (among 4 players) of 260-250-245-245 is probably stable. Given the uncertainty involved with conflict in this game, it is quite possible for the weakest player to beat the strongest player, and all players may decide it is best to avoid conflict and not risk elimination: No further conflict occurs. However, a distribution whereby many or most players (democracy) remain, with smaller and roughly equitable shares of the tokens, is highly unlikely.
Here's why. At the beginning of the game, weaker players will almost certainly be devoured. A player with 19 tokens assumes almost no risk in challenging one with only 1 token, and therefore is likely to do so. Additionally, players are effectively forced to participate in as many conflicts as possible early-on, despite the risk. As players are eliminated, the number of tokens per player increases, and players who failed to engage in any conflict and accumulate more tokens will inevitably become comparatively weak. Then, they will be devoured.
The winning player(s) will not necessarily be those who started with a large number of tokens, but rather those who played aggressively, early in the game, and had a substantial amount of luck as well. In practice, in human societies, notions of merit play almost no role at all.
While this model is only an approximation of any real-world dynamic, it can be argued that it models power distributions in human societies tolerably well. For example, in business, it is often the case that an industry begins with hundreds or thousands of small companies. As some die off, others grow and become large. Unable to compete with their larger competitors, the remaining small survivors may be forced to choose between extinction and absorption by a stronger competitor.
Without active efforts toward a more proportionate distribution, monarchical and oligarchical distributions are the norm. This applies to wealth, power, land, and even mates. For example, in polygamous societies, a few members of the gender allowed to have multiple mates will have many, while some of that gender will have none.