Filling a multicolor urn: an axiomatic analysis

The probabilistic distribution of identical successive units amounts to filling an urn with balls of different colors (one color per agent). The fixed chances methods allocate each unit independently of the current distribution of shares. The Polya–Eggenberger methods place in an urn a fixed number of balls and draw from the urn with replacement of two balls of the color drawn. These methods stand out axiomatically under: a version of Consistency; Increasing Shares (the probability of receiving the next ball is non-decreasing in one''s share), Independence under Transfers (transferring balls across agents is not profitable), and Order Independence (a sequence of successive allocations is as likely as any permuted sequence). On the other hand, Decreasing Shares (the probability of receiving the next ball is non-increasing in one''s share) leads to methods equalizing individual shares either along a fixed standard of comparison, or in proportion to the deviation from a fixed urn. [Copyright &y& Elsevier]