Constrained equal losses
Constrained equal losses (CEL) is a division rule for solving bankruptcy problems. According to this rule, each claimant should lose an equal amount from his or her claim, except that no claimant should receive a negative amount. In the context of taxation, it is known as poll tax. Formal definition. There is a certain amount of money to divide, denoted by "formula_1" (=Estate or Endowment). There are "n" "claimants". Each claimant "i" has a "claim" denoted by "formula_2". Usually, formula_3, that is, the estate is insufficient to satisfy all the claims. The CEL rule says that  each claimant "i" should receive formula_4, where "r" is a constant chosen such that formula_5. The rule can also be described algorithmically as follows: Examples. Examples with two claimants: Examples with three claimants: Usage. In the Jewish law, if several bidders participate in an auction and then revoke their bids simultaneously, they have to compensate the seller for the loss. The loss is divided among the bidders according to the CEL rule. If the first bidder says: "I will [redeem] it for ten selaim," the second: "...for twenty," and a third "...for 24," and the second and third bidders retract  at the same time, we enable the first to redeem it for 10, and we expropriate 7 from the property of both the second and the third. Thus, the Temple treasury collects 24. Similarly, if all three of them retract and the consecrated article is [ultimately] sold for 3, we expropriate 7 selaim from the property of all of them. Characterizations. The CEL rule has several characterizations. It is the only rule satisfying the following sets of axioms: Dual rule. The constrained equal awards (CEA) rule is the "dual" of the CEL rule, that is: for each problem formula_18, we  have formula_19.