A purely probabilistic candle auction

Candle auctions have been used in the past as a variant of the English auction with a random termination time associated either to the going out of a candle or to the falling of a needle inserted in a random position in a burning candle.
In this case such auctions are used by the auctioneer A for the allocation of a good to one of the n bidders b_i of the set B.
Our basic motivation for the use of this type of auctions is the following.
We are planning to use such auctions for the allocation of a chore  at one b_i from the set B whose members have been selected by A using a set of private criteria that do not depend on the willingness to attend of the single bidders.
The to be selected bidder has to be chosen from the set B  given that the available information about these bidders are imprecise or fuzzy. These features prevent the profitable and direct selection of a suitable bidder with the guarantee of choosing the best one.
For this reason we plan to adopt an auction mechanism where the bidders pay for not getting the chore but one of them has to get it though he also receives a compensation for being the wining bidder.
The compensation to the winning bidder derives him form the other bidders, the so called losing bidders, and is accumulated during the various steps or rounds on which the auction is based.