  To divide a "manna" {\Omega} of private items (commodities, workloads, land,
time intervals) between n agents, the worst case measure of fairness is the
welfare guaranteed to each agent, irrespective of others' preferences. If the
manna is non atomic and utilities are continuous (not necessarily monotone or
convex), we can guarantee the minMax utility: that of our agent's best share in
her worst partition of the manna; and implement it by Kuhn's generalisation of
Divide and Choose. The larger Maxmin utility -- of her worst share in her best
partition -- cannot be guaranteed, even for two agents. If for all agents more
manna is better than less (or less is better than more), our Bid & Choose rules
implement guarantees between minMax and Maxmin by letting agents bid for the
smallest (or largest) size of a share they find acceptable.
