Using Bitcoin contracts to run a betting site without the need for deposits?
Giving the operator the power to control the identity of the recipient won't work, since he can participate himself and declare himself the winner. A majority vote also isn't too good because an attacker can make multiple entries, which is cheap to do if he knows he can guarantee a win.

It is necessary that the winner will be decided according to public data (such as the hash of a future block), and that the operator (or majority) will not be able to secure funds before sending payment to the agreed winner.

The only way I can think of is burn-escrow. Each participant sends a tentative payment to the operator which cannot be reversed, it can either be carried through or burned (with a deposit that incentivizes carrying through). Then the operator sends to the winner using his own funds. Then every participant forwards the payment. If the operator does not send to the winner, participants burn the payment and refuse to do business with the operator again.

There is some risk that the operator will be honest but participants will neglect to forward payments, or that the operator will be fraudulent but participants forward payments anyway to get the deposit. But with a properly calibrated deposit, these risks can be mitigated and entered into the pricing.