The main reason for the secret ballot is to prevent vote buying. With the secret ballot, there's a low incentive to buy someone's vote, because there's no way to make sure they held up their side of the deal. Under your plan, candidates could offer a big multiple of the cash prize to the voter whose ballot was selected, if they win.
Make the offering of such cash inducements a serious criminal offense and offer a very high reward (millions) for any voter who acts as a witness for the successful prosecution of a candidate. If voters are simply doing it for the money they could take the bribe from the candidate and then dob them in and collect the reward.
