Magazine Sweepstakes Side Quest - Persona 2: Innocent Sin
The Sweepstakes Side Quest can be started after you defeat Principal Hanya inside the Seven Sister's High. All you need to do to begin this quest is to travel around the city and speak to the various Rumormongers to learn about the rumor involving the sweepstakes. You can collect a total of 3 rumors about the sweepstakes from various Rumormongers and much like with most of the quests in this game, which rumor you choose to spread will change the rewards you can earn.
Below is a quick list of the 3 rumors that you can collect from the various Rumormongers about the sweepstakes.
Chikarin: Easy to win, but prizes are boring.
Toku: Hard to win, but the prizes are good.
Toro: Very hard to win, but the prizes are great.
Once you have collected these rumors the next step is to spread them. For this you'll have to go to the Kuzunoha Detective Agency in Hirasaka and speak with the chief there. He will only let you spread a single rumor about the sweepstakes and once the rumor is spread you can not spread another one.
What this means is make sure you're spreading the rumor you want to spread because once you do there is no going back. I strongly recommend you pick either Toku's rumor, "Hard to win, but the prizes are good" or pick Toro's rumor, "Very hard to win, but the prizes are great".
Toro's rumor, "Very hard to win, but the prizes are great" has some really great items which are good for the entire game. The other two rumors have items which are good for the first half of the game but are quite useless for the rest of the game. Further down this page you can find a list of the rewards you can win depending on which of the choices you make when spreading the rumor.
In order to participate in this quest what you'll need to do is visit any item store in the game and purchase Sweepstakes Magazines (pictured above) from the vendor. The more you buy and turn in the greater your odds of winning are. Once you've purchased some and are ready to turn them in for a prize you'll want to head to the Kuzunoha Detective Agency in Hirasaka and speak with Tamaki (pictured below).
You can give Tamaki all of the Sweepstakes Magazines that you've purchased from a store and she'll submit them for you. After you've done this you will need to take a total of 300 steps inside of a dungeon to pass some time; this is a requirement to advance this quest forward. Once you've taken the 300 steps you'll want to head over to the Silverman Manor located in Rengedai.
At the Silverman Manor you'll find Lisa's father who you'll want to talk to and ask about the Sweepstakes Magazine contest. He'll give you any rewards that you've won or he'll give you the notice that you didn't win anything, either or. In my experience when you choose "Hard to win but the prizes are great" your odds of winning this contest are extremely low - even when you purchase 99 Magazines.
Below is a list of all the items you can win from this contest depending on which rumor you choose to spread.
Easy to win, but the prizes are boring
Hard to win, but the prizes are good
Very hard to win, but the prizes are great