I need to buy 3 tickets for my family.  It looks like I need to have 3 accounts to buy 3 tickets.
Is this correct? 

Tickets? Or badges?

For tickets, you can get one ticket for yourself and a second ticket for yourself. Some events allow you to get multiple extra tickets.

For badges, each badge needs to be tied to an account, though one account can purchase all three badges.

No, you can buy all the badges. You just enter their name. Email address is optional.

While one account can buy all the badges, each person with a badge should have an account.  From this thread:

One account cannot have more than one badge.  It can purchase multiple badges, and if those aren't bought for an account with a specific email, the system will create a dummy account to place that badge on.  We don't encourage that, as the person with the badge won't be able to access the dummy account, but that's what happens when a badge is bought for a name that doesn't have a proper account. Badges are refunded to the account that paid for them, to their original form of payment.  So a refund should not be an issue, though it will make it harder for the person doing the refund.Marian McBrine 
Event Coordinator 
Gen Con LLC 

Accounts with no email address are not active and cannot be accessed by that person. Quite often they are used to assign badges to causing lots of problems for the assignee.

Creating an account and having people link to it assures that they will have access.

Mike Boozer
Customer Service & Event Team Manager
Gen Con LLC