Ventilation IS required. But an open window can suffice for some local codes. In MN though, who wants to open a window in the middle of winter? And who wants to constantly clean off gunk off of their ceiling and surrounding surfaces.

Actual cooking is only 10% of the time you spend in a kitchen. Prep is 70%. It's much better to put a cooking zone on an exterior wall where it can vent straight out and put the prep zone on the island where you can spend 70% of your time facing out. People never envision spending all of their time with their back to the room because they've got their prep zone in a corner, but that's what happens a lot. Real life isn't FoodTV and no one stars in their own cooking show. If they do, then they have a really really big island with a water source and the cooking zone on it. And real ventilation.

I live in a really old house with really really low ceilings. The house has been in my husband's family forever and what my mother in law did for ventilation was a cooktop with downdraft ventilation. It wasn't the highest quality ventilation, but it always worked. I considered doing the same, but we gutted back to the studs and I have the ability to put in direct outside ventilation.

With that said, I also agree with what Hollysprings says about prep space. I moved my cooktop another wall so I could have all my prep space on the island. I hate facing a wall while chopping and prepping. I also do a lot of canning so I spend a lot of time in the kitchen, sometimes 8-10 hours a day in the summer and the majority of the time is most definitely spent at the island not really at the stove-top.

Save youself both aggravation and sbstantial money, and put the cooktop on the perimeter, not the island. Real venting is then easier to install against a wall, and the hood itself will be less expensive. Also think about when you are cooking on an island how much buffer space you need around the cooktop so people are far enough away not to get splattered by what you are cooking.

Islands are so fantastic for prep. If you want the communal idea of an island, think about how much easier it will be for friends and family to help with chopping, mixing and plating on an island with no cooktop. If instead, you are cooking on the island, you are cooking alone, and people need to keep a distance from the hot pans.

Venting is important. Most parents I know do not allow smoking in their homes or around their children - but indoor fumes can also be a health hazard.

Here is a link that might be useful: why vent (NY times article)