The Health Minister has to report back by April on whether he thinks Jersey should have its own radiotherapy unit.
It has been signed by more than 3,000 people.
Health Minister Deputy Richard Renouf has to explore options for delivering a unit here, after a proposition to the States Assembly was approved by 40 votes to one.
Deputy Montfort Tadier lodged the proposition after speaking to Rose. He also told stories of other people who've had to travel off-island for treatment.
The Reform politician says there should be a presumption that Jersey should provide as many services here as possible.
"Many people have asked me this, and this is not meant as a criticism, but if we're building an all-singing, all-dancing hospital with a price tag of £800million, why on earth do we not have a radiotherapy unit built into that already for that price?
There is definitely a human cost in this which can't be underestimated, but also there is an economic cost.
People do like to have the comfort of having their friends, family and their physical home around them whilst they're undergoing treatment and if you live in Southampton or in the immediate area, you can travel there during the day, probably at a comfortable time, and go back to your own home.
You can often, depending on your level of health, keep on working at the same time. I've heard of people having to take five or six weeks off, whereas if they'd been in Jersey all that time, they could have been doing part-time work, they could have popped into the office if they felt well enough."
Around 150 patients from Jersey are sent to Southampton General Hospital to receive radiotherapy.
Deputy Richard Renouf supported the proposition. He has previously said he would be in favour of it, but only if it's safe and affordable.
He told States members that it's crucial for care provided in Jersey to be at least as good as anywhere else, if on-island provision was to be arranged.
"We must have that high-quality service that islanders presently enjoy. All of that will be investigated.
We'll also be investigating the workforce implications, the availability of staff and the skills that are needed and the resilience of the unit and the backup.
We will need, I understand, at least two machines in case one ceases to function. We need to be assured of the quality and assured of the treatment safety.
All those things are being taken into account, along with considering location. Could it be up at Overdale? Could it be elsewhere on the island? It needs a very special type of power supply, we've also got to consider the demand and capacity, the capital costs and the ongoing revenue costs because this would be expensive, but nevertheless, may well be desirable."
The late wife of the Constable of St Peter, Richard Vibert, was treated in Southampton for five weeks.
He went with her for the duration of that treatment, but raised concerns about those who go there for treatment alone - away from their families.
"As the treatment progressed, my wife became weaker throughout the five-week period and in her case, I was able to assist her to get from the apartment to the car and get in and out of the vehicle.
Had she been on her own, all the tasks would have been far more difficult and would have added to what was already a stressful situation.
It's not just the physical issue arising from the treatment, we cannot forget the emotional support that someone undertaking this treatment needs.
There are constant concerns about whether the treatment will be successful or not and as the patient becomes weaker, the smallest issues are magnified and take on far more significance than they deserve.
Again, I could support my wife, but those patients who attended on their own do not have that level of support and it is simply not the same to talk to someone over the phone or by text or email."
The Deputy of St Martin, Steve Luce, abstained from voting - along with the Constable of St Clement.
Deputy Luce's late wife also went for treatment in Southampton.
He says the questions that need to be asked are around the quality of care.
"Do you want the best care? Do you want the best surgeons, the best consultants? Do you want the best cancer hospitals? Those who are working with this awful disease on a daily basis.
We have access to literally world-class treatment in the world's top cancer hospitals and the very top consultancy people who travel from Jersey.
While the Deputy's proposition seems like a wonderful idea on paper, for me, it isn't the answer.
As awful as travelling when you feel so desperately ill is, as awful as it is to be separated from your family when you feel so down, surely we want our islanders to have the very best treatment at the very best hospitals from the very best consultants."
Senator Steve Pallett was the single States member to vote against the proposition.