People perceive risks in different ways. There are several different things that may affect people's risk perception. So who's to decide?
Scientific view
Occurrance
The occurrance of an event can be calculated from historical data or estimated through risk assessment routines. We know that chances of losing your money in lottery are very high but on the other hand you're going to lose only few coins.
Magnitude
Magnitude of adverse effects plays a great deal in risk perception. We know that likelihood of nuclear plant catastrophe is very low but the adverse effects are lethal.
Sphere of influence
If many people are under the influence of adverse effects a risk is higher.
Critic of scientific view
An acceptable risk is rather cultural thing not technical
Risks that cover many people should be accepted or rejected democratically, not by few experts because experts may have hidden agendas.
Problem of liability
In many cases there are several sources of exposure. It is very difficult or even impossible to show that just this source was behind these adverse effects. For example, it took several years to find tobacco industry guilty.
Inestimable damages
Some things are just inestimable. How much you should be paid if you got a cancer? Many people think that f.e. their children's health and money are incommensurable.
Risk perception and nature of risk
Control
If people have control over risk they are more likely to accept a higher risk.
Voluntariness
If risks are imposed on people they are less likely to accept them. You really should ask people's opinion before placing a nuclear plant in a neighbourhood unless you enjoy fierce resistance.
Dread
People are afraid of catastrophes like a nuclear disaster. They don't accept that kind of risk even if the likelihood of occurrance is very low.
Fairness
There are risks that only few people carry but many people enjoy the benefits. Not in my backyard is a typical behaviour when people see that risks and benefits are not in a balance.
Ease of reduction of exposure
If the level of exposure cannot be lowered people are less likely to accept the risk.
Observable risk
People can see that rope dancing is dangerous but they cannot observe, say, magnetic fields. If a person suspects that magnetic fields may cause adverse effects it will be hard times for the sources of exposure.
Familiriaty
Familiriaty of phenomenon linked to risk plays a great deal in risk perception. The more you know about phenomenon more likely you accept the risk.
New risk
People are afraid of new things. Think about Luddites!
Delayed effects
People want to see immediate results. If there are delayed adverse effects, like developing cancer, the risk is hardly accepted.
Cultural acceptability
People are not atomized individuals. Many risks are culturally accepted or rejected. For example, we accept potential risks of aspartame and other food additives but we hardly accept some risks of tribal rites.
Age
Older people tend to perceive risks higher than younger ones. Suicidal teens cannot even think getting paralyzed when parachuting.
Education
Higher education is linked with perception of lower risks.
Media
Hyped risks are perceived bigger than they really are. For example, when there's a plane crash there will be big headlines but a car accident gets hardly mentioned. That's why many people are afraid of flying.
Gender
Women tend to think risks are higher. Men are less likely to bother.
View of life
It surprises me a bit but some studies have found the link between person's view of life and perception of risks. There are quite a few possible ways to categorize these groups but just to name one, people who are more individualistic perceive risks lower than those who favor communalism.
For further information you may see writings by Paul Slovic and Mary Douglas. Information above is gathered from several sources, mainly in Finnish.